Marchetto's Theory of Commixture and Interruptions
19
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Transcript of Marchetto's Theory of Commixture and Interruptions
Mar
chet
to's
Th
eory
of C
omm
ixtu
re a
nd In
terr
upti
ons
Jay R
ahn
Mar
chet
to's
Th
eory
of C
omm
ixtu
re a
nd In
terr
upti
ons
Jay R
ahn
Mar
chet
to's
Th
eory
of C
omm
ixtu
re a
nd In
terr
upti
ons
Jay R
ahn
Mar
chet
to's
Th
eory
of C
omm
ixtu
re a
nd In
terr
upti
ons
Jay R
ahn
Mar
chet
to's
Th
eory
of C
omm
ixtu
re a
nd In
terr
upti
ons
Jay R
ahn
Mar
chet
to's
Th
eory
of C
omm
ixtu
re a
nd In
terr
upti
ons
Jay R
ahn
In h
is Lu
cida
rium
Can
tae P
lana
e (c
a. 1
317-
18),1
Mar
chet
to
of P
adua
pre
sent
s a
form
ulat
ion
of G
rego
rian
cha
nt th
eory
in
whi
ch th
e no
tion
of v
ario
us "
spec
ies"
of f
ourt
hs a
nd fi
fths i
s all-
The p
rese
nt st
udy w
as su
ppor
ted b
y a
rese
arch
time s
tipen
d (fo
r the
aca
- de
mic
year
1984
-85)
whi
ch w
as gr
ante
d by t
he So
cial
Scie
nces
and H
uman
ities
R
esea
rch C
ounc
il of C
anad
a. I a
m in
debt
ed as
wel
l to
Leem
an Pe
rkin
s of C
o-
lum
bia U
nive
rsity
and t
he an
onym
ous r
eade
rs of
my o
rigi
nal re
sear
ch pr
opos
al
to th
e Cou
ncil w
ho m
ade v
alua
ble s
ugge
stio
ns co
ncer
ning
the p
roje
ct an
d to
A
ndre
w H
ughe
s of t
he U
nive
rsity
of T
oron
to w
ho p
rovi
ded
help
ful a
dvic
e ab
out a
n ea
rlie
r for
m of
this
stud
y. I
am al
so gr
atef
ul to
Pat
rici
a Car
pent
er of
C
olum
bia U
nive
rsity
who
intr
oduc
ed m
e to
the p
rese
nt to
pic i
n he
r hist
ory o
f m
usic
theo
ry se
min
ar. N
ever
thel
ess,
one s
houl
d not
e tha
t I a
ssum
e ent
ire r
e-
spon
sibili
ty fo
r any
faul
ts to
be f
ound
here
in.
'An
exem
plar
y edi
tion,
tran
slatio
n, an
d com
men
tary
appe
ars in
Jan
Wil-
lia
m H
erlin
ger,
The
Luc
idar
ium
of M
arch
etto
of P
adua
: A C
ritic
al Ed
ition
, Tr
ansla
tion,
and
Com
men
tary
(Chi
cago
: Uni
vers
ity of
Chi
cago
Pres
s, 19
85),
whi
ch su
pers
edes
the s
ame a
utho
r's "
The L
ucid
ariu
m of
Mar
chet
to of
Pad
ua:
A C
ritic
al Ed
ition
, Tra
nsla
tion,
and
Com
men
tary
" (Ph
.D. d
isser
tatio
n, U
ni-
vers
ity of
Chi
cago
, 197
8, 2
vols.
). H
erlin
ger'
s wor
k is a
mar
ked i
mpr
ovem
ent
on th
e on
ly p
revi
ously
prin
ted v
ersio
n of
the
Luci
dari
um in
Mar
tin G
erbe
rt
(ed.
), Sc
ript
ores
Eccl
esia
stic
i de M
usic
a Sac
ra P
otiss
imum
(St.
Blai
se, 1
748;
re
pr. M
ilan:
Bolle
tino B
iblio
graf
ico M
usic
ale,
1931
; 3 vo
ls.) 3
:64-
121.
Unl
ess
othe
rwise
indi
cate
d, re
fere
nces
belo
w to
the L
ucid
ariu
m re
fer t
o H
erlin
ger'
s 19
85 e
ditio
n of
the
tre
atise
. In
the
1978
diss
erta
tion,
1:2
-14,
H
erlin
ger
pres
ents
conv
inci
ng ev
iden
ce fo
r dat
ing t
he L
ucid
ariu
m (a
nd M
arch
etto
's Po-
m
eriu
m as
wel
l).
In h
is Lu
cida
rium
Can
tae P
lana
e (c
a. 1
317-
18),1
Mar
chet
to
of P
adua
pre
sent
s a
form
ulat
ion
of G
rego
rian
cha
nt th
eory
in
whi
ch th
e no
tion
of v
ario
us "
spec
ies"
of f
ourt
hs a
nd fi
fths i
s all-
The p
rese
nt st
udy w
as su
ppor
ted b
y a
rese
arch
time s
tipen
d (fo
r the
aca
- de
mic
year
1984
-85)
whi
ch w
as gr
ante
d by t
he So
cial
Scie
nces
and H
uman
ities
R
esea
rch C
ounc
il of C
anad
a. I a
m in
debt
ed as
wel
l to
Leem
an Pe
rkin
s of C
o-
lum
bia U
nive
rsity
and t
he an
onym
ous r
eade
rs of
my o
rigi
nal re
sear
ch pr
opos
al
to th
e Cou
ncil w
ho m
ade v
alua
ble s
ugge
stio
ns co
ncer
ning
the p
roje
ct an
d to
A
ndre
w H
ughe
s of t
he U
nive
rsity
of T
oron
to w
ho p
rovi
ded
help
ful a
dvic
e ab
out a
n ea
rlie
r for
m of
this
stud
y. I
am al
so gr
atef
ul to
Pat
rici
a Car
pent
er of
C
olum
bia U
nive
rsity
who
intr
oduc
ed m
e to
the p
rese
nt to
pic i
n he
r hist
ory o
f m
usic
theo
ry se
min
ar. N
ever
thel
ess,
one s
houl
d not
e tha
t I a
ssum
e ent
ire r
e-
spon
sibili
ty fo
r any
faul
ts to
be f
ound
here
in.
'An
exem
plar
y edi
tion,
tran
slatio
n, an
d com
men
tary
appe
ars in
Jan
Wil-
lia
m H
erlin
ger,
The
Luc
idar
ium
of M
arch
etto
of P
adua
: A C
ritic
al Ed
ition
, Tr
ansla
tion,
and
Com
men
tary
(Chi
cago
: Uni
vers
ity of
Chi
cago
Pres
s, 19
85),
whi
ch su
pers
edes
the s
ame a
utho
r's "
The L
ucid
ariu
m of
Mar
chet
to of
Pad
ua:
A C
ritic
al Ed
ition
, Tra
nsla
tion,
and
Com
men
tary
" (Ph
.D. d
isser
tatio
n, U
ni-
vers
ity of
Chi
cago
, 197
8, 2
vols.
). H
erlin
ger'
s wor
k is a
mar
ked i
mpr
ovem
ent
on th
e on
ly p
revi
ously
prin
ted v
ersio
n of
the
Luci
dari
um in
Mar
tin G
erbe
rt
(ed.
), Sc
ript
ores
Eccl
esia
stic
i de M
usic
a Sac
ra P
otiss
imum
(St.
Blai
se, 1
748;
re
pr. M
ilan:
Bolle
tino B
iblio
graf
ico M
usic
ale,
1931
; 3 vo
ls.) 3
:64-
121.
Unl
ess
othe
rwise
indi
cate
d, re
fere
nces
belo
w to
the L
ucid
ariu
m re
fer t
o H
erlin
ger'
s 19
85 e
ditio
n of
the
tre
atise
. In
the
1978
diss
erta
tion,
1:2
-14,
H
erlin
ger
pres
ents
conv
inci
ng ev
iden
ce fo
r dat
ing t
he L
ucid
ariu
m (a
nd M
arch
etto
's Po-
m
eriu
m as
wel
l).
In h
is Lu
cida
rium
Can
tae P
lana
e (c
a. 1
317-
18),1
Mar
chet
to
of P
adua
pre
sent
s a
form
ulat
ion
of G
rego
rian
cha
nt th
eory
in
whi
ch th
e no
tion
of v
ario
us "
spec
ies"
of f
ourt
hs a
nd fi
fths i
s all-
The p
rese
nt st
udy w
as su
ppor
ted b
y a
rese
arch
time s
tipen
d (fo
r the
aca
- de
mic
year
1984
-85)
whi
ch w
as gr
ante
d by t
he So
cial
Scie
nces
and H
uman
ities
R
esea
rch C
ounc
il of C
anad
a. I a
m in
debt
ed as
wel
l to
Leem
an Pe
rkin
s of C
o-
lum
bia U
nive
rsity
and t
he an
onym
ous r
eade
rs of
my o
rigi
nal re
sear
ch pr
opos
al
to th
e Cou
ncil w
ho m
ade v
alua
ble s
ugge
stio
ns co
ncer
ning
the p
roje
ct an
d to
A
ndre
w H
ughe
s of t
he U
nive
rsity
of T
oron
to w
ho p
rovi
ded
help
ful a
dvic
e ab
out a
n ea
rlie
r for
m of
this
stud
y. I
am al
so gr
atef
ul to
Pat
rici
a Car
pent
er of
C
olum
bia U
nive
rsity
who
intr
oduc
ed m
e to
the p
rese
nt to
pic i
n he
r hist
ory o
f m
usic
theo
ry se
min
ar. N
ever
thel
ess,
one s
houl
d not
e tha
t I a
ssum
e ent
ire r
e-
spon
sibili
ty fo
r any
faul
ts to
be f
ound
here
in.
'An
exem
plar
y edi
tion,
tran
slatio
n, an
d com
men
tary
appe
ars in
Jan
Wil-
lia
m H
erlin
ger,
The
Luc
idar
ium
of M
arch
etto
of P
adua
: A C
ritic
al Ed
ition
, Tr
ansla
tion,
and
Com
men
tary
(Chi
cago
: Uni
vers
ity of
Chi
cago
Pres
s, 19
85),
whi
ch su
pers
edes
the s
ame a
utho
r's "
The L
ucid
ariu
m of
Mar
chet
to of
Pad
ua:
A C
ritic
al Ed
ition
, Tra
nsla
tion,
and
Com
men
tary
" (Ph
.D. d
isser
tatio
n, U
ni-
vers
ity of
Chi
cago
, 197
8, 2
vols.
). H
erlin
ger'
s wor
k is a
mar
ked i
mpr
ovem
ent
on th
e on
ly p
revi
ously
prin
ted v
ersio
n of
the
Luci
dari
um in
Mar
tin G
erbe
rt
(ed.
), Sc
ript
ores
Eccl
esia
stic
i de M
usic
a Sac
ra P
otiss
imum
(St.
Blai
se, 1
748;
re
pr. M
ilan:
Bolle
tino B
iblio
graf
ico M
usic
ale,
1931
; 3 vo
ls.) 3
:64-
121.
Unl
ess
othe
rwise
indi
cate
d, re
fere
nces
belo
w to
the L
ucid
ariu
m re
fer t
o H
erlin
ger'
s 19
85 e
ditio
n of
the
tre
atise
. In
the
1978
diss
erta
tion,
1:2
-14,
H
erlin
ger
pres
ents
conv
inci
ng ev
iden
ce fo
r dat
ing t
he L
ucid
ariu
m (a
nd M
arch
etto
's Po-
m
eriu
m as
wel
l).
In h
is Lu
cida
rium
Can
tae P
lana
e (c
a. 1
317-
18),1
Mar
chet
to
of P
adua
pre
sent
s a
form
ulat
ion
of G
rego
rian
cha
nt th
eory
in
whi
ch th
e no
tion
of v
ario
us "
spec
ies"
of f
ourt
hs a
nd fi
fths i
s all-
The p
rese
nt st
udy w
as su
ppor
ted b
y a
rese
arch
time s
tipen
d (fo
r the
aca
- de
mic
year
1984
-85)
whi
ch w
as gr
ante
d by t
he So
cial
Scie
nces
and H
uman
ities
R
esea
rch C
ounc
il of C
anad
a. I a
m in
debt
ed as
wel
l to
Leem
an Pe
rkin
s of C
o-
lum
bia U
nive
rsity
and t
he an
onym
ous r
eade
rs of
my o
rigi
nal re
sear
ch pr
opos
al
to th
e Cou
ncil w
ho m
ade v
alua
ble s
ugge
stio
ns co
ncer
ning
the p
roje
ct an
d to
A
ndre
w H
ughe
s of t
he U
nive
rsity
of T
oron
to w
ho p
rovi
ded
help
ful a
dvic
e ab
out a
n ea
rlie
r for
m of
this
stud
y. I
am al
so gr
atef
ul to
Pat
rici
a Car
pent
er of
C
olum
bia U
nive
rsity
who
intr
oduc
ed m
e to
the p
rese
nt to
pic i
n he
r hist
ory o
f m
usic
theo
ry se
min
ar. N
ever
thel
ess,
one s
houl
d not
e tha
t I a
ssum
e ent
ire r
e-
spon
sibili
ty fo
r any
faul
ts to
be f
ound
here
in.
'An
exem
plar
y edi
tion,
tran
slatio
n, an
d com
men
tary
appe
ars in
Jan
Wil-
lia
m H
erlin
ger,
The
Luc
idar
ium
of M
arch
etto
of P
adua
: A C
ritic
al Ed
ition
, Tr
ansla
tion,
and
Com
men
tary
(Chi
cago
: Uni
vers
ity of
Chi
cago
Pres
s, 19
85),
whi
ch su
pers
edes
the s
ame a
utho
r's "
The L
ucid
ariu
m of
Mar
chet
to of
Pad
ua:
A C
ritic
al Ed
ition
, Tra
nsla
tion,
and
Com
men
tary
" (Ph
.D. d
isser
tatio
n, U
ni-
vers
ity of
Chi
cago
, 197
8, 2
vols.
). H
erlin
ger'
s wor
k is a
mar
ked i
mpr
ovem
ent
on th
e on
ly p
revi
ously
prin
ted v
ersio
n of
the
Luci
dari
um in
Mar
tin G
erbe
rt
(ed.
), Sc
ript
ores
Eccl
esia
stic
i de M
usic
a Sac
ra P
otiss
imum
(St.
Blai
se, 1
748;
re
pr. M
ilan:
Bolle
tino B
iblio
graf
ico M
usic
ale,
1931
; 3 vo
ls.) 3
:64-
121.
Unl
ess
othe
rwise
indi
cate
d, re
fere
nces
belo
w to
the L
ucid
ariu
m re
fer t
o H
erlin
ger'
s 19
85 e
ditio
n of
the
tre
atise
. In
the
1978
diss
erta
tion,
1:2
-14,
H
erlin
ger
pres
ents
conv
inci
ng ev
iden
ce fo
r dat
ing t
he L
ucid
ariu
m (a
nd M
arch
etto
's Po-
m
eriu
m as
wel
l).
In h
is Lu
cida
rium
Can
tae P
lana
e (c
a. 1
317-
18),1
Mar
chet
to
of P
adua
pre
sent
s a
form
ulat
ion
of G
rego
rian
cha
nt th
eory
in
whi
ch th
e no
tion
of v
ario
us "
spec
ies"
of f
ourt
hs a
nd fi
fths i
s all-
The p
rese
nt st
udy w
as su
ppor
ted b
y a
rese
arch
time s
tipen
d (fo
r the
aca
- de
mic
year
1984
-85)
whi
ch w
as gr
ante
d by t
he So
cial
Scie
nces
and H
uman
ities
R
esea
rch C
ounc
il of C
anad
a. I a
m in
debt
ed as
wel
l to
Leem
an Pe
rkin
s of C
o-
lum
bia U
nive
rsity
and t
he an
onym
ous r
eade
rs of
my o
rigi
nal re
sear
ch pr
opos
al
to th
e Cou
ncil w
ho m
ade v
alua
ble s
ugge
stio
ns co
ncer
ning
the p
roje
ct an
d to
A
ndre
w H
ughe
s of t
he U
nive
rsity
of T
oron
to w
ho p
rovi
ded
help
ful a
dvic
e ab
out a
n ea
rlie
r for
m of
this
stud
y. I
am al
so gr
atef
ul to
Pat
rici
a Car
pent
er of
C
olum
bia U
nive
rsity
who
intr
oduc
ed m
e to
the p
rese
nt to
pic i
n he
r hist
ory o
f m
usic
theo
ry se
min
ar. N
ever
thel
ess,
one s
houl
d not
e tha
t I a
ssum
e ent
ire r
e-
spon
sibili
ty fo
r any
faul
ts to
be f
ound
here
in.
'An
exem
plar
y edi
tion,
tran
slatio
n, an
d com
men
tary
appe
ars in
Jan
Wil-
lia
m H
erlin
ger,
The
Luc
idar
ium
of M
arch
etto
of P
adua
: A C
ritic
al Ed
ition
, Tr
ansla
tion,
and
Com
men
tary
(Chi
cago
: Uni
vers
ity of
Chi
cago
Pres
s, 19
85),
whi
ch su
pers
edes
the s
ame a
utho
r's "
The L
ucid
ariu
m of
Mar
chet
to of
Pad
ua:
A C
ritic
al Ed
ition
, Tra
nsla
tion,
and
Com
men
tary
" (Ph
.D. d
isser
tatio
n, U
ni-
vers
ity of
Chi
cago
, 197
8, 2
vols.
). H
erlin
ger'
s wor
k is a
mar
ked i
mpr
ovem
ent
on th
e on
ly p
revi
ously
prin
ted v
ersio
n of
the
Luci
dari
um in
Mar
tin G
erbe
rt
(ed.
), Sc
ript
ores
Eccl
esia
stic
i de M
usic
a Sac
ra P
otiss
imum
(St.
Blai
se, 1
748;
re
pr. M
ilan:
Bolle
tino B
iblio
graf
ico M
usic
ale,
1931
; 3 vo
ls.) 3
:64-
121.
Unl
ess
othe
rwise
indi
cate
d, re
fere
nces
belo
w to
the L
ucid
ariu
m re
fer t
o H
erlin
ger'
s 19
85 e
ditio
n of
the
tre
atise
. In
the
1978
diss
erta
tion,
1:2
-14,
H
erlin
ger
pres
ents
conv
inci
ng ev
iden
ce fo
r dat
ing t
he L
ucid
ariu
m (a
nd M
arch
etto
's Po-
m
eriu
m as
wel
l).
In h
is Lu
cida
rium
Can
tae P
lana
e (c
a. 1
317-
18),1
Mar
chet
to
of P
adua
pre
sent
s a
form
ulat
ion
of G
rego
rian
cha
nt th
eory
in
whi
ch th
e no
tion
of v
ario
us "
spec
ies"
of f
ourt
hs a
nd fi
fths i
s all-
The p
rese
nt st
udy w
as su
ppor
ted b
y a
rese
arch
time s
tipen
d (fo
r the
aca
- de
mic
year
1984
-85)
whi
ch w
as gr
ante
d by t
he So
cial
Scie
nces
and H
uman
ities
R
esea
rch C
ounc
il of C
anad
a. I a
m in
debt
ed as
wel
l to
Leem
an Pe
rkin
s of C
o-
lum
bia U
nive
rsity
and t
he an
onym
ous r
eade
rs of
my o
rigi
nal re
sear
ch pr
opos
al
to th
e Cou
ncil w
ho m
ade v
alua
ble s
ugge
stio
ns co
ncer
ning
the p
roje
ct an
d to
A
ndre
w H
ughe
s of t
he U
nive
rsity
of T
oron
to w
ho p
rovi
ded
help
ful a
dvic
e ab
out a
n ea
rlie
r for
m of
this
stud
y. I
am al
so gr
atef
ul to
Pat
rici
a Car
pent
er of
C
olum
bia U
nive
rsity
who
intr
oduc
ed m
e to
the p
rese
nt to
pic i
n he
r hist
ory o
f m
usic
theo
ry se
min
ar. N
ever
thel
ess,
one s
houl
d not
e tha
t I a
ssum
e ent
ire r
e-
spon
sibili
ty fo
r any
faul
ts to
be f
ound
here
in.
'An
exem
plar
y edi
tion,
tran
slatio
n, an
d com
men
tary
appe
ars in
Jan
Wil-
lia
m H
erlin
ger,
The
Luc
idar
ium
of M
arch
etto
of P
adua
: A C
ritic
al Ed
ition
, Tr
ansla
tion,
and
Com
men
tary
(Chi
cago
: Uni
vers
ity of
Chi
cago
Pres
s, 19
85),
whi
ch su
pers
edes
the s
ame a
utho
r's "
The L
ucid
ariu
m of
Mar
chet
to of
Pad
ua:
A C
ritic
al Ed
ition
, Tra
nsla
tion,
and
Com
men
tary
" (Ph
.D. d
isser
tatio
n, U
ni-
vers
ity of
Chi
cago
, 197
8, 2
vols.
). H
erlin
ger'
s wor
k is a
mar
ked i
mpr
ovem
ent
on th
e on
ly p
revi
ously
prin
ted v
ersio
n of
the
Luci
dari
um in
Mar
tin G
erbe
rt
(ed.
), Sc
ript
ores
Eccl
esia
stic
i de M
usic
a Sac
ra P
otiss
imum
(St.
Blai
se, 1
748;
re
pr. M
ilan:
Bolle
tino B
iblio
graf
ico M
usic
ale,
1931
; 3 vo
ls.) 3
:64-
121.
Unl
ess
othe
rwise
indi
cate
d, re
fere
nces
belo
w to
the L
ucid
ariu
m re
fer t
o H
erlin
ger'
s 19
85 e
ditio
n of
the
tre
atise
. In
the
1978
diss
erta
tion,
1:2
-14,
H
erlin
ger
pres
ents
conv
inci
ng ev
iden
ce fo
r dat
ing t
he L
ucid
ariu
m (a
nd M
arch
etto
's Po-
m
eriu
m as
wel
l).
perv
asiv
e.2
Mar
chet
to's
acco
unt
empl
oys
the
notio
n of
spe
cies
to
des
crib
e no
t onl
y th
e in
terv
allic
con
tent
s an
d m
elod
ic r
ange
s of
var
ious
mod
es,
mel
odie
s, an
d m
elod
ic p
assa
ges,
but a
lso to
de
scri
be w
ays
in w
hich
a m
ode
othe
r th
an t
he m
ain
one
of a
m
elod
y ca
n be
impl
ied
duri
ng th
e co
urse
of a
pie
ce.3
So
radi
cal
is M
arch
etto
's ap
proa
ch,
that
he
atta
cks
trad
ition
al a
ssig
n-
men
ts o
f m
elod
ies
to g
iven
mod
es,
whi
ch,
acco
rdin
g to
him
, ha
d be
en s
impl
istic
ally
bas
ed o
n su
ch a
spec
ts o
f a m
elod
y as
its
rang
e an
d fin
alis;
he
favo
urs
inst
ead
an a
ppro
ach
that
tak
es
mor
e va
riab
les
into
acc
ount
. A
ccor
ding
ly,
in m
any
inst
ance
s, th
e de
scri
ptio
ns o
f m
elod
ies
that
res
ult f
rom
Mar
chet
to's
for-
m
ulat
ion
of m
odal
ity p
rese
nt a
pic
ture
of c
ompl
exity
and
even
2A re
cent
disc
ussio
n of m
odal
ity in
gen
eral
appe
ars in
Har
old S
. Pow
ers,
"Mod
e,"
The N
ew G
rove
Dic
tiona
ry of
Mus
ic an
d Mus
icia
ns 12
:376
-450
(see
es
p. 37
6-41
8). T
he m
ost i
nten
sive d
iscus
sion o
f the
conc
ept o
f spe
cies
appe
ars
in L
ucie
Dik
enm
ann-
Balm
er, T
onsy
stem
und K
irch
ento
ne be
i Joh
anne
s Tin
c-
tori
s (Be
rn an
d Lei
pzig
: Pau
l Hau
pt, 1
935)
. 3M
arch
etto
's sou
rces
for t
he id
ea th
at th
e mod
e of a
pie
ce ca
n cha
nge d
ur-
ing t
he co
urse
of a
mel
ody s
eem
to co
nsist
of ea
rlie
r acc
ount
s of t
he te
rm tr
o-
pus,
whi
ch M
arch
etto
equa
tes t
o mod
us an
d ton
us (i.
e., m
ode)
. In t
he ac
coun
ts
of tr
opus
that
Mar
chet
to to
ok as
his
poin
t of d
epar
ture
, the m
eani
ng of
"co
n-
vers
ion"
is st
ress
ed. S
uch
acco
unts
of tr
opus
appe
ar in
the
anon
ymou
s Alia
M
usic
a, ed
. Jac
ques
Cha
illey
, in P
ublic
atio
ns de
l'In
stitu
t de M
usic
olog
ie de
l'U
nive
rsite
de P
aris
(Par
is: C
entr
e de
Doc
umen
tatio
n Uni
vers
itair
e, 19
65),
no. 6
, p. 1
15; G
uido
of A
rezz
o, T
ract
atus
Cor
rect
oriu
s, ed.
Mar
tin G
erbe
rt, in
perv
asiv
e.2
Mar
chet
to's
acco
unt
empl
oys
the
notio
n of
spe
cies
to
des
crib
e no
t onl
y th
e in
terv
allic
con
tent
s an
d m
elod
ic r
ange
s of
var
ious
mod
es,
mel
odie
s, an
d m
elod
ic p
assa
ges,
but a
lso to
de
scri
be w
ays
in w
hich
a m
ode
othe
r th
an t
he m
ain
one
of a
m
elod
y ca
n be
impl
ied
duri
ng th
e co
urse
of a
pie
ce.3
So
radi
cal
is M
arch
etto
's ap
proa
ch,
that
he
atta
cks
trad
ition
al a
ssig
n-
men
ts o
f m
elod
ies
to g
iven
mod
es,
whi
ch,
acco
rdin
g to
him
, ha
d be
en s
impl
istic
ally
bas
ed o
n su
ch a
spec
ts o
f a m
elod
y as
its
rang
e an
d fin
alis;
he
favo
urs
inst
ead
an a
ppro
ach
that
tak
es
mor
e va
riab
les
into
acc
ount
. A
ccor
ding
ly,
in m
any
inst
ance
s, th
e de
scri
ptio
ns o
f m
elod
ies
that
res
ult f
rom
Mar
chet
to's
for-
m
ulat
ion
of m
odal
ity p
rese
nt a
pic
ture
of c
ompl
exity
and
even
2A re
cent
disc
ussio
n of m
odal
ity in
gen
eral
appe
ars in
Har
old S
. Pow
ers,
"Mod
e,"
The N
ew G
rove
Dic
tiona
ry of
Mus
ic an
d Mus
icia
ns 12
:376
-450
(see
es
p. 37
6-41
8). T
he m
ost i
nten
sive d
iscus
sion o
f the
conc
ept o
f spe
cies
appe
ars
in L
ucie
Dik
enm
ann-
Balm
er, T
onsy
stem
und K
irch
ento
ne be
i Joh
anne
s Tin
c-
tori
s (Be
rn an
d Lei
pzig
: Pau
l Hau
pt, 1
935)
. 3M
arch
etto
's sou
rces
for t
he id
ea th
at th
e mod
e of a
pie
ce ca
n cha
nge d
ur-
ing t
he co
urse
of a
mel
ody s
eem
to co
nsist
of ea
rlie
r acc
ount
s of t
he te
rm tr
o-
pus,
whi
ch M
arch
etto
equa
tes t
o mod
us an
d ton
us (i.
e., m
ode)
. In t
he ac
coun
ts
of tr
opus
that
Mar
chet
to to
ok as
his
poin
t of d
epar
ture
, the m
eani
ng of
"co
n-
vers
ion"
is st
ress
ed. S
uch
acco
unts
of tr
opus
appe
ar in
the
anon
ymou
s Alia
M
usic
a, ed
. Jac
ques
Cha
illey
, in P
ublic
atio
ns de
l'In
stitu
t de M
usic
olog
ie de
l'U
nive
rsite
de P
aris
(Par
is: C
entr
e de
Doc
umen
tatio
n Uni
vers
itair
e, 19
65),
no. 6
, p. 1
15; G
uido
of A
rezz
o, T
ract
atus
Cor
rect
oriu
s, ed.
Mar
tin G
erbe
rt, in
perv
asiv
e.2
Mar
chet
to's
acco
unt
empl
oys
the
notio
n of
spe
cies
to
des
crib
e no
t onl
y th
e in
terv
allic
con
tent
s an
d m
elod
ic r
ange
s of
var
ious
mod
es,
mel
odie
s, an
d m
elod
ic p
assa
ges,
but a
lso to
de
scri
be w
ays
in w
hich
a m
ode
othe
r th
an t
he m
ain
one
of a
m
elod
y ca
n be
impl
ied
duri
ng th
e co
urse
of a
pie
ce.3
So
radi
cal
is M
arch
etto
's ap
proa
ch,
that
he
atta
cks
trad
ition
al a
ssig
n-
men
ts o
f m
elod
ies
to g
iven
mod
es,
whi
ch,
acco
rdin
g to
him
, ha
d be
en s
impl
istic
ally
bas
ed o
n su
ch a
spec
ts o
f a m
elod
y as
its
rang
e an
d fin
alis;
he
favo
urs
inst
ead
an a
ppro
ach
that
tak
es
mor
e va
riab
les
into
acc
ount
. A
ccor
ding
ly,
in m
any
inst
ance
s, th
e de
scri
ptio
ns o
f m
elod
ies
that
res
ult f
rom
Mar
chet
to's
for-
m
ulat
ion
of m
odal
ity p
rese
nt a
pic
ture
of c
ompl
exity
and
even
2A re
cent
disc
ussio
n of m
odal
ity in
gen
eral
appe
ars in
Har
old S
. Pow
ers,
"Mod
e,"
The N
ew G
rove
Dic
tiona
ry of
Mus
ic an
d Mus
icia
ns 12
:376
-450
(see
es
p. 37
6-41
8). T
he m
ost i
nten
sive d
iscus
sion o
f the
conc
ept o
f spe
cies
appe
ars
in L
ucie
Dik
enm
ann-
Balm
er, T
onsy
stem
und K
irch
ento
ne be
i Joh
anne
s Tin
c-
tori
s (Be
rn an
d Lei
pzig
: Pau
l Hau
pt, 1
935)
. 3M
arch
etto
's sou
rces
for t
he id
ea th
at th
e mod
e of a
pie
ce ca
n cha
nge d
ur-
ing t
he co
urse
of a
mel
ody s
eem
to co
nsist
of ea
rlie
r acc
ount
s of t
he te
rm tr
o-
pus,
whi
ch M
arch
etto
equa
tes t
o mod
us an
d ton
us (i.
e., m
ode)
. In t
he ac
coun
ts
of tr
opus
that
Mar
chet
to to
ok as
his
poin
t of d
epar
ture
, the m
eani
ng of
"co
n-
vers
ion"
is st
ress
ed. S
uch
acco
unts
of tr
opus
appe
ar in
the
anon
ymou
s Alia
M
usic
a, ed
. Jac
ques
Cha
illey
, in P
ublic
atio
ns de
l'In
stitu
t de M
usic
olog
ie de
l'U
nive
rsite
de P
aris
(Par
is: C
entr
e de
Doc
umen
tatio
n Uni
vers
itair
e, 19
65),
no. 6
, p. 1
15; G
uido
of A
rezz
o, T
ract
atus
Cor
rect
oriu
s, ed.
Mar
tin G
erbe
rt, in
perv
asiv
e.2
Mar
chet
to's
acco
unt
empl
oys
the
notio
n of
spe
cies
to
des
crib
e no
t onl
y th
e in
terv
allic
con
tent
s an
d m
elod
ic r
ange
s of
var
ious
mod
es,
mel
odie
s, an
d m
elod
ic p
assa
ges,
but a
lso to
de
scri
be w
ays
in w
hich
a m
ode
othe
r th
an t
he m
ain
one
of a
m
elod
y ca
n be
impl
ied
duri
ng th
e co
urse
of a
pie
ce.3
So
radi
cal
is M
arch
etto
's ap
proa
ch,
that
he
atta
cks
trad
ition
al a
ssig
n-
men
ts o
f m
elod
ies
to g
iven
mod
es,
whi
ch,
acco
rdin
g to
him
, ha
d be
en s
impl
istic
ally
bas
ed o
n su
ch a
spec
ts o
f a m
elod
y as
its
rang
e an
d fin
alis;
he
favo
urs
inst
ead
an a
ppro
ach
that
tak
es
mor
e va
riab
les
into
acc
ount
. A
ccor
ding
ly,
in m
any
inst
ance
s, th
e de
scri
ptio
ns o
f m
elod
ies
that
res
ult f
rom
Mar
chet
to's
for-
m
ulat
ion
of m
odal
ity p
rese
nt a
pic
ture
of c
ompl
exity
and
even
2A re
cent
disc
ussio
n of m
odal
ity in
gen
eral
appe
ars in
Har
old S
. Pow
ers,
"Mod
e,"
The N
ew G
rove
Dic
tiona
ry of
Mus
ic an
d Mus
icia
ns 12
:376
-450
(see
es
p. 37
6-41
8). T
he m
ost i
nten
sive d
iscus
sion o
f the
conc
ept o
f spe
cies
appe
ars
in L
ucie
Dik
enm
ann-
Balm
er, T
onsy
stem
und K
irch
ento
ne be
i Joh
anne
s Tin
c-
tori
s (Be
rn an
d Lei
pzig
: Pau
l Hau
pt, 1
935)
. 3M
arch
etto
's sou
rces
for t
he id
ea th
at th
e mod
e of a
pie
ce ca
n cha
nge d
ur-
ing t
he co
urse
of a
mel
ody s
eem
to co
nsist
of ea
rlie
r acc
ount
s of t
he te
rm tr
o-
pus,
whi
ch M
arch
etto
equa
tes t
o mod
us an
d ton
us (i.
e., m
ode)
. In t
he ac
coun
ts
of tr
opus
that
Mar
chet
to to
ok as
his
poin
t of d
epar
ture
, the m
eani
ng of
"co
n-
vers
ion"
is st
ress
ed. S
uch
acco
unts
of tr
opus
appe
ar in
the
anon
ymou
s Alia
M
usic
a, ed
. Jac
ques
Cha
illey
, in P
ublic
atio
ns de
l'In
stitu
t de M
usic
olog
ie de
l'U
nive
rsite
de P
aris
(Par
is: C
entr
e de
Doc
umen
tatio
n Uni
vers
itair
e, 19
65),
no. 6
, p. 1
15; G
uido
of A
rezz
o, T
ract
atus
Cor
rect
oriu
s, ed.
Mar
tin G
erbe
rt, in
perv
asiv
e.2
Mar
chet
to's
acco
unt
empl
oys
the
notio
n of
spe
cies
to
des
crib
e no
t onl
y th
e in
terv
allic
con
tent
s an
d m
elod
ic r
ange
s of
var
ious
mod
es,
mel
odie
s, an
d m
elod
ic p
assa
ges,
but a
lso to
de
scri
be w
ays
in w
hich
a m
ode
othe
r th
an t
he m
ain
one
of a
m
elod
y ca
n be
impl
ied
duri
ng th
e co
urse
of a
pie
ce.3
So
radi
cal
is M
arch
etto
's ap
proa
ch,
that
he
atta
cks
trad
ition
al a
ssig
n-
men
ts o
f m
elod
ies
to g
iven
mod
es,
whi
ch,
acco
rdin
g to
him
, ha
d be
en s
impl
istic
ally
bas
ed o
n su
ch a
spec
ts o
f a m
elod
y as
its
rang
e an
d fin
alis;
he
favo
urs
inst
ead
an a
ppro
ach
that
tak
es
mor
e va
riab
les
into
acc
ount
. A
ccor
ding
ly,
in m
any
inst
ance
s, th
e de
scri
ptio
ns o
f m
elod
ies
that
res
ult f
rom
Mar
chet
to's
for-
m
ulat
ion
of m
odal
ity p
rese
nt a
pic
ture
of c
ompl
exity
and
even
2A re
cent
disc
ussio
n of m
odal
ity in
gen
eral
appe
ars in
Har
old S
. Pow
ers,
"Mod
e,"
The N
ew G
rove
Dic
tiona
ry of
Mus
ic an
d Mus
icia
ns 12
:376
-450
(see
es
p. 37
6-41
8). T
he m
ost i
nten
sive d
iscus
sion o
f the
conc
ept o
f spe
cies
appe
ars
in L
ucie
Dik
enm
ann-
Balm
er, T
onsy
stem
und K
irch
ento
ne be
i Joh
anne
s Tin
c-
tori
s (Be
rn an
d Lei
pzig
: Pau
l Hau
pt, 1
935)
. 3M
arch
etto
's sou
rces
for t
he id
ea th
at th
e mod
e of a
pie
ce ca
n cha
nge d
ur-
ing t
he co
urse
of a
mel
ody s
eem
to co
nsist
of ea
rlie
r acc
ount
s of t
he te
rm tr
o-
pus,
whi
ch M
arch
etto
equa
tes t
o mod
us an
d ton
us (i.
e., m
ode)
. In t
he ac
coun
ts
of tr
opus
that
Mar
chet
to to
ok as
his
poin
t of d
epar
ture
, the m
eani
ng of
"co
n-
vers
ion"
is st
ress
ed. S
uch
acco
unts
of tr
opus
appe
ar in
the
anon
ymou
s Alia
M
usic
a, ed
. Jac
ques
Cha
illey
, in P
ublic
atio
ns de
l'In
stitu
t de M
usic
olog
ie de
l'U
nive
rsite
de P
aris
(Par
is: C
entr
e de
Doc
umen
tatio
n Uni
vers
itair
e, 19
65),
no. 6
, p. 1
15; G
uido
of A
rezz
o, T
ract
atus
Cor
rect
oriu
s, ed.
Mar
tin G
erbe
rt, in
perv
asiv
e.2
Mar
chet
to's
acco
unt
empl
oys
the
notio
n of
spe
cies
to
des
crib
e no
t onl
y th
e in
terv
allic
con
tent
s an
d m
elod
ic r
ange
s of
var
ious
mod
es,
mel
odie
s, an
d m
elod
ic p
assa
ges,
but a
lso to
de
scri
be w
ays
in w
hich
a m
ode
othe
r th
an t
he m
ain
one
of a
m
elod
y ca
n be
impl
ied
duri
ng th
e co
urse
of a
pie
ce.3
So
radi
cal
is M
arch
etto
's ap
proa
ch,
that
he
atta
cks
trad
ition
al a
ssig
n-
men
ts o
f m
elod
ies
to g
iven
mod
es,
whi
ch,
acco
rdin
g to
him
, ha
d be
en s
impl
istic
ally
bas
ed o
n su
ch a
spec
ts o
f a m
elod
y as
its
rang
e an
d fin
alis;
he
favo
urs
inst
ead
an a
ppro
ach
that
tak
es
mor
e va
riab
les
into
acc
ount
. A
ccor
ding
ly,
in m
any
inst
ance
s, th
e de
scri
ptio
ns o
f m
elod
ies
that
res
ult f
rom
Mar
chet
to's
for-
m
ulat
ion
of m
odal
ity p
rese
nt a
pic
ture
of c
ompl
exity
and
even
2A re
cent
disc
ussio
n of m
odal
ity in
gen
eral
appe
ars in
Har
old S
. Pow
ers,
"Mod
e,"
The N
ew G
rove
Dic
tiona
ry of
Mus
ic an
d Mus
icia
ns 12
:376
-450
(see
es
p. 37
6-41
8). T
he m
ost i
nten
sive d
iscus
sion o
f the
conc
ept o
f spe
cies
appe
ars
in L
ucie
Dik
enm
ann-
Balm
er, T
onsy
stem
und K
irch
ento
ne be
i Joh
anne
s Tin
c-
tori
s (Be
rn an
d Lei
pzig
: Pau
l Hau
pt, 1
935)
. 3M
arch
etto
's sou
rces
for t
he id
ea th
at th
e mod
e of a
pie
ce ca
n cha
nge d
ur-
ing t
he co
urse
of a
mel
ody s
eem
to co
nsist
of ea
rlie
r acc
ount
s of t
he te
rm tr
o-
pus,
whi
ch M
arch
etto
equa
tes t
o mod
us an
d ton
us (i.
e., m
ode)
. In t
he ac
coun
ts
of tr
opus
that
Mar
chet
to to
ok as
his
poin
t of d
epar
ture
, the m
eani
ng of
"co
n-
vers
ion"
is st
ress
ed. S
uch
acco
unts
of tr
opus
appe
ar in
the
anon
ymou
s Alia
M
usic
a, ed
. Jac
ques
Cha
illey
, in P
ublic
atio
ns de
l'In
stitu
t de M
usic
olog
ie de
l'U
nive
rsite
de P
aris
(Par
is: C
entr
e de
Doc
umen
tatio
n Uni
vers
itair
e, 19
65),
no. 6
, p. 1
15; G
uido
of A
rezz
o, T
ract
atus
Cor
rect
oriu
s, ed.
Mar
tin G
erbe
rt, in
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
118
Mus
ic Th
eory
Spec
trum
11
8 M
usic
Theo
ry Sp
ectr
um
118
Mus
ic Th
eory
Spec
trum
11
8 M
usic
Theo
ry Sp
ectr
um
118
Mus
ic Th
eory
Spec
trum
11
8 M
usic
Theo
ry Sp
ectr
um
ambi
guity
in m
elod
ic st
ruct
ure t
hat i
s lac
king
in ea
rlie
r tre
at-
men
ts of
chan
t. Of l
ess i
mpo
rtan
ce to
Mar
chet
to th
an to
earl
ier
wri
ters
on m
odal
theo
ry ar
e suc
h gro
ss fe
atur
es of
who
le m
elo-
di
es as
thei
r hig
hest
, low
est,
and l
ast n
otes
. Ind
eed w
ith re
gard
to
the t
radi
tiona
lly sa
cros
anct
final
is, he
poi
nts o
ut th
at a
thir
d-
mod
e mel
ody m
ight
end o
n D
3 (r
athe
r tha
n E3)
and
still
be re
- ga
rded
as a
thir
d-m
ode m
elod
y bec
ause
of th
e mel
odic
prog
res-
sio
ns th
at p
rece
de it
s fin
al no
te.4
He
furt
her e
mph
asiz
es th
at
Scri
ptor
es Ec
cles
iast
ici 2:
51; a
nd T
heog
er of
Met
z, M
usic
a, ed
. Mar
tin G
er-
bert
, in
Scri
ptor
es Ec
cles
iast
ici 2
:190
a. W
illi A
pel,
in h
is G
rego
rian
Cha
nt
(Blo
omin
gton
: Indi
ana U
nive
rsity
Pres
s, 19
58), 1
42-4
3 an
d 172
-78,
disc
usse
s ca
ses o
f wha
t he t
erm
s "to
nal in
stab
ility
" in
theo
ry an
d pra
ctic
e. Su
ffice
it to
re
mar
k at t
his p
oint
that
the p
ossib
ility
that
a m
elod
y mig
ht en
d in
a di
ffere
nt
mod
e tha
n it b
egin
s was
disc
usse
d as e
arly
as th
e nin
th ce
ntur
y by R
egin
o in h
is D
e H
arm
onic
a Ins
titut
ione
, ed.
Ger
bert
, in
Scri
ptor
es Ec
cles
iast
ici 1
: 231
b.
Earl
y ins
tanc
es of
this
phen
omen
on (i
.e.,
befo
re th
e Lu
cida
rium
) are
dis-
cu
ssed
in U
rban
us Bo
mm
, Der
Wec
hsel
der M
odal
itdts
best
imm
ung in
der T
ra-
ditio
n der
Mes
sges
ange
, and G
. Jac
obst
hal, D
ie ch
rom
atisc
he Alte
ratio
n im
li-
turg
ische
n Ges
ang d
er ab
endl
dndi
shen
Kir
che (
Berl
in: 1
897;
repr
. Hild
eshe
im:
G. O
lms,
1970
). Oth
er ea
rly a
ccou
nts a
ppea
r in th
e Alia
Mus
ica,
ed. G
erbe
rt,
in Sc
ript
ores
Eccl
esia
stic
i 1:14
0a; M
S Lei
pzig
, Uni
vers
itats
bibl
ioth
ek, la
t. 14
02
(ed.
H.
Sow
a, i
n Q
uelle
n zu
r Tr
ansf
orm
atio
n der
Ant
ipho
nen
[Kas
sel:
Bare
nrei
ter,
1935
]); an
d the
Ton
ale S
anct
i Ber
nard
i disc
usse
d in
Kar
l-Wer
ner
Gum
pel, Z
ur In
terp
reta
tion de
r Ton
us-D
efin
ition
des "
Tona
le Sa
ncti B
erna
rdi"
(M
ainz
: Aka
dem
ie d
er W
issen
scha
ft und
der
Lite
ratu
r, A
bhan
dlun
gen d
er
Gei
stes
-und
Sozi
alw
issen
scha
ftlic
hen K
lass
e, Ja
hrga
ng 19
59),
no. 2
(Wie
sba-
de
n: A
kade
mie
der W
issen
scha
ften u
nd de
r Lite
ratu
r im M
ainz
, Ste
iner
), 50-
51
. Also
impo
rtan
t is J
ohan
nes A
fflig
emen
sis's s
tate
men
t tha
t the
mod
e of a
m
elod
y is n
ot m
erel
y det
erm
ined
by th
e mel
ody'
s end
ing (
cf. D
e Mus
ica c
um
Tona
rio,
ed. J
os. S
mits
van W
aesb
ergh
e [R
ome:
Am
eric
an In
stitu
te of
Mus
i- co
logy
, 195
0 (C
orpu
s Scr
ipto
rum
Mus
ica,
1)]
110,
tran
s. W
arre
n Bab
b in
C
laud
e Pal
isca'
s edi
tion o
f Huc
bald
, Gui
do an
d Joh
n O
n Mus
ic: T
hree
Med
ie-
val T
reat
ises [N
ew H
aven
: Yal
e Uni
vers
ity Pr
ess,
1978
], 133
). The
equa
ting o
f to
nus, t
ropu
s and
mod
us ca
n be t
race
d to H
ucba
ld's H
arm
onia
, the S
colic
a en-
ch
iria
dis, G
uido
's Mic
rolo
gus a
nd E
pist
ola;
Joha
nnes
Affl
igem
ensis
's Mus
ica,
an
d Ber
no's
Mus
ica,
as H
erlin
ger p
oint
s out
in h
is ed
ition
of th
e Luc
idar
ium
, no
te a,
p. 3
71.
4Luc
idar
ium
, book
11, c
hap.
3, cl
ause
s 1-1
2, p
p. 39
0-95
, and
the e
xam
ple
for t
he fo
urth
mod
e in L
ucid
ariu
m, 11
,4,1
24, p
p. 44
6-47
. Fra
nchi
no G
affu
rio
ambi
guity
in m
elod
ic st
ruct
ure t
hat i
s lac
king
in ea
rlie
r tre
at-
men
ts of
chan
t. Of l
ess i
mpo
rtan
ce to
Mar
chet
to th
an to
earl
ier
wri
ters
on m
odal
theo
ry ar
e suc
h gro
ss fe
atur
es of
who
le m
elo-
di
es as
thei
r hig
hest
, low
est,
and l
ast n
otes
. Ind
eed w
ith re
gard
to
the t
radi
tiona
lly sa
cros
anct
final
is, he
poi
nts o
ut th
at a
thir
d-
mod
e mel
ody m
ight
end o
n D
3 (r
athe
r tha
n E3)
and
still
be re
- ga
rded
as a
thir
d-m
ode m
elod
y bec
ause
of th
e mel
odic
prog
res-
sio
ns th
at p
rece
de it
s fin
al no
te.4
He
furt
her e
mph
asiz
es th
at
Scri
ptor
es Ec
cles
iast
ici 2:
51; a
nd T
heog
er of
Met
z, M
usic
a, ed
. Mar
tin G
er-
bert
, in
Scri
ptor
es Ec
cles
iast
ici 2
:190
a. W
illi A
pel,
in h
is G
rego
rian
Cha
nt
(Blo
omin
gton
: Indi
ana U
nive
rsity
Pres
s, 19
58), 1
42-4
3 an
d 172
-78,
disc
usse
s ca
ses o
f wha
t he t
erm
s "to
nal in
stab
ility
" in
theo
ry an
d pra
ctic
e. Su
ffice
it to
re
mar
k at t
his p
oint
that
the p
ossib
ility
that
a m
elod
y mig
ht en
d in
a di
ffere
nt
mod
e tha
n it b
egin
s was
disc
usse
d as e
arly
as th
e nin
th ce
ntur
y by R
egin
o in h
is D
e H
arm
onic
a Ins
titut
ione
, ed.
Ger
bert
, in
Scri
ptor
es Ec
cles
iast
ici 1
: 231
b.
Earl
y ins
tanc
es of
this
phen
omen
on (i
.e.,
befo
re th
e Lu
cida
rium
) are
dis-
cu
ssed
in U
rban
us Bo
mm
, Der
Wec
hsel
der M
odal
itdts
best
imm
ung in
der T
ra-
ditio
n der
Mes
sges
ange
, and G
. Jac
obst
hal, D
ie ch
rom
atisc
he Alte
ratio
n im
li-
turg
ische
n Ges
ang d
er ab
endl
dndi
shen
Kir
che (
Berl
in: 1
897;
repr
. Hild
eshe
im:
G. O
lms,
1970
). Oth
er ea
rly a
ccou
nts a
ppea
r in th
e Alia
Mus
ica,
ed. G
erbe
rt,
in Sc
ript
ores
Eccl
esia
stic
i 1:14
0a; M
S Lei
pzig
, Uni
vers
itats
bibl
ioth
ek, la
t. 14
02
(ed.
H.
Sow
a, i
n Q
uelle
n zu
r Tr
ansf
orm
atio
n der
Ant
ipho
nen
[Kas
sel:
Bare
nrei
ter,
1935
]); an
d the
Ton
ale S
anct
i Ber
nard
i disc
usse
d in
Kar
l-Wer
ner
Gum
pel, Z
ur In
terp
reta
tion de
r Ton
us-D
efin
ition
des "
Tona
le Sa
ncti B
erna
rdi"
(M
ainz
: Aka
dem
ie d
er W
issen
scha
ft und
der
Lite
ratu
r, A
bhan
dlun
gen d
er
Gei
stes
-und
Sozi
alw
issen
scha
ftlic
hen K
lass
e, Ja
hrga
ng 19
59),
no. 2
(Wie
sba-
de
n: A
kade
mie
der W
issen
scha
ften u
nd de
r Lite
ratu
r im M
ainz
, Ste
iner
), 50-
51
. Also
impo
rtan
t is J
ohan
nes A
fflig
emen
sis's s
tate
men
t tha
t the
mod
e of a
m
elod
y is n
ot m
erel
y det
erm
ined
by th
e mel
ody'
s end
ing (
cf. D
e Mus
ica c
um
Tona
rio,
ed. J
os. S
mits
van W
aesb
ergh
e [R
ome:
Am
eric
an In
stitu
te of
Mus
i- co
logy
, 195
0 (C
orpu
s Scr
ipto
rum
Mus
ica,
1)]
110,
tran
s. W
arre
n Bab
b in
C
laud
e Pal
isca'
s edi
tion o
f Huc
bald
, Gui
do an
d Joh
n O
n Mus
ic: T
hree
Med
ie-
val T
reat
ises [N
ew H
aven
: Yal
e Uni
vers
ity Pr
ess,
1978
], 133
). The
equa
ting o
f to
nus, t
ropu
s and
mod
us ca
n be t
race
d to H
ucba
ld's H
arm
onia
, the S
colic
a en-
ch
iria
dis, G
uido
's Mic
rolo
gus a
nd E
pist
ola;
Joha
nnes
Affl
igem
ensis
's Mus
ica,
an
d Ber
no's
Mus
ica,
as H
erlin
ger p
oint
s out
in h
is ed
ition
of th
e Luc
idar
ium
, no
te a,
p. 3
71.
4Luc
idar
ium
, book
11, c
hap.
3, cl
ause
s 1-1
2, p
p. 39
0-95
, and
the e
xam
ple
for t
he fo
urth
mod
e in L
ucid
ariu
m, 11
,4,1
24, p
p. 44
6-47
. Fra
nchi
no G
affu
rio
ambi
guity
in m
elod
ic st
ruct
ure t
hat i
s lac
king
in ea
rlie
r tre
at-
men
ts of
chan
t. Of l
ess i
mpo
rtan
ce to
Mar
chet
to th
an to
earl
ier
wri
ters
on m
odal
theo
ry ar
e suc
h gro
ss fe
atur
es of
who
le m
elo-
di
es as
thei
r hig
hest
, low
est,
and l
ast n
otes
. Ind
eed w
ith re
gard
to
the t
radi
tiona
lly sa
cros
anct
final
is, he
poi
nts o
ut th
at a
thir
d-
mod
e mel
ody m
ight
end o
n D
3 (r
athe
r tha
n E3)
and
still
be re
- ga
rded
as a
thir
d-m
ode m
elod
y bec
ause
of th
e mel
odic
prog
res-
sio
ns th
at p
rece
de it
s fin
al no
te.4
He
furt
her e
mph
asiz
es th
at
Scri
ptor
es Ec
cles
iast
ici 2:
51; a
nd T
heog
er of
Met
z, M
usic
a, ed
. Mar
tin G
er-
bert
, in
Scri
ptor
es Ec
cles
iast
ici 2
:190
a. W
illi A
pel,
in h
is G
rego
rian
Cha
nt
(Blo
omin
gton
: Indi
ana U
nive
rsity
Pres
s, 19
58), 1
42-4
3 an
d 172
-78,
disc
usse
s ca
ses o
f wha
t he t
erm
s "to
nal in
stab
ility
" in
theo
ry an
d pra
ctic
e. Su
ffice
it to
re
mar
k at t
his p
oint
that
the p
ossib
ility
that
a m
elod
y mig
ht en
d in
a di
ffere
nt
mod
e tha
n it b
egin
s was
disc
usse
d as e
arly
as th
e nin
th ce
ntur
y by R
egin
o in h
is D
e H
arm
onic
a Ins
titut
ione
, ed.
Ger
bert
, in
Scri
ptor
es Ec
cles
iast
ici 1
: 231
b.
Earl
y ins
tanc
es of
this
phen
omen
on (i
.e.,
befo
re th
e Lu
cida
rium
) are
dis-
cu
ssed
in U
rban
us Bo
mm
, Der
Wec
hsel
der M
odal
itdts
best
imm
ung in
der T
ra-
ditio
n der
Mes
sges
ange
, and G
. Jac
obst
hal, D
ie ch
rom
atisc
he Alte
ratio
n im
li-
turg
ische
n Ges
ang d
er ab
endl
dndi
shen
Kir
che (
Berl
in: 1
897;
repr
. Hild
eshe
im:
G. O
lms,
1970
). Oth
er ea
rly a
ccou
nts a
ppea
r in th
e Alia
Mus
ica,
ed. G
erbe
rt,
in Sc
ript
ores
Eccl
esia
stic
i 1:14
0a; M
S Lei
pzig
, Uni
vers
itats
bibl
ioth
ek, la
t. 14
02
(ed.
H.
Sow
a, i
n Q
uelle
n zu
r Tr
ansf
orm
atio
n der
Ant
ipho
nen
[Kas
sel:
Bare
nrei
ter,
1935
]); an
d the
Ton
ale S
anct
i Ber
nard
i disc
usse
d in
Kar
l-Wer
ner
Gum
pel, Z
ur In
terp
reta
tion de
r Ton
us-D
efin
ition
des "
Tona
le Sa
ncti B
erna
rdi"
(M
ainz
: Aka
dem
ie d
er W
issen
scha
ft und
der
Lite
ratu
r, A
bhan
dlun
gen d
er
Gei
stes
-und
Sozi
alw
issen
scha
ftlic
hen K
lass
e, Ja
hrga
ng 19
59),
no. 2
(Wie
sba-
de
n: A
kade
mie
der W
issen
scha
ften u
nd de
r Lite
ratu
r im M
ainz
, Ste
iner
), 50-
51
. Also
impo
rtan
t is J
ohan
nes A
fflig
emen
sis's s
tate
men
t tha
t the
mod
e of a
m
elod
y is n
ot m
erel
y det
erm
ined
by th
e mel
ody'
s end
ing (
cf. D
e Mus
ica c
um
Tona
rio,
ed. J
os. S
mits
van W
aesb
ergh
e [R
ome:
Am
eric
an In
stitu
te of
Mus
i- co
logy
, 195
0 (C
orpu
s Scr
ipto
rum
Mus
ica,
1)]
110,
tran
s. W
arre
n Bab
b in
C
laud
e Pal
isca'
s edi
tion o
f Huc
bald
, Gui
do an
d Joh
n O
n Mus
ic: T
hree
Med
ie-
val T
reat
ises [N
ew H
aven
: Yal
e Uni
vers
ity Pr
ess,
1978
], 133
). The
equa
ting o
f to
nus, t
ropu
s and
mod
us ca
n be t
race
d to H
ucba
ld's H
arm
onia
, the S
colic
a en-
ch
iria
dis, G
uido
's Mic
rolo
gus a
nd E
pist
ola;
Joha
nnes
Affl
igem
ensis
's Mus
ica,
an
d Ber
no's
Mus
ica,
as H
erlin
ger p
oint
s out
in h
is ed
ition
of th
e Luc
idar
ium
, no
te a,
p. 3
71.
4Luc
idar
ium
, book
11, c
hap.
3, cl
ause
s 1-1
2, p
p. 39
0-95
, and
the e
xam
ple
for t
he fo
urth
mod
e in L
ucid
ariu
m, 11
,4,1
24, p
p. 44
6-47
. Fra
nchi
no G
affu
rio
ambi
guity
in m
elod
ic st
ruct
ure t
hat i
s lac
king
in ea
rlie
r tre
at-
men
ts of
chan
t. Of l
ess i
mpo
rtan
ce to
Mar
chet
to th
an to
earl
ier
wri
ters
on m
odal
theo
ry ar
e suc
h gro
ss fe
atur
es of
who
le m
elo-
di
es as
thei
r hig
hest
, low
est,
and l
ast n
otes
. Ind
eed w
ith re
gard
to
the t
radi
tiona
lly sa
cros
anct
final
is, he
poi
nts o
ut th
at a
thir
d-
mod
e mel
ody m
ight
end o
n D
3 (r
athe
r tha
n E3)
and
still
be re
- ga
rded
as a
thir
d-m
ode m
elod
y bec
ause
of th
e mel
odic
prog
res-
sio
ns th
at p
rece
de it
s fin
al no
te.4
He
furt
her e
mph
asiz
es th
at
Scri
ptor
es Ec
cles
iast
ici 2:
51; a
nd T
heog
er of
Met
z, M
usic
a, ed
. Mar
tin G
er-
bert
, in
Scri
ptor
es Ec
cles
iast
ici 2
:190
a. W
illi A
pel,
in h
is G
rego
rian
Cha
nt
(Blo
omin
gton
: Indi
ana U
nive
rsity
Pres
s, 19
58), 1
42-4
3 an
d 172
-78,
disc
usse
s ca
ses o
f wha
t he t
erm
s "to
nal in
stab
ility
" in
theo
ry an
d pra
ctic
e. Su
ffice
it to
re
mar
k at t
his p
oint
that
the p
ossib
ility
that
a m
elod
y mig
ht en
d in
a di
ffere
nt
mod
e tha
n it b
egin
s was
disc
usse
d as e
arly
as th
e nin
th ce
ntur
y by R
egin
o in h
is D
e H
arm
onic
a Ins
titut
ione
, ed.
Ger
bert
, in
Scri
ptor
es Ec
cles
iast
ici 1
: 231
b.
Earl
y ins
tanc
es of
this
phen
omen
on (i
.e.,
befo
re th
e Lu
cida
rium
) are
dis-
cu
ssed
in U
rban
us Bo
mm
, Der
Wec
hsel
der M
odal
itdts
best
imm
ung in
der T
ra-
ditio
n der
Mes
sges
ange
, and G
. Jac
obst
hal, D
ie ch
rom
atisc
he Alte
ratio
n im
li-
turg
ische
n Ges
ang d
er ab
endl
dndi
shen
Kir
che (
Berl
in: 1
897;
repr
. Hild
eshe
im:
G. O
lms,
1970
). Oth
er ea
rly a
ccou
nts a
ppea
r in th
e Alia
Mus
ica,
ed. G
erbe
rt,
in Sc
ript
ores
Eccl
esia
stic
i 1:14
0a; M
S Lei
pzig
, Uni
vers
itats
bibl
ioth
ek, la
t. 14
02
(ed.
H.
Sow
a, i
n Q
uelle
n zu
r Tr
ansf
orm
atio
n der
Ant
ipho
nen
[Kas
sel:
Bare
nrei
ter,
1935
]); an
d the
Ton
ale S
anct
i Ber
nard
i disc
usse
d in
Kar
l-Wer
ner
Gum
pel, Z
ur In
terp
reta
tion de
r Ton
us-D
efin
ition
des "
Tona
le Sa
ncti B
erna
rdi"
(M
ainz
: Aka
dem
ie d
er W
issen
scha
ft und
der
Lite
ratu
r, A
bhan
dlun
gen d
er
Gei
stes
-und
Sozi
alw
issen
scha
ftlic
hen K
lass
e, Ja
hrga
ng 19
59),
no. 2
(Wie
sba-
de
n: A
kade
mie
der W
issen
scha
ften u
nd de
r Lite
ratu
r im M
ainz
, Ste
iner
), 50-
51
. Also
impo
rtan
t is J
ohan
nes A
fflig
emen
sis's s
tate
men
t tha
t the
mod
e of a
m
elod
y is n
ot m
erel
y det
erm
ined
by th
e mel
ody'
s end
ing (
cf. D
e Mus
ica c
um
Tona
rio,
ed. J
os. S
mits
van W
aesb
ergh
e [R
ome:
Am
eric
an In
stitu
te of
Mus
i- co
logy
, 195
0 (C
orpu
s Scr
ipto
rum
Mus
ica,
1)]
110,
tran
s. W
arre
n Bab
b in
C
laud
e Pal
isca'
s edi
tion o
f Huc
bald
, Gui
do an
d Joh
n O
n Mus
ic: T
hree
Med
ie-
val T
reat
ises [N
ew H
aven
: Yal
e Uni
vers
ity Pr
ess,
1978
], 133
). The
equa
ting o
f to
nus, t
ropu
s and
mod
us ca
n be t
race
d to H
ucba
ld's H
arm
onia
, the S
colic
a en-
ch
iria
dis, G
uido
's Mic
rolo
gus a
nd E
pist
ola;
Joha
nnes
Affl
igem
ensis
's Mus
ica,
an
d Ber
no's
Mus
ica,
as H
erlin
ger p
oint
s out
in h
is ed
ition
of th
e Luc
idar
ium
, no
te a,
p. 3
71.
4Luc
idar
ium
, book
11, c
hap.
3, cl
ause
s 1-1
2, p
p. 39
0-95
, and
the e
xam
ple
for t
he fo
urth
mod
e in L
ucid
ariu
m, 11
,4,1
24, p
p. 44
6-47
. Fra
nchi
no G
affu
rio
ambi
guity
in m
elod
ic st
ruct
ure t
hat i
s lac
king
in ea
rlie
r tre
at-
men
ts of
chan
t. Of l
ess i
mpo
rtan
ce to
Mar
chet
to th
an to
earl
ier
wri
ters
on m
odal
theo
ry ar
e suc
h gro
ss fe
atur
es of
who
le m
elo-
di
es as
thei
r hig
hest
, low
est,
and l
ast n
otes
. Ind
eed w
ith re
gard
to
the t
radi
tiona
lly sa
cros
anct
final
is, he
poi
nts o
ut th
at a
thir
d-
mod
e mel
ody m
ight
end o
n D
3 (r
athe
r tha
n E3)
and
still
be re
- ga
rded
as a
thir
d-m
ode m
elod
y bec
ause
of th
e mel
odic
prog
res-
sio
ns th
at p
rece
de it
s fin
al no
te.4
He
furt
her e
mph
asiz
es th
at
Scri
ptor
es Ec
cles
iast
ici 2:
51; a
nd T
heog
er of
Met
z, M
usic
a, ed
. Mar
tin G
er-
bert
, in
Scri
ptor
es Ec
cles
iast
ici 2
:190
a. W
illi A
pel,
in h
is G
rego
rian
Cha
nt
(Blo
omin
gton
: Indi
ana U
nive
rsity
Pres
s, 19
58), 1
42-4
3 an
d 172
-78,
disc
usse
s ca
ses o
f wha
t he t
erm
s "to
nal in
stab
ility
" in
theo
ry an
d pra
ctic
e. Su
ffice
it to
re
mar
k at t
his p
oint
that
the p
ossib
ility
that
a m
elod
y mig
ht en
d in
a di
ffere
nt
mod
e tha
n it b
egin
s was
disc
usse
d as e
arly
as th
e nin
th ce
ntur
y by R
egin
o in h
is D
e H
arm
onic
a Ins
titut
ione
, ed.
Ger
bert
, in
Scri
ptor
es Ec
cles
iast
ici 1
: 231
b.
Earl
y ins
tanc
es of
this
phen
omen
on (i
.e.,
befo
re th
e Lu
cida
rium
) are
dis-
cu
ssed
in U
rban
us Bo
mm
, Der
Wec
hsel
der M
odal
itdts
best
imm
ung in
der T
ra-
ditio
n der
Mes
sges
ange
, and G
. Jac
obst
hal, D
ie ch
rom
atisc
he Alte
ratio
n im
li-
turg
ische
n Ges
ang d
er ab
endl
dndi
shen
Kir
che (
Berl
in: 1
897;
repr
. Hild
eshe
im:
G. O
lms,
1970
). Oth
er ea
rly a
ccou
nts a
ppea
r in th
e Alia
Mus
ica,
ed. G
erbe
rt,
in Sc
ript
ores
Eccl
esia
stic
i 1:14
0a; M
S Lei
pzig
, Uni
vers
itats
bibl
ioth
ek, la
t. 14
02
(ed.
H.
Sow
a, i
n Q
uelle
n zu
r Tr
ansf
orm
atio
n der
Ant
ipho
nen
[Kas
sel:
Bare
nrei
ter,
1935
]); an
d the
Ton
ale S
anct
i Ber
nard
i disc
usse
d in
Kar
l-Wer
ner
Gum
pel, Z
ur In
terp
reta
tion de
r Ton
us-D
efin
ition
des "
Tona
le Sa
ncti B
erna
rdi"
(M
ainz
: Aka
dem
ie d
er W
issen
scha
ft und
der
Lite
ratu
r, A
bhan
dlun
gen d
er
Gei
stes
-und
Sozi
alw
issen
scha
ftlic
hen K
lass
e, Ja
hrga
ng 19
59),
no. 2
(Wie
sba-
de
n: A
kade
mie
der W
issen
scha
ften u
nd de
r Lite
ratu
r im M
ainz
, Ste
iner
), 50-
51
. Also
impo
rtan
t is J
ohan
nes A
fflig
emen
sis's s
tate
men
t tha
t the
mod
e of a
m
elod
y is n
ot m
erel
y det
erm
ined
by th
e mel
ody'
s end
ing (
cf. D
e Mus
ica c
um
Tona
rio,
ed. J
os. S
mits
van W
aesb
ergh
e [R
ome:
Am
eric
an In
stitu
te of
Mus
i- co
logy
, 195
0 (C
orpu
s Scr
ipto
rum
Mus
ica,
1)]
110,
tran
s. W
arre
n Bab
b in
C
laud
e Pal
isca'
s edi
tion o
f Huc
bald
, Gui
do an
d Joh
n O
n Mus
ic: T
hree
Med
ie-
val T
reat
ises [N
ew H
aven
: Yal
e Uni
vers
ity Pr
ess,
1978
], 133
). The
equa
ting o
f to
nus, t
ropu
s and
mod
us ca
n be t
race
d to H
ucba
ld's H
arm
onia
, the S
colic
a en-
ch
iria
dis, G
uido
's Mic
rolo
gus a
nd E
pist
ola;
Joha
nnes
Affl
igem
ensis
's Mus
ica,
an
d Ber
no's
Mus
ica,
as H
erlin
ger p
oint
s out
in h
is ed
ition
of th
e Luc
idar
ium
, no
te a,
p. 3
71.
4Luc
idar
ium
, book
11, c
hap.
3, cl
ause
s 1-1
2, p
p. 39
0-95
, and
the e
xam
ple
for t
he fo
urth
mod
e in L
ucid
ariu
m, 11
,4,1
24, p
p. 44
6-47
. Fra
nchi
no G
affu
rio
ambi
guity
in m
elod
ic st
ruct
ure t
hat i
s lac
king
in ea
rlie
r tre
at-
men
ts of
chan
t. Of l
ess i
mpo
rtan
ce to
Mar
chet
to th
an to
earl
ier
wri
ters
on m
odal
theo
ry ar
e suc
h gro
ss fe
atur
es of
who
le m
elo-
di
es as
thei
r hig
hest
, low
est,
and l
ast n
otes
. Ind
eed w
ith re
gard
to
the t
radi
tiona
lly sa
cros
anct
final
is, he
poi
nts o
ut th
at a
thir
d-
mod
e mel
ody m
ight
end o
n D
3 (r
athe
r tha
n E3)
and
still
be re
- ga
rded
as a
thir
d-m
ode m
elod
y bec
ause
of th
e mel
odic
prog
res-
sio
ns th
at p
rece
de it
s fin
al no
te.4
He
furt
her e
mph
asiz
es th
at
Scri
ptor
es Ec
cles
iast
ici 2:
51; a
nd T
heog
er of
Met
z, M
usic
a, ed
. Mar
tin G
er-
bert
, in
Scri
ptor
es Ec
cles
iast
ici 2
:190
a. W
illi A
pel,
in h
is G
rego
rian
Cha
nt
(Blo
omin
gton
: Indi
ana U
nive
rsity
Pres
s, 19
58), 1
42-4
3 an
d 172
-78,
disc
usse
s ca
ses o
f wha
t he t
erm
s "to
nal in
stab
ility
" in
theo
ry an
d pra
ctic
e. Su
ffice
it to
re
mar
k at t
his p
oint
that
the p
ossib
ility
that
a m
elod
y mig
ht en
d in
a di
ffere
nt
mod
e tha
n it b
egin
s was
disc
usse
d as e
arly
as th
e nin
th ce
ntur
y by R
egin
o in h
is D
e H
arm
onic
a Ins
titut
ione
, ed.
Ger
bert
, in
Scri
ptor
es Ec
cles
iast
ici 1
: 231
b.
Earl
y ins
tanc
es of
this
phen
omen
on (i
.e.,
befo
re th
e Lu
cida
rium
) are
dis-
cu
ssed
in U
rban
us Bo
mm
, Der
Wec
hsel
der M
odal
itdts
best
imm
ung in
der T
ra-
ditio
n der
Mes
sges
ange
, and G
. Jac
obst
hal, D
ie ch
rom
atisc
he Alte
ratio
n im
li-
turg
ische
n Ges
ang d
er ab
endl
dndi
shen
Kir
che (
Berl
in: 1
897;
repr
. Hild
eshe
im:
G. O
lms,
1970
). Oth
er ea
rly a
ccou
nts a
ppea
r in th
e Alia
Mus
ica,
ed. G
erbe
rt,
in Sc
ript
ores
Eccl
esia
stic
i 1:14
0a; M
S Lei
pzig
, Uni
vers
itats
bibl
ioth
ek, la
t. 14
02
(ed.
H.
Sow
a, i
n Q
uelle
n zu
r Tr
ansf
orm
atio
n der
Ant
ipho
nen
[Kas
sel:
Bare
nrei
ter,
1935
]); an
d the
Ton
ale S
anct
i Ber
nard
i disc
usse
d in
Kar
l-Wer
ner
Gum
pel, Z
ur In
terp
reta
tion de
r Ton
us-D
efin
ition
des "
Tona
le Sa
ncti B
erna
rdi"
(M
ainz
: Aka
dem
ie d
er W
issen
scha
ft und
der
Lite
ratu
r, A
bhan
dlun
gen d
er
Gei
stes
-und
Sozi
alw
issen
scha
ftlic
hen K
lass
e, Ja
hrga
ng 19
59),
no. 2
(Wie
sba-
de
n: A
kade
mie
der W
issen
scha
ften u
nd de
r Lite
ratu
r im M
ainz
, Ste
iner
), 50-
51
. Also
impo
rtan
t is J
ohan
nes A
fflig
emen
sis's s
tate
men
t tha
t the
mod
e of a
m
elod
y is n
ot m
erel
y det
erm
ined
by th
e mel
ody'
s end
ing (
cf. D
e Mus
ica c
um
Tona
rio,
ed. J
os. S
mits
van W
aesb
ergh
e [R
ome:
Am
eric
an In
stitu
te of
Mus
i- co
logy
, 195
0 (C
orpu
s Scr
ipto
rum
Mus
ica,
1)]
110,
tran
s. W
arre
n Bab
b in
C
laud
e Pal
isca'
s edi
tion o
f Huc
bald
, Gui
do an
d Joh
n O
n Mus
ic: T
hree
Med
ie-
val T
reat
ises [N
ew H
aven
: Yal
e Uni
vers
ity Pr
ess,
1978
], 133
). The
equa
ting o
f to
nus, t
ropu
s and
mod
us ca
n be t
race
d to H
ucba
ld's H
arm
onia
, the S
colic
a en-
ch
iria
dis, G
uido
's Mic
rolo
gus a
nd E
pist
ola;
Joha
nnes
Affl
igem
ensis
's Mus
ica,
an
d Ber
no's
Mus
ica,
as H
erlin
ger p
oint
s out
in h
is ed
ition
of th
e Luc
idar
ium
, no
te a,
p. 3
71.
4Luc
idar
ium
, book
11, c
hap.
3, cl
ause
s 1-1
2, p
p. 39
0-95
, and
the e
xam
ple
for t
he fo
urth
mod
e in L
ucid
ariu
m, 11
,4,1
24, p
p. 44
6-47
. Fra
nchi
no G
affu
rio
ther
e is a
gre
y ar
ea b
etw
een
the
trad
ition
al ca
tego
ries
of a
u-
then
tic a
nd p
laga
l,5 an
d in
trod
uces
prev
ious
ly un
reco
gniz
ed
dist
inct
ions
amon
g per
fect
, im
perf
ect,
plup
erfe
ct, a
nd m
ixed
ra
nges
.6
The s
ense
one g
ets o
n re
adin
g Mar
chet
to's t
reat
ise is
that
he
is m
ore c
once
rned
with
the e
ffect
of lo
cal e
vent
s on
the w
hole
th
an ar
e pre
viou
s wri
ters
. His
rem
arks
stri
ke on
e as v
ery m
od-
dism
issed
the
first
pass
age c
ited
abov
e in
a m
argi
nal n
ote
on h
is co
py of
the
trea
tise (
MS.
147
3, T
rem
ezzo
, Pri
vate
Libr
ary o
f Cou
nt G
. L. S
ola-
Cab
iati,
p.
50) s
ayin
g tha
t "ac
cord
ing t
o Br
othe
r Joh
anne
s God
enba
ch [i
.e.,
Gaf
furi
o's
teac
her B
onad
ies,
see
Cle
men
t Mill
er, "
Earl
y Gaf
furi
ana:
New
Ans
wer
s to
Old
Que
stio
ns,"
Mus
ical
Qua
rter
ly 56
(197
0): 3
79], t
his r
easo
n is n
ot go
od, b
e-
caus
e [an
exam
ple o
f] a m
elod
y tha
t doe
s not
hav
e con
sona
nce a
t its
end i
s not
gi
ven.
" A m
elod
y illu
stra
ting M
arch
etto
's poi
nt in
the f
irst
pass
age i
s pro
vide
d in
the s
econ
d pa
ssag
e. In
deed
, in
the v
ario
us so
urce
s of t
he L
ucid
ariu
m, th
e se
vera
l var
iant
s of t
he m
elod
y, w
hich
is su
ppos
ed to
illu
stra
te th
e fou
rth m
ode
acco
rdin
g to
Mar
chet
to, e
nd on
D3,
a ca
se th
at is
par
alle
l to th
e hyp
othe
tical
in
stan
ce M
arch
etto
pose
s in
the f
irst
pass
age.
In th
is st
udy,
pitc
hes a
re de
sig-
nate
d acc
ordi
ng to
the n
otat
ion s
ugge
sted
by th
e Aco
ustic
al So
ciet
y of A
mer
- ic
a: m
iddl
e c is
rend
ered
as C
4, th
e not
e bel
ow it
as B
3, th
e not
e abo
ve as
D4,
et
c. 5S
ee es
peci
ally
Luc
idar
ium
, 12, 1
, 14-
45,
pp. 5
22-3
3, w
hich
is de
vote
d to
"mel
odie
s whi
ch on
the b
asis
of th
eir a
scen
t are
not a
uthe
ntic
and o
n th
e bas
is of
thei
r des
cent
[are
not]
plag
al."
Con
cern
with
such
prob
lem
s can
be tr
aced
ba
ck to
the a
nony
mou
s Dia
logu
s de M
usic
a, ca
. 100
0, ed
. Ger
bert
, in S
crip
- to
res E
ccle
siast
ici 1
:251
-64,
and
the
anon
ymou
s thi
rtee
nth-
cent
ury S
umm
a M
usic
ae, e
d. G
erbe
rt, in
Scr
ipto
res E
ccle
siast
ici 3
:189
-248
and
225f
. On
the
auth
orsh
ip of
the D
ialo
gus,
see
Mic
hel H
uglo
, "L'
aute
ur du
'Dia
logu
e sur
la
mus
ique
' attr
ibu6
e O
don,
" R
evue
de
Mus
icol
ogie
55/2
(196
9): 1
19-7
1. S
ee
also
note
30 b
elow
. 6S
ee es
peci
ally
Luc
idar
ium
, 11,
2, 2
0-33
, pp
. 378
-89.
On t
he im
port
ance
of
thes
e am
bitu
s dist
inct
ions
, whi
ch tr
avel
led w
ith th
e ide
a of
"co
mm
ixtu
re"
disc
usse
d bel
ow, s
ee K
laus
Wol
fgan
g Nie
m6l
ler,
"Zu
r Ton
us-L
ehre
der i
ta-
lieni
sche
n Mus
ikth
eori
e des
aus
gehe
nden
Mitt
elal
ter,
" Kir
chen
mus
ikal
ische
s Ja
hrbu
ch 60
(195
6): 2
3-32
. Th
ese d
istin
ctio
ns w
ere p
artic
ular
ly ch
arac
teri
stic
of
Ital
ian m
usic
theo
ry un
til ab
out 1
500.
Rec
ogni
tion o
f plu
perf
ect r
ange
s was
pr
epar
ed by
the a
nony
mou
s aut
hor o
f the
Dia
logu
s 1:2
59ff.
(see
not
e 5 ab
ove)
, w
ho ac
know
ledg
ed an
expa
nsio
n of r
ange
s fro
m an
octa
ve to
a n
inth
or te
nth,
de
pend
ing o
n th
e mod
e inv
olve
d.
ther
e is a
gre
y ar
ea b
etw
een
the
trad
ition
al ca
tego
ries
of a
u-
then
tic a
nd p
laga
l,5 an
d in
trod
uces
prev
ious
ly un
reco
gniz
ed
dist
inct
ions
amon
g per
fect
, im
perf
ect,
plup
erfe
ct, a
nd m
ixed
ra
nges
.6
The s
ense
one g
ets o
n re
adin
g Mar
chet
to's t
reat
ise is
that
he
is m
ore c
once
rned
with
the e
ffect
of lo
cal e
vent
s on
the w
hole
th
an ar
e pre
viou
s wri
ters
. His
rem
arks
stri
ke on
e as v
ery m
od-
dism
issed
the
first
pass
age c
ited
abov
e in
a m
argi
nal n
ote
on h
is co
py of
the
trea
tise (
MS.
147
3, T
rem
ezzo
, Pri
vate
Libr
ary o
f Cou
nt G
. L. S
ola-
Cab
iati,
p.
50) s
ayin
g tha
t "ac
cord
ing t
o Br
othe
r Joh
anne
s God
enba
ch [i
.e.,
Gaf
furi
o's
teac
her B
onad
ies,
see
Cle
men
t Mill
er, "
Earl
y Gaf
furi
ana:
New
Ans
wer
s to
Old
Que
stio
ns,"
Mus
ical
Qua
rter
ly 56
(197
0): 3
79], t
his r
easo
n is n
ot go
od, b
e-
caus
e [an
exam
ple o
f] a m
elod
y tha
t doe
s not
hav
e con
sona
nce a
t its
end i
s not
gi
ven.
" A m
elod
y illu
stra
ting M
arch
etto
's poi
nt in
the f
irst
pass
age i
s pro
vide
d in
the s
econ
d pa
ssag
e. In
deed
, in
the v
ario
us so
urce
s of t
he L
ucid
ariu
m, th
e se
vera
l var
iant
s of t
he m
elod
y, w
hich
is su
ppos
ed to
illu
stra
te th
e fou
rth m
ode
acco
rdin
g to
Mar
chet
to, e
nd on
D3,
a ca
se th
at is
par
alle
l to th
e hyp
othe
tical
in
stan
ce M
arch
etto
pose
s in
the f
irst
pass
age.
In th
is st
udy,
pitc
hes a
re de
sig-
nate
d acc
ordi
ng to
the n
otat
ion s
ugge
sted
by th
e Aco
ustic
al So
ciet
y of A
mer
- ic
a: m
iddl
e c is
rend
ered
as C
4, th
e not
e bel
ow it
as B
3, th
e not
e abo
ve as
D4,
et
c. 5S
ee es
peci
ally
Luc
idar
ium
, 12, 1
, 14-
45,
pp. 5
22-3
3, w
hich
is de
vote
d to
"mel
odie
s whi
ch on
the b
asis
of th
eir a
scen
t are
not a
uthe
ntic
and o
n th
e bas
is of
thei
r des
cent
[are
not]
plag
al."
Con
cern
with
such
prob
lem
s can
be tr
aced
ba
ck to
the a
nony
mou
s Dia
logu
s de M
usic
a, ca
. 100
0, ed
. Ger
bert
, in S
crip
- to
res E
ccle
siast
ici 1
:251
-64,
and
the
anon
ymou
s thi
rtee
nth-
cent
ury S
umm
a M
usic
ae, e
d. G
erbe
rt, in
Scr
ipto
res E
ccle
siast
ici 3
:189
-248
and
225f
. On
the
auth
orsh
ip of
the D
ialo
gus,
see
Mic
hel H
uglo
, "L'
aute
ur du
'Dia
logu
e sur
la
mus
ique
' attr
ibu6
e O
don,
" R
evue
de
Mus
icol
ogie
55/2
(196
9): 1
19-7
1. S
ee
also
note
30 b
elow
. 6S
ee es
peci
ally
Luc
idar
ium
, 11,
2, 2
0-33
, pp
. 378
-89.
On t
he im
port
ance
of
thes
e am
bitu
s dist
inct
ions
, whi
ch tr
avel
led w
ith th
e ide
a of
"co
mm
ixtu
re"
disc
usse
d bel
ow, s
ee K
laus
Wol
fgan
g Nie
m6l
ler,
"Zu
r Ton
us-L
ehre
der i
ta-
lieni
sche
n Mus
ikth
eori
e des
aus
gehe
nden
Mitt
elal
ter,
" Kir
chen
mus
ikal
ische
s Ja
hrbu
ch 60
(195
6): 2
3-32
. Th
ese d
istin
ctio
ns w
ere p
artic
ular
ly ch
arac
teri
stic
of
Ital
ian m
usic
theo
ry un
til ab
out 1
500.
Rec
ogni
tion o
f plu
perf
ect r
ange
s was
pr
epar
ed by
the a
nony
mou
s aut
hor o
f the
Dia
logu
s 1:2
59ff.
(see
not
e 5 ab
ove)
, w
ho ac
know
ledg
ed an
expa
nsio
n of r
ange
s fro
m an
octa
ve to
a n
inth
or te
nth,
de
pend
ing o
n th
e mod
e inv
olve
d.
ther
e is a
gre
y ar
ea b
etw
een
the
trad
ition
al ca
tego
ries
of a
u-
then
tic a
nd p
laga
l,5 an
d in
trod
uces
prev
ious
ly un
reco
gniz
ed
dist
inct
ions
amon
g per
fect
, im
perf
ect,
plup
erfe
ct, a
nd m
ixed
ra
nges
.6
The s
ense
one g
ets o
n re
adin
g Mar
chet
to's t
reat
ise is
that
he
is m
ore c
once
rned
with
the e
ffect
of lo
cal e
vent
s on
the w
hole
th
an ar
e pre
viou
s wri
ters
. His
rem
arks
stri
ke on
e as v
ery m
od-
dism
issed
the
first
pass
age c
ited
abov
e in
a m
argi
nal n
ote
on h
is co
py of
the
trea
tise (
MS.
147
3, T
rem
ezzo
, Pri
vate
Libr
ary o
f Cou
nt G
. L. S
ola-
Cab
iati,
p.
50) s
ayin
g tha
t "ac
cord
ing t
o Br
othe
r Joh
anne
s God
enba
ch [i
.e.,
Gaf
furi
o's
teac
her B
onad
ies,
see
Cle
men
t Mill
er, "
Earl
y Gaf
furi
ana:
New
Ans
wer
s to
Old
Que
stio
ns,"
Mus
ical
Qua
rter
ly 56
(197
0): 3
79], t
his r
easo
n is n
ot go
od, b
e-
caus
e [an
exam
ple o
f] a m
elod
y tha
t doe
s not
hav
e con
sona
nce a
t its
end i
s not
gi
ven.
" A m
elod
y illu
stra
ting M
arch
etto
's poi
nt in
the f
irst
pass
age i
s pro
vide
d in
the s
econ
d pa
ssag
e. In
deed
, in
the v
ario
us so
urce
s of t
he L
ucid
ariu
m, th
e se
vera
l var
iant
s of t
he m
elod
y, w
hich
is su
ppos
ed to
illu
stra
te th
e fou
rth m
ode
acco
rdin
g to
Mar
chet
to, e
nd on
D3,
a ca
se th
at is
par
alle
l to th
e hyp
othe
tical
in
stan
ce M
arch
etto
pose
s in
the f
irst
pass
age.
In th
is st
udy,
pitc
hes a
re de
sig-
nate
d acc
ordi
ng to
the n
otat
ion s
ugge
sted
by th
e Aco
ustic
al So
ciet
y of A
mer
- ic
a: m
iddl
e c is
rend
ered
as C
4, th
e not
e bel
ow it
as B
3, th
e not
e abo
ve as
D4,
et
c. 5S
ee es
peci
ally
Luc
idar
ium
, 12, 1
, 14-
45,
pp. 5
22-3
3, w
hich
is de
vote
d to
"mel
odie
s whi
ch on
the b
asis
of th
eir a
scen
t are
not a
uthe
ntic
and o
n th
e bas
is of
thei
r des
cent
[are
not]
plag
al."
Con
cern
with
such
prob
lem
s can
be tr
aced
ba
ck to
the a
nony
mou
s Dia
logu
s de M
usic
a, ca
. 100
0, ed
. Ger
bert
, in S
crip
- to
res E
ccle
siast
ici 1
:251
-64,
and
the
anon
ymou
s thi
rtee
nth-
cent
ury S
umm
a M
usic
ae, e
d. G
erbe
rt, in
Scr
ipto
res E
ccle
siast
ici 3
:189
-248
and
225f
. On
the
auth
orsh
ip of
the D
ialo
gus,
see
Mic
hel H
uglo
, "L'
aute
ur du
'Dia
logu
e sur
la
mus
ique
' attr
ibu6
e O
don,
" R
evue
de
Mus
icol
ogie
55/2
(196
9): 1
19-7
1. S
ee
also
note
30 b
elow
. 6S
ee es
peci
ally
Luc
idar
ium
, 11,
2, 2
0-33
, pp
. 378
-89.
On t
he im
port
ance
of
thes
e am
bitu
s dist
inct
ions
, whi
ch tr
avel
led w
ith th
e ide
a of
"co
mm
ixtu
re"
disc
usse
d bel
ow, s
ee K
laus
Wol
fgan
g Nie
m6l
ler,
"Zu
r Ton
us-L
ehre
der i
ta-
lieni
sche
n Mus
ikth
eori
e des
aus
gehe
nden
Mitt
elal
ter,
" Kir
chen
mus
ikal
ische
s Ja
hrbu
ch 60
(195
6): 2
3-32
. Th
ese d
istin
ctio
ns w
ere p
artic
ular
ly ch
arac
teri
stic
of
Ital
ian m
usic
theo
ry un
til ab
out 1
500.
Rec
ogni
tion o
f plu
perf
ect r
ange
s was
pr
epar
ed by
the a
nony
mou
s aut
hor o
f the
Dia
logu
s 1:2
59ff.
(see
not
e 5 ab
ove)
, w
ho ac
know
ledg
ed an
expa
nsio
n of r
ange
s fro
m an
octa
ve to
a n
inth
or te
nth,
de
pend
ing o
n th
e mod
e inv
olve
d.
ther
e is a
gre
y ar
ea b
etw
een
the
trad
ition
al ca
tego
ries
of a
u-
then
tic a
nd p
laga
l,5 an
d in
trod
uces
prev
ious
ly un
reco
gniz
ed
dist
inct
ions
amon
g per
fect
, im
perf
ect,
plup
erfe
ct, a
nd m
ixed
ra
nges
.6
The s
ense
one g
ets o
n re
adin
g Mar
chet
to's t
reat
ise is
that
he
is m
ore c
once
rned
with
the e
ffect
of lo
cal e
vent
s on
the w
hole
th
an ar
e pre
viou
s wri
ters
. His
rem
arks
stri
ke on
e as v
ery m
od-
dism
issed
the
first
pass
age c
ited
abov
e in
a m
argi
nal n
ote
on h
is co
py of
the
trea
tise (
MS.
147
3, T
rem
ezzo
, Pri
vate
Libr
ary o
f Cou
nt G
. L. S
ola-
Cab
iati,
p.
50) s
ayin
g tha
t "ac
cord
ing t
o Br
othe
r Joh
anne
s God
enba
ch [i
.e.,
Gaf
furi
o's
teac
her B
onad
ies,
see
Cle
men
t Mill
er, "
Earl
y Gaf
furi
ana:
New
Ans
wer
s to
Old
Que
stio
ns,"
Mus
ical
Qua
rter
ly 56
(197
0): 3
79], t
his r
easo
n is n
ot go
od, b
e-
caus
e [an
exam
ple o
f] a m
elod
y tha
t doe
s not
hav
e con
sona
nce a
t its
end i
s not
gi
ven.
" A m
elod
y illu
stra
ting M
arch
etto
's poi
nt in
the f
irst
pass
age i
s pro
vide
d in
the s
econ
d pa
ssag
e. In
deed
, in
the v
ario
us so
urce
s of t
he L
ucid
ariu
m, th
e se
vera
l var
iant
s of t
he m
elod
y, w
hich
is su
ppos
ed to
illu
stra
te th
e fou
rth m
ode
acco
rdin
g to
Mar
chet
to, e
nd on
D3,
a ca
se th
at is
par
alle
l to th
e hyp
othe
tical
in
stan
ce M
arch
etto
pose
s in
the f
irst
pass
age.
In th
is st
udy,
pitc
hes a
re de
sig-
nate
d acc
ordi
ng to
the n
otat
ion s
ugge
sted
by th
e Aco
ustic
al So
ciet
y of A
mer
- ic
a: m
iddl
e c is
rend
ered
as C
4, th
e not
e bel
ow it
as B
3, th
e not
e abo
ve as
D4,
et
c. 5S
ee es
peci
ally
Luc
idar
ium
, 12, 1
, 14-
45,
pp. 5
22-3
3, w
hich
is de
vote
d to
"mel
odie
s whi
ch on
the b
asis
of th
eir a
scen
t are
not a
uthe
ntic
and o
n th
e bas
is of
thei
r des
cent
[are
not]
plag
al."
Con
cern
with
such
prob
lem
s can
be tr
aced
ba
ck to
the a
nony
mou
s Dia
logu
s de M
usic
a, ca
. 100
0, ed
. Ger
bert
, in S
crip
- to
res E
ccle
siast
ici 1
:251
-64,
and
the
anon
ymou
s thi
rtee
nth-
cent
ury S
umm
a M
usic
ae, e
d. G
erbe
rt, in
Scr
ipto
res E
ccle
siast
ici 3
:189
-248
and
225f
. On
the
auth
orsh
ip of
the D
ialo
gus,
see
Mic
hel H
uglo
, "L'
aute
ur du
'Dia
logu
e sur
la
mus
ique
' attr
ibu6
e O
don,
" R
evue
de
Mus
icol
ogie
55/2
(196
9): 1
19-7
1. S
ee
also
note
30 b
elow
. 6S
ee es
peci
ally
Luc
idar
ium
, 11,
2, 2
0-33
, pp
. 378
-89.
On t
he im
port
ance
of
thes
e am
bitu
s dist
inct
ions
, whi
ch tr
avel
led w
ith th
e ide
a of
"co
mm
ixtu
re"
disc
usse
d bel
ow, s
ee K
laus
Wol
fgan
g Nie
m6l
ler,
"Zu
r Ton
us-L
ehre
der i
ta-
lieni
sche
n Mus
ikth
eori
e des
aus
gehe
nden
Mitt
elal
ter,
" Kir
chen
mus
ikal
ische
s Ja
hrbu
ch 60
(195
6): 2
3-32
. Th
ese d
istin
ctio
ns w
ere p
artic
ular
ly ch
arac
teri
stic
of
Ital
ian m
usic
theo
ry un
til ab
out 1
500.
Rec
ogni
tion o
f plu
perf
ect r
ange
s was
pr
epar
ed by
the a
nony
mou
s aut
hor o
f the
Dia
logu
s 1:2
59ff.
(see
not
e 5 ab
ove)
, w
ho ac
know
ledg
ed an
expa
nsio
n of r
ange
s fro
m an
octa
ve to
a n
inth
or te
nth,
de
pend
ing o
n th
e mod
e inv
olve
d.
ther
e is a
gre
y ar
ea b
etw
een
the
trad
ition
al ca
tego
ries
of a
u-
then
tic a
nd p
laga
l,5 an
d in
trod
uces
prev
ious
ly un
reco
gniz
ed
dist
inct
ions
amon
g per
fect
, im
perf
ect,
plup
erfe
ct, a
nd m
ixed
ra
nges
.6
The s
ense
one g
ets o
n re
adin
g Mar
chet
to's t
reat
ise is
that
he
is m
ore c
once
rned
with
the e
ffect
of lo
cal e
vent
s on
the w
hole
th
an ar
e pre
viou
s wri
ters
. His
rem
arks
stri
ke on
e as v
ery m
od-
dism
issed
the
first
pass
age c
ited
abov
e in
a m
argi
nal n
ote
on h
is co
py of
the
trea
tise (
MS.
147
3, T
rem
ezzo
, Pri
vate
Libr
ary o
f Cou
nt G
. L. S
ola-
Cab
iati,
p.
50) s
ayin
g tha
t "ac
cord
ing t
o Br
othe
r Joh
anne
s God
enba
ch [i
.e.,
Gaf
furi
o's
teac
her B
onad
ies,
see
Cle
men
t Mill
er, "
Earl
y Gaf
furi
ana:
New
Ans
wer
s to
Old
Que
stio
ns,"
Mus
ical
Qua
rter
ly 56
(197
0): 3
79], t
his r
easo
n is n
ot go
od, b
e-
caus
e [an
exam
ple o
f] a m
elod
y tha
t doe
s not
hav
e con
sona
nce a
t its
end i
s not
gi
ven.
" A m
elod
y illu
stra
ting M
arch
etto
's poi
nt in
the f
irst
pass
age i
s pro
vide
d in
the s
econ
d pa
ssag
e. In
deed
, in
the v
ario
us so
urce
s of t
he L
ucid
ariu
m, th
e se
vera
l var
iant
s of t
he m
elod
y, w
hich
is su
ppos
ed to
illu
stra
te th
e fou
rth m
ode
acco
rdin
g to
Mar
chet
to, e
nd on
D3,
a ca
se th
at is
par
alle
l to th
e hyp
othe
tical
in
stan
ce M
arch
etto
pose
s in
the f
irst
pass
age.
In th
is st
udy,
pitc
hes a
re de
sig-
nate
d acc
ordi
ng to
the n
otat
ion s
ugge
sted
by th
e Aco
ustic
al So
ciet
y of A
mer
- ic
a: m
iddl
e c is
rend
ered
as C
4, th
e not
e bel
ow it
as B
3, th
e not
e abo
ve as
D4,
et
c. 5S
ee es
peci
ally
Luc
idar
ium
, 12, 1
, 14-
45,
pp. 5
22-3
3, w
hich
is de
vote
d to
"mel
odie
s whi
ch on
the b
asis
of th
eir a
scen
t are
not a
uthe
ntic
and o
n th
e bas
is of
thei
r des
cent
[are
not]
plag
al."
Con
cern
with
such
prob
lem
s can
be tr
aced
ba
ck to
the a
nony
mou
s Dia
logu
s de M
usic
a, ca
. 100
0, ed
. Ger
bert
, in S
crip
- to
res E
ccle
siast
ici 1
:251
-64,
and
the
anon
ymou
s thi
rtee
nth-
cent
ury S
umm
a M
usic
ae, e
d. G
erbe
rt, in
Scr
ipto
res E
ccle
siast
ici 3
:189
-248
and
225f
. On
the
auth
orsh
ip of
the D
ialo
gus,
see
Mic
hel H
uglo
, "L'
aute
ur du
'Dia
logu
e sur
la
mus
ique
' attr
ibu6
e O
don,
" R
evue
de
Mus
icol
ogie
55/2
(196
9): 1
19-7
1. S
ee
also
note
30 b
elow
. 6S
ee es
peci
ally
Luc
idar
ium
, 11,
2, 2
0-33
, pp
. 378
-89.
On t
he im
port
ance
of
thes
e am
bitu
s dist
inct
ions
, whi
ch tr
avel
led w
ith th
e ide
a of
"co
mm
ixtu
re"
disc
usse
d bel
ow, s
ee K
laus
Wol
fgan
g Nie
m6l
ler,
"Zu
r Ton
us-L
ehre
der i
ta-
lieni
sche
n Mus
ikth
eori
e des
aus
gehe
nden
Mitt
elal
ter,
" Kir
chen
mus
ikal
ische
s Ja
hrbu
ch 60
(195
6): 2
3-32
. Th
ese d
istin
ctio
ns w
ere p
artic
ular
ly ch
arac
teri
stic
of
Ital
ian m
usic
theo
ry un
til ab
out 1
500.
Rec
ogni
tion o
f plu
perf
ect r
ange
s was
pr
epar
ed by
the a
nony
mou
s aut
hor o
f the
Dia
logu
s 1:2
59ff.
(see
not
e 5 ab
ove)
, w
ho ac
know
ledg
ed an
expa
nsio
n of r
ange
s fro
m an
octa
ve to
a n
inth
or te
nth,
de
pend
ing o
n th
e mod
e inv
olve
d.
ther
e is a
gre
y ar
ea b
etw
een
the
trad
ition
al ca
tego
ries
of a
u-
then
tic a
nd p
laga
l,5 an
d in
trod
uces
prev
ious
ly un
reco
gniz
ed
dist
inct
ions
amon
g per
fect
, im
perf
ect,
plup
erfe
ct, a
nd m
ixed
ra
nges
.6
The s
ense
one g
ets o
n re
adin
g Mar
chet
to's t
reat
ise is
that
he
is m
ore c
once
rned
with
the e
ffect
of lo
cal e
vent
s on
the w
hole
th
an ar
e pre
viou
s wri
ters
. His
rem
arks
stri
ke on
e as v
ery m
od-
dism
issed
the
first
pass
age c
ited
abov
e in
a m
argi
nal n
ote
on h
is co
py of
the
trea
tise (
MS.
147
3, T
rem
ezzo
, Pri
vate
Libr
ary o
f Cou
nt G
. L. S
ola-
Cab
iati,
p.
50) s
ayin
g tha
t "ac
cord
ing t
o Br
othe
r Joh
anne
s God
enba
ch [i
.e.,
Gaf
furi
o's
teac
her B
onad
ies,
see
Cle
men
t Mill
er, "
Earl
y Gaf
furi
ana:
New
Ans
wer
s to
Old
Que
stio
ns,"
Mus
ical
Qua
rter
ly 56
(197
0): 3
79], t
his r
easo
n is n
ot go
od, b
e-
caus
e [an
exam
ple o
f] a m
elod
y tha
t doe
s not
hav
e con
sona
nce a
t its
end i
s not
gi
ven.
" A m
elod
y illu
stra
ting M
arch
etto
's poi
nt in
the f
irst
pass
age i
s pro
vide
d in
the s
econ
d pa
ssag
e. In
deed
, in
the v
ario
us so
urce
s of t
he L
ucid
ariu
m, th
e se
vera
l var
iant
s of t
he m
elod
y, w
hich
is su
ppos
ed to
illu
stra
te th
e fou
rth m
ode
acco
rdin
g to
Mar
chet
to, e
nd on
D3,
a ca
se th
at is
par
alle
l to th
e hyp
othe
tical
in
stan
ce M
arch
etto
pose
s in
the f
irst
pass
age.
In th
is st
udy,
pitc
hes a
re de
sig-
nate
d acc
ordi
ng to
the n
otat
ion s
ugge
sted
by th
e Aco
ustic
al So
ciet
y of A
mer
- ic
a: m
iddl
e c is
rend
ered
as C
4, th
e not
e bel
ow it
as B
3, th
e not
e abo
ve as
D4,
et
c. 5S
ee es
peci
ally
Luc
idar
ium
, 12, 1
, 14-
45,
pp. 5
22-3
3, w
hich
is de
vote
d to
"mel
odie
s whi
ch on
the b
asis
of th
eir a
scen
t are
not a
uthe
ntic
and o
n th
e bas
is of
thei
r des
cent
[are
not]
plag
al."
Con
cern
with
such
prob
lem
s can
be tr
aced
ba
ck to
the a
nony
mou
s Dia
logu
s de M
usic
a, ca
. 100
0, ed
. Ger
bert
, in S
crip
- to
res E
ccle
siast
ici 1
:251
-64,
and
the
anon
ymou
s thi
rtee
nth-
cent
ury S
umm
a M
usic
ae, e
d. G
erbe
rt, in
Scr
ipto
res E
ccle
siast
ici 3
:189
-248
and
225f
. On
the
auth
orsh
ip of
the D
ialo
gus,
see
Mic
hel H
uglo
, "L'
aute
ur du
'Dia
logu
e sur
la
mus
ique
' attr
ibu6
e O
don,
" R
evue
de
Mus
icol
ogie
55/2
(196
9): 1
19-7
1. S
ee
also
note
30 b
elow
. 6S
ee es
peci
ally
Luc
idar
ium
, 11,
2, 2
0-33
, pp
. 378
-89.
On t
he im
port
ance
of
thes
e am
bitu
s dist
inct
ions
, whi
ch tr
avel
led w
ith th
e ide
a of
"co
mm
ixtu
re"
disc
usse
d bel
ow, s
ee K
laus
Wol
fgan
g Nie
m6l
ler,
"Zu
r Ton
us-L
ehre
der i
ta-
lieni
sche
n Mus
ikth
eori
e des
aus
gehe
nden
Mitt
elal
ter,
" Kir
chen
mus
ikal
ische
s Ja
hrbu
ch 60
(195
6): 2
3-32
. Th
ese d
istin
ctio
ns w
ere p
artic
ular
ly ch
arac
teri
stic
of
Ital
ian m
usic
theo
ry un
til ab
out 1
500.
Rec
ogni
tion o
f plu
perf
ect r
ange
s was
pr
epar
ed by
the a
nony
mou
s aut
hor o
f the
Dia
logu
s 1:2
59ff.
(see
not
e 5 ab
ove)
, w
ho ac
know
ledg
ed an
expa
nsio
n of r
ange
s fro
m an
octa
ve to
a n
inth
or te
nth,
de
pend
ing o
n th
e mod
e inv
olve
d.
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
119
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
119
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
119
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
119
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
119
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
119
ern i
n th
at he
is co
ncer
ned w
ith re
latio
nshi
ps be
twee
n loc
al or
fo
regr
ound
feat
ures
and
glob
al or
bac
kgro
und s
truc
ture
s. In-
de
ed, i
n m
any w
ays,
he a
ppea
rs to
hav
e und
erta
ken m
elod
ic
anal
ysis i
n pa
rt fo
r its
own
sake
rath
er th
an m
erel
y to
clas
sify
and c
odify
the t
radi
tiona
l chan
t mel
odie
s.7
Am
ong t
he m
any n
ovel
ties t
hat M
arch
etto
intr
oduc
es in
the
Luci
dari
um is
the n
otio
n of "
com
mix
ture
."8 A
ccor
ding
to M
ar-
chet
to's
acco
unt,
a giv
en m
elod
y may
be co
nsid
ered
to b
e not
m
erel
y in
a s
ingl
e mod
e, b
ut a
lso to
pas
s thr
ough
, or
to b
e "c
omm
ixed
with
," ot
her m
odes
dur
ing i
ts pr
ogre
ss. M
arch
etto
de
als w
ith th
is id
ea of
com
mix
ture
mos
t ext
ensiv
ely i
n th
e sec
- tio
n on
"in
terr
uptio
ns" a
t the
end
of th
e ele
vent
h boo
k of
the
Luci
dari
um.9
Sinc
e the
conc
ept o
f com
mix
ture
repr
esen
ts su
ch
a ra
dica
l dev
elop
men
t in m
odal
theo
ry, a
nd be
caus
e it w
as in
- co
rpor
ated
into
the w
ork
of la
ter w
rite
rs du
ring
the n
ext t
wo
cent
urie
s,10 I
feel
that
it is
one
of M
arch
etto
's mos
t im
port
ant
7Thi
s is n
ot to
den
y tha
t mod
al cl
assif
icat
ion a
nd th
e mos
t app
ropr
iate
way
to
not
ate i
ndiv
idua
l mel
odie
s are
recu
rren
t conc
erns
for M
arch
etto
. Thr
ough
- ou
t the
Luc
idar
ium
, he g
ener
ates
stru
ctur
es fr
om fo
regr
ound
to b
ackg
roun
d,
as di
scus
sed b
elow
. 8T
hrou
ghou
t this
stud
y "co
mm
ixtu
re" i
s use
d to
tran
slate
the L
atin
term
co
mm
ixtio
. Thi
s usa
ge is
mod
elle
d on
the
prac
tice o
f Pow
ers,
"Mod
e."
Leo
Trei
tler'
s term
"int
erm
ixtu
re" (i
n "T
one S
yste
m in
the S
ecul
ar W
orks
of G
uil-
laum
e D
ufay
," J
ourn
al of
the
Am
eric
an M
usic
olog
ical
Soci
ety
18/2
[196
5]:
131-
69, e
sp. 1
34, n
ote 8
) has
muc
h to
reco
mm
end i
t, bu
t in
the p
rese
nt st
udy,
La
tin ro
ots a
re pr
eser
ved a
s far
as pr
actic
al in
Eng
lish t
rans
latio
ns of
tech
nica
l te
rms i
n or
der t
o fa
cilit
ate r
eadi
ng of
the o
rigi
nal tr
eatis
es. H
erlin
ger,
in op
p.
cit.,
pass
im, a
nd A
lber
t Sea
y in
his t
rans
latio
n of T
inct
oris'
s Lib
er de
Nat
ura e
t Pr
opri
etat
e Ton
orum
, Col
orad
o Col
lege
Mus
ic Pr
ess t
rans
latio
ns, no
. 2 (C
olo-
ra
do Sp
ring
s: C
olor
ado C
olle
ge M
usic
Pres
s, 19
67)p
assim
, use
"m
ingl
ed" a
nd
"mix
ed" f
or th
e Lat
in co
mm
ixta
and m
ixta
in op
posit
e way
s. 9L
ucid
ariu
m, 11
, 4, 2
31-5
0, p
p. 5
09-1
9. N
ote t
hat H
erlin
ger e
mpl
oys t
he
term
"int
erm
edia
tion"
to tr
ansla
te M
arch
etto
's wor
d int
erru
ptio
; agai
n, ho
w-
ever
, I op
t for
the c
ogna
te (c
f. no
te 8
, abo
ve).
"?C
f. Nie
m6l
ler,
"Zu
r Ton
us-L
ehre
," on
the i
mpo
rtan
ce of
the n
otio
n of
co
mm
ixtu
re an
d its
virt
ually
excl
usiv
e use
by I
talia
n the
orist
s (in
clud
ing t
heo-
ri
sts f
rom
the N
orth
base
d in
Ital
y) un
til ca
. 150
0.
ern i
n th
at he
is co
ncer
ned w
ith re
latio
nshi
ps be
twee
n loc
al or
fo
regr
ound
feat
ures
and
glob
al or
bac
kgro
und s
truc
ture
s. In-
de
ed, i
n m
any w
ays,
he a
ppea
rs to
hav
e und
erta
ken m
elod
ic
anal
ysis i
n pa
rt fo
r its
own
sake
rath
er th
an m
erel
y to
clas
sify
and c
odify
the t
radi
tiona
l chan
t mel
odie
s.7
Am
ong t
he m
any n
ovel
ties t
hat M
arch
etto
intr
oduc
es in
the
Luci
dari
um is
the n
otio
n of "
com
mix
ture
."8 A
ccor
ding
to M
ar-
chet
to's
acco
unt,
a giv
en m
elod
y may
be co
nsid
ered
to b
e not
m
erel
y in
a s
ingl
e mod
e, b
ut a
lso to
pas
s thr
ough
, or
to b
e "c
omm
ixed
with
," ot
her m
odes
dur
ing i
ts pr
ogre
ss. M
arch
etto
de
als w
ith th
is id
ea of
com
mix
ture
mos
t ext
ensiv
ely i
n th
e sec
- tio
n on
"in
terr
uptio
ns" a
t the
end
of th
e ele
vent
h boo
k of
the
Luci
dari
um.9
Sinc
e the
conc
ept o
f com
mix
ture
repr
esen
ts su
ch
a ra
dica
l dev
elop
men
t in m
odal
theo
ry, a
nd be
caus
e it w
as in
- co
rpor
ated
into
the w
ork
of la
ter w
rite
rs du
ring
the n
ext t
wo
cent
urie
s,10 I
feel
that
it is
one
of M
arch
etto
's mos
t im
port
ant
7Thi
s is n
ot to
den
y tha
t mod
al cl
assif
icat
ion a
nd th
e mos
t app
ropr
iate
way
to
not
ate i
ndiv
idua
l mel
odie
s are
recu
rren
t conc
erns
for M
arch
etto
. Thr
ough
- ou
t the
Luc
idar
ium
, he g
ener
ates
stru
ctur
es fr
om fo
regr
ound
to b
ackg
roun
d,
as di
scus
sed b
elow
. 8T
hrou
ghou
t this
stud
y "co
mm
ixtu
re" i
s use
d to
tran
slate
the L
atin
term
co
mm
ixtio
. Thi
s usa
ge is
mod
elle
d on
the
prac
tice o
f Pow
ers,
"Mod
e."
Leo
Trei
tler'
s term
"int
erm
ixtu
re" (i
n "T
one S
yste
m in
the S
ecul
ar W
orks
of G
uil-
laum
e D
ufay
," J
ourn
al of
the
Am
eric
an M
usic
olog
ical
Soci
ety
18/2
[196
5]:
131-
69, e
sp. 1
34, n
ote 8
) has
muc
h to
reco
mm
end i
t, bu
t in
the p
rese
nt st
udy,
La
tin ro
ots a
re pr
eser
ved a
s far
as pr
actic
al in
Eng
lish t
rans
latio
ns of
tech
nica
l te
rms i
n or
der t
o fa
cilit
ate r
eadi
ng of
the o
rigi
nal tr
eatis
es. H
erlin
ger,
in op
p.
cit.,
pass
im, a
nd A
lber
t Sea
y in
his t
rans
latio
n of T
inct
oris'
s Lib
er de
Nat
ura e
t Pr
opri
etat
e Ton
orum
, Col
orad
o Col
lege
Mus
ic Pr
ess t
rans
latio
ns, no
. 2 (C
olo-
ra
do Sp
ring
s: C
olor
ado C
olle
ge M
usic
Pres
s, 19
67)p
assim
, use
"m
ingl
ed" a
nd
"mix
ed" f
or th
e Lat
in co
mm
ixta
and m
ixta
in op
posit
e way
s. 9L
ucid
ariu
m, 11
, 4, 2
31-5
0, p
p. 5
09-1
9. N
ote t
hat H
erlin
ger e
mpl
oys t
he
term
"int
erm
edia
tion"
to tr
ansla
te M
arch
etto
's wor
d int
erru
ptio
; agai
n, ho
w-
ever
, I op
t for
the c
ogna
te (c
f. no
te 8
, abo
ve).
"?C
f. Nie
m6l
ler,
"Zu
r Ton
us-L
ehre
," on
the i
mpo
rtan
ce of
the n
otio
n of
co
mm
ixtu
re an
d its
virt
ually
excl
usiv
e use
by I
talia
n the
orist
s (in
clud
ing t
heo-
ri
sts f
rom
the N
orth
base
d in
Ital
y) un
til ca
. 150
0.
ern i
n th
at he
is co
ncer
ned w
ith re
latio
nshi
ps be
twee
n loc
al or
fo
regr
ound
feat
ures
and
glob
al or
bac
kgro
und s
truc
ture
s. In-
de
ed, i
n m
any w
ays,
he a
ppea
rs to
hav
e und
erta
ken m
elod
ic
anal
ysis i
n pa
rt fo
r its
own
sake
rath
er th
an m
erel
y to
clas
sify
and c
odify
the t
radi
tiona
l chan
t mel
odie
s.7
Am
ong t
he m
any n
ovel
ties t
hat M
arch
etto
intr
oduc
es in
the
Luci
dari
um is
the n
otio
n of "
com
mix
ture
."8 A
ccor
ding
to M
ar-
chet
to's
acco
unt,
a giv
en m
elod
y may
be co
nsid
ered
to b
e not
m
erel
y in
a s
ingl
e mod
e, b
ut a
lso to
pas
s thr
ough
, or
to b
e "c
omm
ixed
with
," ot
her m
odes
dur
ing i
ts pr
ogre
ss. M
arch
etto
de
als w
ith th
is id
ea of
com
mix
ture
mos
t ext
ensiv
ely i
n th
e sec
- tio
n on
"in
terr
uptio
ns" a
t the
end
of th
e ele
vent
h boo
k of
the
Luci
dari
um.9
Sinc
e the
conc
ept o
f com
mix
ture
repr
esen
ts su
ch
a ra
dica
l dev
elop
men
t in m
odal
theo
ry, a
nd be
caus
e it w
as in
- co
rpor
ated
into
the w
ork
of la
ter w
rite
rs du
ring
the n
ext t
wo
cent
urie
s,10 I
feel
that
it is
one
of M
arch
etto
's mos
t im
port
ant
7Thi
s is n
ot to
den
y tha
t mod
al cl
assif
icat
ion a
nd th
e mos
t app
ropr
iate
way
to
not
ate i
ndiv
idua
l mel
odie
s are
recu
rren
t conc
erns
for M
arch
etto
. Thr
ough
- ou
t the
Luc
idar
ium
, he g
ener
ates
stru
ctur
es fr
om fo
regr
ound
to b
ackg
roun
d,
as di
scus
sed b
elow
. 8T
hrou
ghou
t this
stud
y "co
mm
ixtu
re" i
s use
d to
tran
slate
the L
atin
term
co
mm
ixtio
. Thi
s usa
ge is
mod
elle
d on
the
prac
tice o
f Pow
ers,
"Mod
e."
Leo
Trei
tler'
s term
"int
erm
ixtu
re" (i
n "T
one S
yste
m in
the S
ecul
ar W
orks
of G
uil-
laum
e D
ufay
," J
ourn
al of
the
Am
eric
an M
usic
olog
ical
Soci
ety
18/2
[196
5]:
131-
69, e
sp. 1
34, n
ote 8
) has
muc
h to
reco
mm
end i
t, bu
t in
the p
rese
nt st
udy,
La
tin ro
ots a
re pr
eser
ved a
s far
as pr
actic
al in
Eng
lish t
rans
latio
ns of
tech
nica
l te
rms i
n or
der t
o fa
cilit
ate r
eadi
ng of
the o
rigi
nal tr
eatis
es. H
erlin
ger,
in op
p.
cit.,
pass
im, a
nd A
lber
t Sea
y in
his t
rans
latio
n of T
inct
oris'
s Lib
er de
Nat
ura e
t Pr
opri
etat
e Ton
orum
, Col
orad
o Col
lege
Mus
ic Pr
ess t
rans
latio
ns, no
. 2 (C
olo-
ra
do Sp
ring
s: C
olor
ado C
olle
ge M
usic
Pres
s, 19
67)p
assim
, use
"m
ingl
ed" a
nd
"mix
ed" f
or th
e Lat
in co
mm
ixta
and m
ixta
in op
posit
e way
s. 9L
ucid
ariu
m, 11
, 4, 2
31-5
0, p
p. 5
09-1
9. N
ote t
hat H
erlin
ger e
mpl
oys t
he
term
"int
erm
edia
tion"
to tr
ansla
te M
arch
etto
's wor
d int
erru
ptio
; agai
n, ho
w-
ever
, I op
t for
the c
ogna
te (c
f. no
te 8
, abo
ve).
"?C
f. Nie
m6l
ler,
"Zu
r Ton
us-L
ehre
," on
the i
mpo
rtan
ce of
the n
otio
n of
co
mm
ixtu
re an
d its
virt
ually
excl
usiv
e use
by I
talia
n the
orist
s (in
clud
ing t
heo-
ri
sts f
rom
the N
orth
base
d in
Ital
y) un
til ca
. 150
0.
ern i
n th
at he
is co
ncer
ned w
ith re
latio
nshi
ps be
twee
n loc
al or
fo
regr
ound
feat
ures
and
glob
al or
bac
kgro
und s
truc
ture
s. In-
de
ed, i
n m
any w
ays,
he a
ppea
rs to
hav
e und
erta
ken m
elod
ic
anal
ysis i
n pa
rt fo
r its
own
sake
rath
er th
an m
erel
y to
clas
sify
and c
odify
the t
radi
tiona
l chan
t mel
odie
s.7
Am
ong t
he m
any n
ovel
ties t
hat M
arch
etto
intr
oduc
es in
the
Luci
dari
um is
the n
otio
n of "
com
mix
ture
."8 A
ccor
ding
to M
ar-
chet
to's
acco
unt,
a giv
en m
elod
y may
be co
nsid
ered
to b
e not
m
erel
y in
a s
ingl
e mod
e, b
ut a
lso to
pas
s thr
ough
, or
to b
e "c
omm
ixed
with
," ot
her m
odes
dur
ing i
ts pr
ogre
ss. M
arch
etto
de
als w
ith th
is id
ea of
com
mix
ture
mos
t ext
ensiv
ely i
n th
e sec
- tio
n on
"in
terr
uptio
ns" a
t the
end
of th
e ele
vent
h boo
k of
the
Luci
dari
um.9
Sinc
e the
conc
ept o
f com
mix
ture
repr
esen
ts su
ch
a ra
dica
l dev
elop
men
t in m
odal
theo
ry, a
nd be
caus
e it w
as in
- co
rpor
ated
into
the w
ork
of la
ter w
rite
rs du
ring
the n
ext t
wo
cent
urie
s,10 I
feel
that
it is
one
of M
arch
etto
's mos
t im
port
ant
7Thi
s is n
ot to
den
y tha
t mod
al cl
assif
icat
ion a
nd th
e mos
t app
ropr
iate
way
to
not
ate i
ndiv
idua
l mel
odie
s are
recu
rren
t conc
erns
for M
arch
etto
. Thr
ough
- ou
t the
Luc
idar
ium
, he g
ener
ates
stru
ctur
es fr
om fo
regr
ound
to b
ackg
roun
d,
as di
scus
sed b
elow
. 8T
hrou
ghou
t this
stud
y "co
mm
ixtu
re" i
s use
d to
tran
slate
the L
atin
term
co
mm
ixtio
. Thi
s usa
ge is
mod
elle
d on
the
prac
tice o
f Pow
ers,
"Mod
e."
Leo
Trei
tler'
s term
"int
erm
ixtu
re" (i
n "T
one S
yste
m in
the S
ecul
ar W
orks
of G
uil-
laum
e D
ufay
," J
ourn
al of
the
Am
eric
an M
usic
olog
ical
Soci
ety
18/2
[196
5]:
131-
69, e
sp. 1
34, n
ote 8
) has
muc
h to
reco
mm
end i
t, bu
t in
the p
rese
nt st
udy,
La
tin ro
ots a
re pr
eser
ved a
s far
as pr
actic
al in
Eng
lish t
rans
latio
ns of
tech
nica
l te
rms i
n or
der t
o fa
cilit
ate r
eadi
ng of
the o
rigi
nal tr
eatis
es. H
erlin
ger,
in op
p.
cit.,
pass
im, a
nd A
lber
t Sea
y in
his t
rans
latio
n of T
inct
oris'
s Lib
er de
Nat
ura e
t Pr
opri
etat
e Ton
orum
, Col
orad
o Col
lege
Mus
ic Pr
ess t
rans
latio
ns, no
. 2 (C
olo-
ra
do Sp
ring
s: C
olor
ado C
olle
ge M
usic
Pres
s, 19
67)p
assim
, use
"m
ingl
ed" a
nd
"mix
ed" f
or th
e Lat
in co
mm
ixta
and m
ixta
in op
posit
e way
s. 9L
ucid
ariu
m, 11
, 4, 2
31-5
0, p
p. 5
09-1
9. N
ote t
hat H
erlin
ger e
mpl
oys t
he
term
"int
erm
edia
tion"
to tr
ansla
te M
arch
etto
's wor
d int
erru
ptio
; agai
n, ho
w-
ever
, I op
t for
the c
ogna
te (c
f. no
te 8
, abo
ve).
"?C
f. Nie
m6l
ler,
"Zu
r Ton
us-L
ehre
," on
the i
mpo
rtan
ce of
the n
otio
n of
co
mm
ixtu
re an
d its
virt
ually
excl
usiv
e use
by I
talia
n the
orist
s (in
clud
ing t
heo-
ri
sts f
rom
the N
orth
base
d in
Ital
y) un
til ca
. 150
0.
ern i
n th
at he
is co
ncer
ned w
ith re
latio
nshi
ps be
twee
n loc
al or
fo
regr
ound
feat
ures
and
glob
al or
bac
kgro
und s
truc
ture
s. In-
de
ed, i
n m
any w
ays,
he a
ppea
rs to
hav
e und
erta
ken m
elod
ic
anal
ysis i
n pa
rt fo
r its
own
sake
rath
er th
an m
erel
y to
clas
sify
and c
odify
the t
radi
tiona
l chan
t mel
odie
s.7
Am
ong t
he m
any n
ovel
ties t
hat M
arch
etto
intr
oduc
es in
the
Luci
dari
um is
the n
otio
n of "
com
mix
ture
."8 A
ccor
ding
to M
ar-
chet
to's
acco
unt,
a giv
en m
elod
y may
be co
nsid
ered
to b
e not
m
erel
y in
a s
ingl
e mod
e, b
ut a
lso to
pas
s thr
ough
, or
to b
e "c
omm
ixed
with
," ot
her m
odes
dur
ing i
ts pr
ogre
ss. M
arch
etto
de
als w
ith th
is id
ea of
com
mix
ture
mos
t ext
ensiv
ely i
n th
e sec
- tio
n on
"in
terr
uptio
ns" a
t the
end
of th
e ele
vent
h boo
k of
the
Luci
dari
um.9
Sinc
e the
conc
ept o
f com
mix
ture
repr
esen
ts su
ch
a ra
dica
l dev
elop
men
t in m
odal
theo
ry, a
nd be
caus
e it w
as in
- co
rpor
ated
into
the w
ork
of la
ter w
rite
rs du
ring
the n
ext t
wo
cent
urie
s,10 I
feel
that
it is
one
of M
arch
etto
's mos
t im
port
ant
7Thi
s is n
ot to
den
y tha
t mod
al cl
assif
icat
ion a
nd th
e mos
t app
ropr
iate
way
to
not
ate i
ndiv
idua
l mel
odie
s are
recu
rren
t conc
erns
for M
arch
etto
. Thr
ough
- ou
t the
Luc
idar
ium
, he g
ener
ates
stru
ctur
es fr
om fo
regr
ound
to b
ackg
roun
d,
as di
scus
sed b
elow
. 8T
hrou
ghou
t this
stud
y "co
mm
ixtu
re" i
s use
d to
tran
slate
the L
atin
term
co
mm
ixtio
. Thi
s usa
ge is
mod
elle
d on
the
prac
tice o
f Pow
ers,
"Mod
e."
Leo
Trei
tler'
s term
"int
erm
ixtu
re" (i
n "T
one S
yste
m in
the S
ecul
ar W
orks
of G
uil-
laum
e D
ufay
," J
ourn
al of
the
Am
eric
an M
usic
olog
ical
Soci
ety
18/2
[196
5]:
131-
69, e
sp. 1
34, n
ote 8
) has
muc
h to
reco
mm
end i
t, bu
t in
the p
rese
nt st
udy,
La
tin ro
ots a
re pr
eser
ved a
s far
as pr
actic
al in
Eng
lish t
rans
latio
ns of
tech
nica
l te
rms i
n or
der t
o fa
cilit
ate r
eadi
ng of
the o
rigi
nal tr
eatis
es. H
erlin
ger,
in op
p.
cit.,
pass
im, a
nd A
lber
t Sea
y in
his t
rans
latio
n of T
inct
oris'
s Lib
er de
Nat
ura e
t Pr
opri
etat
e Ton
orum
, Col
orad
o Col
lege
Mus
ic Pr
ess t
rans
latio
ns, no
. 2 (C
olo-
ra
do Sp
ring
s: C
olor
ado C
olle
ge M
usic
Pres
s, 19
67)p
assim
, use
"m
ingl
ed" a
nd
"mix
ed" f
or th
e Lat
in co
mm
ixta
and m
ixta
in op
posit
e way
s. 9L
ucid
ariu
m, 11
, 4, 2
31-5
0, p
p. 5
09-1
9. N
ote t
hat H
erlin
ger e
mpl
oys t
he
term
"int
erm
edia
tion"
to tr
ansla
te M
arch
etto
's wor
d int
erru
ptio
; agai
n, ho
w-
ever
, I op
t for
the c
ogna
te (c
f. no
te 8
, abo
ve).
"?C
f. Nie
m6l
ler,
"Zu
r Ton
us-L
ehre
," on
the i
mpo
rtan
ce of
the n
otio
n of
co
mm
ixtu
re an
d its
virt
ually
excl
usiv
e use
by I
talia
n the
orist
s (in
clud
ing t
heo-
ri
sts f
rom
the N
orth
base
d in
Ital
y) un
til ca
. 150
0.
ern i
n th
at he
is co
ncer
ned w
ith re
latio
nshi
ps be
twee
n loc
al or
fo
regr
ound
feat
ures
and
glob
al or
bac
kgro
und s
truc
ture
s. In-
de
ed, i
n m
any w
ays,
he a
ppea
rs to
hav
e und
erta
ken m
elod
ic
anal
ysis i
n pa
rt fo
r its
own
sake
rath
er th
an m
erel
y to
clas
sify
and c
odify
the t
radi
tiona
l chan
t mel
odie
s.7
Am
ong t
he m
any n
ovel
ties t
hat M
arch
etto
intr
oduc
es in
the
Luci
dari
um is
the n
otio
n of "
com
mix
ture
."8 A
ccor
ding
to M
ar-
chet
to's
acco
unt,
a giv
en m
elod
y may
be co
nsid
ered
to b
e not
m
erel
y in
a s
ingl
e mod
e, b
ut a
lso to
pas
s thr
ough
, or
to b
e "c
omm
ixed
with
," ot
her m
odes
dur
ing i
ts pr
ogre
ss. M
arch
etto
de
als w
ith th
is id
ea of
com
mix
ture
mos
t ext
ensiv
ely i
n th
e sec
- tio
n on
"in
terr
uptio
ns" a
t the
end
of th
e ele
vent
h boo
k of
the
Luci
dari
um.9
Sinc
e the
conc
ept o
f com
mix
ture
repr
esen
ts su
ch
a ra
dica
l dev
elop
men
t in m
odal
theo
ry, a
nd be
caus
e it w
as in
- co
rpor
ated
into
the w
ork
of la
ter w
rite
rs du
ring
the n
ext t
wo
cent
urie
s,10 I
feel
that
it is
one
of M
arch
etto
's mos
t im
port
ant
7Thi
s is n
ot to
den
y tha
t mod
al cl
assif
icat
ion a
nd th
e mos
t app
ropr
iate
way
to
not
ate i
ndiv
idua
l mel
odie
s are
recu
rren
t conc
erns
for M
arch
etto
. Thr
ough
- ou
t the
Luc
idar
ium
, he g
ener
ates
stru
ctur
es fr
om fo
regr
ound
to b
ackg
roun
d,
as di
scus
sed b
elow
. 8T
hrou
ghou
t this
stud
y "co
mm
ixtu
re" i
s use
d to
tran
slate
the L
atin
term
co
mm
ixtio
. Thi
s usa
ge is
mod
elle
d on
the
prac
tice o
f Pow
ers,
"Mod
e."
Leo
Trei
tler'
s term
"int
erm
ixtu
re" (i
n "T
one S
yste
m in
the S
ecul
ar W
orks
of G
uil-
laum
e D
ufay
," J
ourn
al of
the
Am
eric
an M
usic
olog
ical
Soci
ety
18/2
[196
5]:
131-
69, e
sp. 1
34, n
ote 8
) has
muc
h to
reco
mm
end i
t, bu
t in
the p
rese
nt st
udy,
La
tin ro
ots a
re pr
eser
ved a
s far
as pr
actic
al in
Eng
lish t
rans
latio
ns of
tech
nica
l te
rms i
n or
der t
o fa
cilit
ate r
eadi
ng of
the o
rigi
nal tr
eatis
es. H
erlin
ger,
in op
p.
cit.,
pass
im, a
nd A
lber
t Sea
y in
his t
rans
latio
n of T
inct
oris'
s Lib
er de
Nat
ura e
t Pr
opri
etat
e Ton
orum
, Col
orad
o Col
lege
Mus
ic Pr
ess t
rans
latio
ns, no
. 2 (C
olo-
ra
do Sp
ring
s: C
olor
ado C
olle
ge M
usic
Pres
s, 19
67)p
assim
, use
"m
ingl
ed" a
nd
"mix
ed" f
or th
e Lat
in co
mm
ixta
and m
ixta
in op
posit
e way
s. 9L
ucid
ariu
m, 11
, 4, 2
31-5
0, p
p. 5
09-1
9. N
ote t
hat H
erlin
ger e
mpl
oys t
he
term
"int
erm
edia
tion"
to tr
ansla
te M
arch
etto
's wor
d int
erru
ptio
; agai
n, ho
w-
ever
, I op
t for
the c
ogna
te (c
f. no
te 8
, abo
ve).
"?C
f. Nie
m6l
ler,
"Zu
r Ton
us-L
ehre
," on
the i
mpo
rtan
ce of
the n
otio
n of
co
mm
ixtu
re an
d its
virt
ually
excl
usiv
e use
by I
talia
n the
orist
s (in
clud
ing t
heo-
ri
sts f
rom
the N
orth
base
d in
Ital
y) un
til ca
. 150
0.
cont
ribu
tions
to t
he f
orm
ulat
ion
of m
odal
ity. A
ccor
ding
ly,
muc
h of t
his s
tudy
is d
evot
ed to
the
notio
n of
com
mix
ture
as
pres
ente
d by M
arch
etto
, par
ticul
arly
as he
appl
ies it
in th
e sec
- tio
n on
inte
rrup
tions
in th
e Luc
idar
ium
. In or
der t
o und
erst
and
this
part
of th
e tre
atise
, how
ever
, I fe
el th
at on
e m
ust d
efin
e tw
o typ
es of
not
es: s
peci
al no
tes i
n a m
elod
ic pr
ogre
ssio
n, an
d or
ient
ing n
otes
in a
give
n mod
e.
Spec
ial a
nd O
rien
ting N
otes
One
shou
ld ob
serv
e at t
he ou
tset
of th
is disc
ussio
n tha
t Mar
- ch
etto
at n
o po
int u
ses t
he te
rms s
peci
al or
ori
entin
g or e
ven
rem
ote s
ynon
yms fo
r the
se w
ords
. Nev
erth
eles
s, I b
elie
ve th
at
the c
once
pts w
hich
can b
e con
veye
d by a
n ade
quat
e def
initi
on
of sp
ecia
l and
orie
ntin
g not
es a
re im
plic
it in
his a
ccou
nt, a
nd
inde
ed, th
at on
e can
not b
egin
to u
nder
stan
d Mar
chet
to's t
reat
- m
ent o
f com
mix
ture
with
out r
ecou
rse t
o suc
h ide
as.
I wou
ld d
efin
e spe
cial
not
es a
s one
s tha
t (a)
lie
at th
e ex-
tr
emes
of
dire
ct u
pwar
d or
dow
nwar
d mel
odic
pro
gres
sions
an
d/or
(b) a
re m
embe
rs of
a le
ap. T
he n
otes
D3,
A3,
and
D3
that
are m
arke
d by x
's in
Exa
mpl
e 1 ar
e spe
cial
by vi
rtue
of b
e-
Exam
ple 1
. Dir
ect u
pwar
d and
dow
nwar
d pro
gres
sions
(afte
r Lu
cida
rium
, 11, 4
, 231
, pp.
508-
09).
Extr
emes
are m
arke
d x.
dP-,,
- .
, N
11
x
x x
upw
ard
dow
nwar
d pr
ogre
ssio
n pr
ogre
ssio
n
ing t
he ex
trem
es (i.
e., a
t the
top
or bo
ttom
) of t
he up
war
d pro
- gr
essio
n fro
m D
3 to
A3
or o
f the
dow
nwar
d pro
gres
sion f
rom
A
3 to
D3.
The
not
es m
arke
d by y
's in
Exa
mpl
e 2 ar
e spe
cial
by
virt
ue of
thei
r bel
ongi
ng to
the l
eaps
from
E3 t
o A
3, a
nd fr
om
A3
to D
3.
This
idea
of sp
ecia
l not
es de
fines
wha
t I be
lieve
cert
ain m
od-
ern w
rite
rs on
com
mix
ture
mea
n whe
n the
y say
that
a giv
en m
e-
cont
ribu
tions
to t
he f
orm
ulat
ion
of m
odal
ity. A
ccor
ding
ly,
muc
h of t
his s
tudy
is d
evot
ed to
the
notio
n of
com
mix
ture
as
pres
ente
d by M
arch
etto
, par
ticul
arly
as he
appl
ies it
in th
e sec
- tio
n on
inte
rrup
tions
in th
e Luc
idar
ium
. In or
der t
o und
erst
and
this
part
of th
e tre
atise
, how
ever
, I fe
el th
at on
e m
ust d
efin
e tw
o typ
es of
not
es: s
peci
al no
tes i
n a m
elod
ic pr
ogre
ssio
n, an
d or
ient
ing n
otes
in a
give
n mod
e.
Spec
ial a
nd O
rien
ting N
otes
One
shou
ld ob
serv
e at t
he ou
tset
of th
is disc
ussio
n tha
t Mar
- ch
etto
at n
o po
int u
ses t
he te
rms s
peci
al or
ori
entin
g or e
ven
rem
ote s
ynon
yms fo
r the
se w
ords
. Nev
erth
eles
s, I b
elie
ve th
at
the c
once
pts w
hich
can b
e con
veye
d by a
n ade
quat
e def
initi
on
of sp
ecia
l and
orie
ntin
g not
es a
re im
plic
it in
his a
ccou
nt, a
nd
inde
ed, th
at on
e can
not b
egin
to u
nder
stan
d Mar
chet
to's t
reat
- m
ent o
f com
mix
ture
with
out r
ecou
rse t
o suc
h ide
as.
I wou
ld d
efin
e spe
cial
not
es a
s one
s tha
t (a)
lie
at th
e ex-
tr
emes
of
dire
ct u
pwar
d or
dow
nwar
d mel
odic
pro
gres
sions
an
d/or
(b) a
re m
embe
rs of
a le
ap. T
he n
otes
D3,
A3,
and
D3
that
are m
arke
d by x
's in
Exa
mpl
e 1 ar
e spe
cial
by vi
rtue
of b
e-
Exam
ple 1
. Dir
ect u
pwar
d and
dow
nwar
d pro
gres
sions
(afte
r Lu
cida
rium
, 11, 4
, 231
, pp.
508-
09).
Extr
emes
are m
arke
d x.
dP-,,
- .
, N
11
x
x x
upw
ard
dow
nwar
d pr
ogre
ssio
n pr
ogre
ssio
n
ing t
he ex
trem
es (i.
e., a
t the
top
or bo
ttom
) of t
he up
war
d pro
- gr
essio
n fro
m D
3 to
A3
or o
f the
dow
nwar
d pro
gres
sion f
rom
A
3 to
D3.
The
not
es m
arke
d by y
's in
Exa
mpl
e 2 ar
e spe
cial
by
virt
ue of
thei
r bel
ongi
ng to
the l
eaps
from
E3 t
o A
3, a
nd fr
om
A3
to D
3.
This
idea
of sp
ecia
l not
es de
fines
wha
t I be
lieve
cert
ain m
od-
ern w
rite
rs on
com
mix
ture
mea
n whe
n the
y say
that
a giv
en m
e-
cont
ribu
tions
to t
he f
orm
ulat
ion
of m
odal
ity. A
ccor
ding
ly,
muc
h of t
his s
tudy
is d
evot
ed to
the
notio
n of
com
mix
ture
as
pres
ente
d by M
arch
etto
, par
ticul
arly
as he
appl
ies it
in th
e sec
- tio
n on
inte
rrup
tions
in th
e Luc
idar
ium
. In or
der t
o und
erst
and
this
part
of th
e tre
atise
, how
ever
, I fe
el th
at on
e m
ust d
efin
e tw
o typ
es of
not
es: s
peci
al no
tes i
n a m
elod
ic pr
ogre
ssio
n, an
d or
ient
ing n
otes
in a
give
n mod
e.
Spec
ial a
nd O
rien
ting N
otes
One
shou
ld ob
serv
e at t
he ou
tset
of th
is disc
ussio
n tha
t Mar
- ch
etto
at n
o po
int u
ses t
he te
rms s
peci
al or
ori
entin
g or e
ven
rem
ote s
ynon
yms fo
r the
se w
ords
. Nev
erth
eles
s, I b
elie
ve th
at
the c
once
pts w
hich
can b
e con
veye
d by a
n ade
quat
e def
initi
on
of sp
ecia
l and
orie
ntin
g not
es a
re im
plic
it in
his a
ccou
nt, a
nd
inde
ed, th
at on
e can
not b
egin
to u
nder
stan
d Mar
chet
to's t
reat
- m
ent o
f com
mix
ture
with
out r
ecou
rse t
o suc
h ide
as.
I wou
ld d
efin
e spe
cial
not
es a
s one
s tha
t (a)
lie
at th
e ex-
tr
emes
of
dire
ct u
pwar
d or
dow
nwar
d mel
odic
pro
gres
sions
an
d/or
(b) a
re m
embe
rs of
a le
ap. T
he n
otes
D3,
A3,
and
D3
that
are m
arke
d by x
's in
Exa
mpl
e 1 ar
e spe
cial
by vi
rtue
of b
e-
Exam
ple 1
. Dir
ect u
pwar
d and
dow
nwar
d pro
gres
sions
(afte
r Lu
cida
rium
, 11, 4
, 231
, pp.
508-
09).
Extr
emes
are m
arke
d x.
dP-,,
- .
, N
11
x
x x
upw
ard
dow
nwar
d pr
ogre
ssio
n pr
ogre
ssio
n
ing t
he ex
trem
es (i.
e., a
t the
top
or bo
ttom
) of t
he up
war
d pro
- gr
essio
n fro
m D
3 to
A3
or o
f the
dow
nwar
d pro
gres
sion f
rom
A
3 to
D3.
The
not
es m
arke
d by y
's in
Exa
mpl
e 2 ar
e spe
cial
by
virt
ue of
thei
r bel
ongi
ng to
the l
eaps
from
E3 t
o A
3, a
nd fr
om
A3
to D
3.
This
idea
of sp
ecia
l not
es de
fines
wha
t I be
lieve
cert
ain m
od-
ern w
rite
rs on
com
mix
ture
mea
n whe
n the
y say
that
a giv
en m
e-
cont
ribu
tions
to t
he f
orm
ulat
ion
of m
odal
ity. A
ccor
ding
ly,
muc
h of t
his s
tudy
is d
evot
ed to
the
notio
n of
com
mix
ture
as
pres
ente
d by M
arch
etto
, par
ticul
arly
as he
appl
ies it
in th
e sec
- tio
n on
inte
rrup
tions
in th
e Luc
idar
ium
. In or
der t
o und
erst
and
this
part
of th
e tre
atise
, how
ever
, I fe
el th
at on
e m
ust d
efin
e tw
o typ
es of
not
es: s
peci
al no
tes i
n a m
elod
ic pr
ogre
ssio
n, an
d or
ient
ing n
otes
in a
give
n mod
e.
Spec
ial a
nd O
rien
ting N
otes
One
shou
ld ob
serv
e at t
he ou
tset
of th
is disc
ussio
n tha
t Mar
- ch
etto
at n
o po
int u
ses t
he te
rms s
peci
al or
ori
entin
g or e
ven
rem
ote s
ynon
yms fo
r the
se w
ords
. Nev
erth
eles
s, I b
elie
ve th
at
the c
once
pts w
hich
can b
e con
veye
d by a
n ade
quat
e def
initi
on
of sp
ecia
l and
orie
ntin
g not
es a
re im
plic
it in
his a
ccou
nt, a
nd
inde
ed, th
at on
e can
not b
egin
to u
nder
stan
d Mar
chet
to's t
reat
- m
ent o
f com
mix
ture
with
out r
ecou
rse t
o suc
h ide
as.
I wou
ld d
efin
e spe
cial
not
es a
s one
s tha
t (a)
lie
at th
e ex-
tr
emes
of
dire
ct u
pwar
d or
dow
nwar
d mel
odic
pro
gres
sions
an
d/or
(b) a
re m
embe
rs of
a le
ap. T
he n
otes
D3,
A3,
and
D3
that
are m
arke
d by x
's in
Exa
mpl
e 1 ar
e spe
cial
by vi
rtue
of b
e-
Exam
ple 1
. Dir
ect u
pwar
d and
dow
nwar
d pro
gres
sions
(afte
r Lu
cida
rium
, 11, 4
, 231
, pp.
508-
09).
Extr
emes
are m
arke
d x.
dP-,,
- .
, N
11
x
x x
upw
ard
dow
nwar
d pr
ogre
ssio
n pr
ogre
ssio
n
ing t
he ex
trem
es (i.
e., a
t the
top
or bo
ttom
) of t
he up
war
d pro
- gr
essio
n fro
m D
3 to
A3
or o
f the
dow
nwar
d pro
gres
sion f
rom
A
3 to
D3.
The
not
es m
arke
d by y
's in
Exa
mpl
e 2 ar
e spe
cial
by
virt
ue of
thei
r bel
ongi
ng to
the l
eaps
from
E3 t
o A
3, a
nd fr
om
A3
to D
3.
This
idea
of sp
ecia
l not
es de
fines
wha
t I be
lieve
cert
ain m
od-
ern w
rite
rs on
com
mix
ture
mea
n whe
n the
y say
that
a giv
en m
e-
cont
ribu
tions
to t
he f
orm
ulat
ion
of m
odal
ity. A
ccor
ding
ly,
muc
h of t
his s
tudy
is d
evot
ed to
the
notio
n of
com
mix
ture
as
pres
ente
d by M
arch
etto
, par
ticul
arly
as he
appl
ies it
in th
e sec
- tio
n on
inte
rrup
tions
in th
e Luc
idar
ium
. In or
der t
o und
erst
and
this
part
of th
e tre
atise
, how
ever
, I fe
el th
at on
e m
ust d
efin
e tw
o typ
es of
not
es: s
peci
al no
tes i
n a m
elod
ic pr
ogre
ssio
n, an
d or
ient
ing n
otes
in a
give
n mod
e.
Spec
ial a
nd O
rien
ting N
otes
One
shou
ld ob
serv
e at t
he ou
tset
of th
is disc
ussio
n tha
t Mar
- ch
etto
at n
o po
int u
ses t
he te
rms s
peci
al or
ori
entin
g or e
ven
rem
ote s
ynon
yms fo
r the
se w
ords
. Nev
erth
eles
s, I b
elie
ve th
at
the c
once
pts w
hich
can b
e con
veye
d by a
n ade
quat
e def
initi
on
of sp
ecia
l and
orie
ntin
g not
es a
re im
plic
it in
his a
ccou
nt, a
nd
inde
ed, th
at on
e can
not b
egin
to u
nder
stan
d Mar
chet
to's t
reat
- m
ent o
f com
mix
ture
with
out r
ecou
rse t
o suc
h ide
as.
I wou
ld d
efin
e spe
cial
not
es a
s one
s tha
t (a)
lie
at th
e ex-
tr
emes
of
dire
ct u
pwar
d or
dow
nwar
d mel
odic
pro
gres
sions
an
d/or
(b) a
re m
embe
rs of
a le
ap. T
he n
otes
D3,
A3,
and
D3
that
are m
arke
d by x
's in
Exa
mpl
e 1 ar
e spe
cial
by vi
rtue
of b
e-
Exam
ple 1
. Dir
ect u
pwar
d and
dow
nwar
d pro
gres
sions
(afte
r Lu
cida
rium
, 11, 4
, 231
, pp.
508-
09).
Extr
emes
are m
arke
d x.
dP-,,
- .
, N
11
x
x x
upw
ard
dow
nwar
d pr
ogre
ssio
n pr
ogre
ssio
n
ing t
he ex
trem
es (i.
e., a
t the
top
or bo
ttom
) of t
he up
war
d pro
- gr
essio
n fro
m D
3 to
A3
or o
f the
dow
nwar
d pro
gres
sion f
rom
A
3 to
D3.
The
not
es m
arke
d by y
's in
Exa
mpl
e 2 ar
e spe
cial
by
virt
ue of
thei
r bel
ongi
ng to
the l
eaps
from
E3 t
o A
3, a
nd fr
om
A3
to D
3.
This
idea
of sp
ecia
l not
es de
fines
wha
t I be
lieve
cert
ain m
od-
ern w
rite
rs on
com
mix
ture
mea
n whe
n the
y say
that
a giv
en m
e-
cont
ribu
tions
to t
he f
orm
ulat
ion
of m
odal
ity. A
ccor
ding
ly,
muc
h of t
his s
tudy
is d
evot
ed to
the
notio
n of
com
mix
ture
as
pres
ente
d by M
arch
etto
, par
ticul
arly
as he
appl
ies it
in th
e sec
- tio
n on
inte
rrup
tions
in th
e Luc
idar
ium
. In or
der t
o und
erst
and
this
part
of th
e tre
atise
, how
ever
, I fe
el th
at on
e m
ust d
efin
e tw
o typ
es of
not
es: s
peci
al no
tes i
n a m
elod
ic pr
ogre
ssio
n, an
d or
ient
ing n
otes
in a
give
n mod
e.
Spec
ial a
nd O
rien
ting N
otes
One
shou
ld ob
serv
e at t
he ou
tset
of th
is disc
ussio
n tha
t Mar
- ch
etto
at n
o po
int u
ses t
he te
rms s
peci
al or
ori
entin
g or e
ven
rem
ote s
ynon
yms fo
r the
se w
ords
. Nev
erth
eles
s, I b
elie
ve th
at
the c
once
pts w
hich
can b
e con
veye
d by a
n ade
quat
e def
initi
on
of sp
ecia
l and
orie
ntin
g not
es a
re im
plic
it in
his a
ccou
nt, a
nd
inde
ed, th
at on
e can
not b
egin
to u
nder
stan
d Mar
chet
to's t
reat
- m
ent o
f com
mix
ture
with
out r
ecou
rse t
o suc
h ide
as.
I wou
ld d
efin
e spe
cial
not
es a
s one
s tha
t (a)
lie
at th
e ex-
tr
emes
of
dire
ct u
pwar
d or
dow
nwar
d mel
odic
pro
gres
sions
an
d/or
(b) a
re m
embe
rs of
a le
ap. T
he n
otes
D3,
A3,
and
D3
that
are m
arke
d by x
's in
Exa
mpl
e 1 ar
e spe
cial
by vi
rtue
of b
e-
Exam
ple 1
. Dir
ect u
pwar
d and
dow
nwar
d pro
gres
sions
(afte
r Lu
cida
rium
, 11, 4
, 231
, pp.
508-
09).
Extr
emes
are m
arke
d x.
dP-,,
- .
, N
11
x
x x
upw
ard
dow
nwar
d pr
ogre
ssio
n pr
ogre
ssio
n
ing t
he ex
trem
es (i.
e., a
t the
top
or bo
ttom
) of t
he up
war
d pro
- gr
essio
n fro
m D
3 to
A3
or o
f the
dow
nwar
d pro
gres
sion f
rom
A
3 to
D3.
The
not
es m
arke
d by y
's in
Exa
mpl
e 2 ar
e spe
cial
by
virt
ue of
thei
r bel
ongi
ng to
the l
eaps
from
E3 t
o A
3, a
nd fr
om
A3
to D
3.
This
idea
of sp
ecia
l not
es de
fines
wha
t I be
lieve
cert
ain m
od-
ern w
rite
rs on
com
mix
ture
mea
n whe
n the
y say
that
a giv
en m
e-
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
120
Mus
ic Th
eory
Spec
trum
12
0 M
usic
Theo
ry Sp
ectr
um
120
Mus
ic Th
eory
Spec
trum
12
0 M
usic
Theo
ry Sp
ectr
um
120
Mus
ic Th
eory
Spec
trum
12
0 M
usic
Theo
ry Sp
ectr
um
Exam
ple 2
. Mel
odic
prog
ress
ion in
volv
ing l
eaps
(afte
r Luc
ida-
ri
um, 1
1, 4,
233
, pp.
510-
11).
Her
e and
in fo
llow
ing e
xam
ples
, m
embe
rs of
leap
s are
mar
ked y
and
extr
emes
x.
y y
y x
x x
x x
x x
lodi
c pro
gres
sion "
emph
asise
s" or
"out
lines
" giv
en in
terv
als;
l1
inde
ed, o
ne co
uld s
ay th
at D
3-A
3 an
d A3-
D3
are o
utlin
ed in
Ex
ampl
e 1, a
nd D
3-A
3,
A3-
E3,
E3-A
3,
A3-
F3,
A3-
E3,
E3-G
3, a
nd G
3-E3
are
outli
ned i
n Exa
mpl
e 2. H
owev
er, I
do
not b
elie
ve th
at th
e not
ion o
f an i
nter
val be
ing o
utlin
ed sh
ould
be
carr
ied t
oo fa
r if o
ne h
opes
to u
nder
stan
d Mar
chet
to's a
c-
coun
t fully
. Rat
her o
ne m
ust fo
cus p
rim
arily
on th
e ide
a of i
ndi-
vidu
al no
tes b
eing
spec
ial, a
nd on
ly se
cond
arily
on th
e ide
a of
two s
uch n
otes
form
ing t
he ou
tline
of a
n int
erva
l.12
Impl
icit i
n M
arch
etto
's ver
sion o
f mod
al th
eory
is th
e ide
a th
at ea
ch m
ode h
as or
ient
ing n
otes
. Aga
in on
e sho
uld o
bser
ve
that
Mar
chet
to do
es no
t use
the p
hras
e ori
entin
g not
e or e
ven
a re
mot
e syn
onym
ther
eof.
Inst
ead,
the
conc
ept o
r ide
a of
ori
- en
ting n
otes
is im
plic
it in
his d
iscus
sion.
Com
mon
to a
ll th
e m
odes
in M
arch
etto
's acc
ount
is a
set o
f pitc
h cl
asse
s cor
res-
po
ndin
g to
the
"whi
te-n
ote"
or d
iato
nic c
olle
ctio
n, w
ith th
e tr
aditi
onal
poss
ibili
ty th
at Bl
mig
ht su
bstit
ute fo
r B-n
atur
al un
- de
r cer
tain
circ
umst
ance
s.13 Be
yond
this
com
mon
basis
for a
ll
"See
, for
exam
ple,
Pet
er B
ergq
uist
, "M
ode a
nd P
olyp
hony
arou
nd 15
00:
Theo
ry an
d Pra
ctic
e," M
usic
Foru
m 1 (
1967
): 10
3.
'2Th
is is n
ot to
den
y tha
t tw
o sp
ecia
l not
es a
four
th or
fifth
apar
t impl
y a
give
n mod
e mor
e str
ongl
y tha
n a si
ngle
spec
ial n
ote i
n iso
latio
n. O
n th
is po
int
see c
rite
rion
3 bel
ow.
'3A
lthou
gh M
arch
etto
is ju
stly
fam
ous f
or h
is de
taile
d tr
eatm
ent o
f chr
o-
mat
icism
earl
ier o
n in t
he L
ucid
ariu
m (see
Jan W
. Her
linge
r, "M
arch
etto
's Di-
visio
n of t
he W
hole
Ton
e," M
usic
The
ory S
pect
rum
3 [19
81]: 7
4-83
), he
show
s hi
mse
lf to b
e disi
nclin
ed to
adm
it ext
ensio
ns of
the m
odal
syst
em be
yond
B b i
n th
e lat
er po
rtio
ns of
the w
ork w
hich
are t
he fo
cus o
f thi
s disc
ussio
n. Se
e, fo
r ex
ampl
e, hi
s avo
idan
ce of
Eb a
nd F#
in L
ucid
ariu
m, 11
, 4, 3
2, p
p. 40
6-07
, and
11
,4, 3
7-45
, pp.
410-
15, r
espe
ctiv
ely.
The r
ecog
nitio
n of B
t in a
dditi
on to
the
Exam
ple 2
. Mel
odic
prog
ress
ion in
volv
ing l
eaps
(afte
r Luc
ida-
ri
um, 1
1, 4,
233
, pp.
510-
11).
Her
e and
in fo
llow
ing e
xam
ples
, m
embe
rs of
leap
s are
mar
ked y
and
extr
emes
x.
y y
y x
x x
x x
x x
lodi
c pro
gres
sion "
emph
asise
s" or
"out
lines
" giv
en in
terv
als;
l1
inde
ed, o
ne co
uld s
ay th
at D
3-A
3 an
d A3-
D3
are o
utlin
ed in
Ex
ampl
e 1, a
nd D
3-A
3,
A3-
E3,
E3-A
3,
A3-
F3,
A3-
E3,
E3-G
3, a
nd G
3-E3
are
outli
ned i
n Exa
mpl
e 2. H
owev
er, I
do
not b
elie
ve th
at th
e not
ion o
f an i
nter
val be
ing o
utlin
ed sh
ould
be
carr
ied t
oo fa
r if o
ne h
opes
to u
nder
stan
d Mar
chet
to's a
c-
coun
t fully
. Rat
her o
ne m
ust fo
cus p
rim
arily
on th
e ide
a of i
ndi-
vidu
al no
tes b
eing
spec
ial, a
nd on
ly se
cond
arily
on th
e ide
a of
two s
uch n
otes
form
ing t
he ou
tline
of a
n int
erva
l.12
Impl
icit i
n M
arch
etto
's ver
sion o
f mod
al th
eory
is th
e ide
a th
at ea
ch m
ode h
as or
ient
ing n
otes
. Aga
in on
e sho
uld o
bser
ve
that
Mar
chet
to do
es no
t use
the p
hras
e ori
entin
g not
e or e
ven
a re
mot
e syn
onym
ther
eof.
Inst
ead,
the
conc
ept o
r ide
a of
ori
- en
ting n
otes
is im
plic
it in
his d
iscus
sion.
Com
mon
to a
ll th
e m
odes
in M
arch
etto
's acc
ount
is a
set o
f pitc
h cl
asse
s cor
res-
po
ndin
g to
the
"whi
te-n
ote"
or d
iato
nic c
olle
ctio
n, w
ith th
e tr
aditi
onal
poss
ibili
ty th
at Bl
mig
ht su
bstit
ute fo
r B-n
atur
al un
- de
r cer
tain
circ
umst
ance
s.13 Be
yond
this
com
mon
basis
for a
ll
"See
, for
exam
ple,
Pet
er B
ergq
uist
, "M
ode a
nd P
olyp
hony
arou
nd 15
00:
Theo
ry an
d Pra
ctic
e," M
usic
Foru
m 1 (
1967
): 10
3.
'2Th
is is n
ot to
den
y tha
t tw
o sp
ecia
l not
es a
four
th or
fifth
apar
t impl
y a
give
n mod
e mor
e str
ongl
y tha
n a si
ngle
spec
ial n
ote i
n iso
latio
n. O
n th
is po
int
see c
rite
rion
3 bel
ow.
'3A
lthou
gh M
arch
etto
is ju
stly
fam
ous f
or h
is de
taile
d tr
eatm
ent o
f chr
o-
mat
icism
earl
ier o
n in t
he L
ucid
ariu
m (see
Jan W
. Her
linge
r, "M
arch
etto
's Di-
visio
n of t
he W
hole
Ton
e," M
usic
The
ory S
pect
rum
3 [19
81]: 7
4-83
), he
show
s hi
mse
lf to b
e disi
nclin
ed to
adm
it ext
ensio
ns of
the m
odal
syst
em be
yond
B b i
n th
e lat
er po
rtio
ns of
the w
ork w
hich
are t
he fo
cus o
f thi
s disc
ussio
n. Se
e, fo
r ex
ampl
e, hi
s avo
idan
ce of
Eb a
nd F#
in L
ucid
ariu
m, 11
, 4, 3
2, p
p. 40
6-07
, and
11
,4, 3
7-45
, pp.
410-
15, r
espe
ctiv
ely.
The r
ecog
nitio
n of B
t in a
dditi
on to
the
Exam
ple 2
. Mel
odic
prog
ress
ion in
volv
ing l
eaps
(afte
r Luc
ida-
ri
um, 1
1, 4,
233
, pp.
510-
11).
Her
e and
in fo
llow
ing e
xam
ples
, m
embe
rs of
leap
s are
mar
ked y
and
extr
emes
x.
y y
y x
x x
x x
x x
lodi
c pro
gres
sion "
emph
asise
s" or
"out
lines
" giv
en in
terv
als;
l1
inde
ed, o
ne co
uld s
ay th
at D
3-A
3 an
d A3-
D3
are o
utlin
ed in
Ex
ampl
e 1, a
nd D
3-A
3,
A3-
E3,
E3-A
3,
A3-
F3,
A3-
E3,
E3-G
3, a
nd G
3-E3
are
outli
ned i
n Exa
mpl
e 2. H
owev
er, I
do
not b
elie
ve th
at th
e not
ion o
f an i
nter
val be
ing o
utlin
ed sh
ould
be
carr
ied t
oo fa
r if o
ne h
opes
to u
nder
stan
d Mar
chet
to's a
c-
coun
t fully
. Rat
her o
ne m
ust fo
cus p
rim
arily
on th
e ide
a of i
ndi-
vidu
al no
tes b
eing
spec
ial, a
nd on
ly se
cond
arily
on th
e ide
a of
two s
uch n
otes
form
ing t
he ou
tline
of a
n int
erva
l.12
Impl
icit i
n M
arch
etto
's ver
sion o
f mod
al th
eory
is th
e ide
a th
at ea
ch m
ode h
as or
ient
ing n
otes
. Aga
in on
e sho
uld o
bser
ve
that
Mar
chet
to do
es no
t use
the p
hras
e ori
entin
g not
e or e
ven
a re
mot
e syn
onym
ther
eof.
Inst
ead,
the
conc
ept o
r ide
a of
ori
- en
ting n
otes
is im
plic
it in
his d
iscus
sion.
Com
mon
to a
ll th
e m
odes
in M
arch
etto
's acc
ount
is a
set o
f pitc
h cl
asse
s cor
res-
po
ndin
g to
the
"whi
te-n
ote"
or d
iato
nic c
olle
ctio
n, w
ith th
e tr
aditi
onal
poss
ibili
ty th
at Bl
mig
ht su
bstit
ute fo
r B-n
atur
al un
- de
r cer
tain
circ
umst
ance
s.13 Be
yond
this
com
mon
basis
for a
ll
"See
, for
exam
ple,
Pet
er B
ergq
uist
, "M
ode a
nd P
olyp
hony
arou
nd 15
00:
Theo
ry an
d Pra
ctic
e," M
usic
Foru
m 1 (
1967
): 10
3.
'2Th
is is n
ot to
den
y tha
t tw
o sp
ecia
l not
es a
four
th or
fifth
apar
t impl
y a
give
n mod
e mor
e str
ongl
y tha
n a si
ngle
spec
ial n
ote i
n iso
latio
n. O
n th
is po
int
see c
rite
rion
3 bel
ow.
'3A
lthou
gh M
arch
etto
is ju
stly
fam
ous f
or h
is de
taile
d tr
eatm
ent o
f chr
o-
mat
icism
earl
ier o
n in t
he L
ucid
ariu
m (see
Jan W
. Her
linge
r, "M
arch
etto
's Di-
visio
n of t
he W
hole
Ton
e," M
usic
The
ory S
pect
rum
3 [19
81]: 7
4-83
), he
show
s hi
mse
lf to b
e disi
nclin
ed to
adm
it ext
ensio
ns of
the m
odal
syst
em be
yond
B b i
n th
e lat
er po
rtio
ns of
the w
ork w
hich
are t
he fo
cus o
f thi
s disc
ussio
n. Se
e, fo
r ex
ampl
e, hi
s avo
idan
ce of
Eb a
nd F#
in L
ucid
ariu
m, 11
, 4, 3
2, p
p. 40
6-07
, and
11
,4, 3
7-45
, pp.
410-
15, r
espe
ctiv
ely.
The r
ecog
nitio
n of B
t in a
dditi
on to
the
Exam
ple 2
. Mel
odic
prog
ress
ion in
volv
ing l
eaps
(afte
r Luc
ida-
ri
um, 1
1, 4,
233
, pp.
510-
11).
Her
e and
in fo
llow
ing e
xam
ples
, m
embe
rs of
leap
s are
mar
ked y
and
extr
emes
x.
y y
y x
x x
x x
x x
lodi
c pro
gres
sion "
emph
asise
s" or
"out
lines
" giv
en in
terv
als;
l1
inde
ed, o
ne co
uld s
ay th
at D
3-A
3 an
d A3-
D3
are o
utlin
ed in
Ex
ampl
e 1, a
nd D
3-A
3,
A3-
E3,
E3-A
3,
A3-
F3,
A3-
E3,
E3-G
3, a
nd G
3-E3
are
outli
ned i
n Exa
mpl
e 2. H
owev
er, I
do
not b
elie
ve th
at th
e not
ion o
f an i
nter
val be
ing o
utlin
ed sh
ould
be
carr
ied t
oo fa
r if o
ne h
opes
to u
nder
stan
d Mar
chet
to's a
c-
coun
t fully
. Rat
her o
ne m
ust fo
cus p
rim
arily
on th
e ide
a of i
ndi-
vidu
al no
tes b
eing
spec
ial, a
nd on
ly se
cond
arily
on th
e ide
a of
two s
uch n
otes
form
ing t
he ou
tline
of a
n int
erva
l.12
Impl
icit i
n M
arch
etto
's ver
sion o
f mod
al th
eory
is th
e ide
a th
at ea
ch m
ode h
as or
ient
ing n
otes
. Aga
in on
e sho
uld o
bser
ve
that
Mar
chet
to do
es no
t use
the p
hras
e ori
entin
g not
e or e
ven
a re
mot
e syn
onym
ther
eof.
Inst
ead,
the
conc
ept o
r ide
a of
ori
- en
ting n
otes
is im
plic
it in
his d
iscus
sion.
Com
mon
to a
ll th
e m
odes
in M
arch
etto
's acc
ount
is a
set o
f pitc
h cl
asse
s cor
res-
po
ndin
g to
the
"whi
te-n
ote"
or d
iato
nic c
olle
ctio
n, w
ith th
e tr
aditi
onal
poss
ibili
ty th
at Bl
mig
ht su
bstit
ute fo
r B-n
atur
al un
- de
r cer
tain
circ
umst
ance
s.13 Be
yond
this
com
mon
basis
for a
ll
"See
, for
exam
ple,
Pet
er B
ergq
uist
, "M
ode a
nd P
olyp
hony
arou
nd 15
00:
Theo
ry an
d Pra
ctic
e," M
usic
Foru
m 1 (
1967
): 10
3.
'2Th
is is n
ot to
den
y tha
t tw
o sp
ecia
l not
es a
four
th or
fifth
apar
t impl
y a
give
n mod
e mor
e str
ongl
y tha
n a si
ngle
spec
ial n
ote i
n iso
latio
n. O
n th
is po
int
see c
rite
rion
3 bel
ow.
'3A
lthou
gh M
arch
etto
is ju
stly
fam
ous f
or h
is de
taile
d tr
eatm
ent o
f chr
o-
mat
icism
earl
ier o
n in t
he L
ucid
ariu
m (see
Jan W
. Her
linge
r, "M
arch
etto
's Di-
visio
n of t
he W
hole
Ton
e," M
usic
The
ory S
pect
rum
3 [19
81]: 7
4-83
), he
show
s hi
mse
lf to b
e disi
nclin
ed to
adm
it ext
ensio
ns of
the m
odal
syst
em be
yond
B b i
n th
e lat
er po
rtio
ns of
the w
ork w
hich
are t
he fo
cus o
f thi
s disc
ussio
n. Se
e, fo
r ex
ampl
e, hi
s avo
idan
ce of
Eb a
nd F#
in L
ucid
ariu
m, 11
, 4, 3
2, p
p. 40
6-07
, and
11
,4, 3
7-45
, pp.
410-
15, r
espe
ctiv
ely.
The r
ecog
nitio
n of B
t in a
dditi
on to
the
Exam
ple 2
. Mel
odic
prog
ress
ion in
volv
ing l
eaps
(afte
r Luc
ida-
ri
um, 1
1, 4,
233
, pp.
510-
11).
Her
e and
in fo
llow
ing e
xam
ples
, m
embe
rs of
leap
s are
mar
ked y
and
extr
emes
x.
y y
y x
x x
x x
x x
lodi
c pro
gres
sion "
emph
asise
s" or
"out
lines
" giv
en in
terv
als;
l1
inde
ed, o
ne co
uld s
ay th
at D
3-A
3 an
d A3-
D3
are o
utlin
ed in
Ex
ampl
e 1, a
nd D
3-A
3,
A3-
E3,
E3-A
3,
A3-
F3,
A3-
E3,
E3-G
3, a
nd G
3-E3
are
outli
ned i
n Exa
mpl
e 2. H
owev
er, I
do
not b
elie
ve th
at th
e not
ion o
f an i
nter
val be
ing o
utlin
ed sh
ould
be
carr
ied t
oo fa
r if o
ne h
opes
to u
nder
stan
d Mar
chet
to's a
c-
coun
t fully
. Rat
her o
ne m
ust fo
cus p
rim
arily
on th
e ide
a of i
ndi-
vidu
al no
tes b
eing
spec
ial, a
nd on
ly se
cond
arily
on th
e ide
a of
two s
uch n
otes
form
ing t
he ou
tline
of a
n int
erva
l.12
Impl
icit i
n M
arch
etto
's ver
sion o
f mod
al th
eory
is th
e ide
a th
at ea
ch m
ode h
as or
ient
ing n
otes
. Aga
in on
e sho
uld o
bser
ve
that
Mar
chet
to do
es no
t use
the p
hras
e ori
entin
g not
e or e
ven
a re
mot
e syn
onym
ther
eof.
Inst
ead,
the
conc
ept o
r ide
a of
ori
- en
ting n
otes
is im
plic
it in
his d
iscus
sion.
Com
mon
to a
ll th
e m
odes
in M
arch
etto
's acc
ount
is a
set o
f pitc
h cl
asse
s cor
res-
po
ndin
g to
the
"whi
te-n
ote"
or d
iato
nic c
olle
ctio
n, w
ith th
e tr
aditi
onal
poss
ibili
ty th
at Bl
mig
ht su
bstit
ute fo
r B-n
atur
al un
- de
r cer
tain
circ
umst
ance
s.13 Be
yond
this
com
mon
basis
for a
ll
"See
, for
exam
ple,
Pet
er B
ergq
uist
, "M
ode a
nd P
olyp
hony
arou
nd 15
00:
Theo
ry an
d Pra
ctic
e," M
usic
Foru
m 1 (
1967
): 10
3.
'2Th
is is n
ot to
den
y tha
t tw
o sp
ecia
l not
es a
four
th or
fifth
apar
t impl
y a
give
n mod
e mor
e str
ongl
y tha
n a si
ngle
spec
ial n
ote i
n iso
latio
n. O
n th
is po
int
see c
rite
rion
3 bel
ow.
'3A
lthou
gh M
arch
etto
is ju
stly
fam
ous f
or h
is de
taile
d tr
eatm
ent o
f chr
o-
mat
icism
earl
ier o
n in t
he L
ucid
ariu
m (see
Jan W
. Her
linge
r, "M
arch
etto
's Di-
visio
n of t
he W
hole
Ton
e," M
usic
The
ory S
pect
rum
3 [19
81]: 7
4-83
), he
show
s hi
mse
lf to b
e disi
nclin
ed to
adm
it ext
ensio
ns of
the m
odal
syst
em be
yond
B b i
n th
e lat
er po
rtio
ns of
the w
ork w
hich
are t
he fo
cus o
f thi
s disc
ussio
n. Se
e, fo
r ex
ampl
e, hi
s avo
idan
ce of
Eb a
nd F#
in L
ucid
ariu
m, 11
, 4, 3
2, p
p. 40
6-07
, and
11
,4, 3
7-45
, pp.
410-
15, r
espe
ctiv
ely.
The r
ecog
nitio
n of B
t in a
dditi
on to
the
Exam
ple 2
. Mel
odic
prog
ress
ion in
volv
ing l
eaps
(afte
r Luc
ida-
ri
um, 1
1, 4,
233
, pp.
510-
11).
Her
e and
in fo
llow
ing e
xam
ples
, m
embe
rs of
leap
s are
mar
ked y
and
extr
emes
x.
y y
y x
x x
x x
x x
lodi
c pro
gres
sion "
emph
asise
s" or
"out
lines
" giv
en in
terv
als;
l1
inde
ed, o
ne co
uld s
ay th
at D
3-A
3 an
d A3-
D3
are o
utlin
ed in
Ex
ampl
e 1, a
nd D
3-A
3,
A3-
E3,
E3-A
3,
A3-
F3,
A3-
E3,
E3-G
3, a
nd G
3-E3
are
outli
ned i
n Exa
mpl
e 2. H
owev
er, I
do
not b
elie
ve th
at th
e not
ion o
f an i
nter
val be
ing o
utlin
ed sh
ould
be
carr
ied t
oo fa
r if o
ne h
opes
to u
nder
stan
d Mar
chet
to's a
c-
coun
t fully
. Rat
her o
ne m
ust fo
cus p
rim
arily
on th
e ide
a of i
ndi-
vidu
al no
tes b
eing
spec
ial, a
nd on
ly se
cond
arily
on th
e ide
a of
two s
uch n
otes
form
ing t
he ou
tline
of a
n int
erva
l.12
Impl
icit i
n M
arch
etto
's ver
sion o
f mod
al th
eory
is th
e ide
a th
at ea
ch m
ode h
as or
ient
ing n
otes
. Aga
in on
e sho
uld o
bser
ve
that
Mar
chet
to do
es no
t use
the p
hras
e ori
entin
g not
e or e
ven
a re
mot
e syn
onym
ther
eof.
Inst
ead,
the
conc
ept o
r ide
a of
ori
- en
ting n
otes
is im
plic
it in
his d
iscus
sion.
Com
mon
to a
ll th
e m
odes
in M
arch
etto
's acc
ount
is a
set o
f pitc
h cl
asse
s cor
res-
po
ndin
g to
the
"whi
te-n
ote"
or d
iato
nic c
olle
ctio
n, w
ith th
e tr
aditi
onal
poss
ibili
ty th
at Bl
mig
ht su
bstit
ute fo
r B-n
atur
al un
- de
r cer
tain
circ
umst
ance
s.13 Be
yond
this
com
mon
basis
for a
ll
"See
, for
exam
ple,
Pet
er B
ergq
uist
, "M
ode a
nd P
olyp
hony
arou
nd 15
00:
Theo
ry an
d Pra
ctic
e," M
usic
Foru
m 1 (
1967
): 10
3.
'2Th
is is n
ot to
den
y tha
t tw
o sp
ecia
l not
es a
four
th or
fifth
apar
t impl
y a
give
n mod
e mor
e str
ongl
y tha
n a si
ngle
spec
ial n
ote i
n iso
latio
n. O
n th
is po
int
see c
rite
rion
3 bel
ow.
'3A
lthou
gh M
arch
etto
is ju
stly
fam
ous f
or h
is de
taile
d tr
eatm
ent o
f chr
o-
mat
icism
earl
ier o
n in t
he L
ucid
ariu
m (see
Jan W
. Her
linge
r, "M
arch
etto
's Di-
visio
n of t
he W
hole
Ton
e," M
usic
The
ory S
pect
rum
3 [19
81]: 7
4-83
), he
show
s hi
mse
lf to b
e disi
nclin
ed to
adm
it ext
ensio
ns of
the m
odal
syst
em be
yond
B b i
n th
e lat
er po
rtio
ns of
the w
ork w
hich
are t
he fo
cus o
f thi
s disc
ussio
n. Se
e, fo
r ex
ampl
e, hi
s avo
idan
ce of
Eb a
nd F#
in L
ucid
ariu
m, 11
, 4, 3
2, p
p. 40
6-07
, and
11
,4, 3
7-45
, pp.
410-
15, r
espe
ctiv
ely.
The r
ecog
nitio
n of B
t in a
dditi
on to
the
the
mod
es, M
arch
etto
reco
gniz
es a
num
ber o
f fe
atur
es th
at
char
acte
rize
indi
vidu
al m
odes
. Fir
st, l
ike
prev
ious
theo
rist
s, M
arch
etto
ackn
owle
dges
that
each
mod
e has
a pr
imar
y ori
ent-
ing
pitc
h: fo
r mod
es I
and
II, t
his p
rim
ary o
rien
ting n
ote,
or
final
is, is
D3;
for m
odes
III a
nd IV
, E3;
for m
odes
V a
nd V
I, F3
; and
for m
odes
VII
and
VII
I, G
3. L
ike p
revi
ous a
utho
rs,
agai
n, M
arch
etto
ass
ocia
tes a
spe
cific
"pe
rfec
t" ra
nge w
ith
each
mod
e, su
ch th
at fo
r mod
es sh
arin
g the
sam
e fin
alis (
e.g.
, D
3 fo
r I a
nd II
) one
can
dist
ingu
ish hi
gher
and
low
er, o
r au-
th
entic
and p
laga
l form
s, re
spec
tivel
y, as
in T
able
1.14
Tabl
e 1.
Sum
mar
y of p
erfe
ct ra
nges
of a
uthe
ntic
and
plag
al
mod
es ac
cord
ing t
o Lu
cida
rium
, 11, 2
, 1-3
5, p
p. 3
72-9
1
Type
of m
ode
Low
est d
egre
e H
ighe
st de
gree
au
then
tic
VII
or I
8 pl
agal
V
5 o
r 6
the
mod
es, M
arch
etto
reco
gniz
es a
num
ber o
f fe
atur
es th
at
char
acte
rize
indi
vidu
al m
odes
. Fir
st, l
ike
prev
ious
theo
rist
s, M
arch
etto
ackn
owle
dges
that
each
mod
e has
a pr
imar
y ori
ent-
ing
pitc
h: fo
r mod
es I
and
II, t
his p
rim
ary o
rien
ting n
ote,
or
final
is, is
D3;
for m
odes
III a
nd IV
, E3;
for m
odes
V a
nd V
I, F3
; and
for m
odes
VII
and
VII
I, G
3. L
ike p
revi
ous a
utho
rs,
agai
n, M
arch
etto
ass
ocia
tes a
spe
cific
"pe
rfec
t" ra
nge w
ith
each
mod
e, su
ch th
at fo
r mod
es sh
arin
g the
sam
e fin
alis (
e.g.
, D
3 fo
r I a
nd II
) one
can
dist
ingu
ish hi
gher
and
low
er, o
r au-
th
entic
and p
laga
l form
s, re
spec
tivel
y, as
in T
able
1.14
Tabl
e 1.
Sum
mar
y of p
erfe
ct ra
nges
of a
uthe
ntic
and
plag
al
mod
es ac
cord
ing t
o Lu
cida
rium
, 11, 2
, 1-3
5, p
p. 3
72-9
1
Type
of m
ode
Low
est d
egre
e H
ighe
st de
gree
au
then
tic
VII
or I
8 pl
agal
V
5 o
r 6
the
mod
es, M
arch
etto
reco
gniz
es a
num
ber o
f fe
atur
es th
at
char
acte
rize
indi
vidu
al m
odes
. Fir
st, l
ike
prev
ious
theo
rist
s, M
arch
etto
ackn
owle
dges
that
each
mod
e has
a pr
imar
y ori
ent-
ing
pitc
h: fo
r mod
es I
and
II, t
his p
rim
ary o
rien
ting n
ote,
or
final
is, is
D3;
for m
odes
III a
nd IV
, E3;
for m
odes
V a
nd V
I, F3
; and
for m
odes
VII
and
VII
I, G
3. L
ike p
revi
ous a
utho
rs,
agai
n, M
arch
etto
ass
ocia
tes a
spe
cific
"pe
rfec
t" ra
nge w
ith
each
mod
e, su
ch th
at fo
r mod
es sh
arin
g the
sam
e fin
alis (
e.g.
, D
3 fo
r I a
nd II
) one
can
dist
ingu
ish hi
gher
and
low
er, o
r au-
th
entic
and p
laga
l form
s, re
spec
tivel
y, as
in T
able
1.14
Tabl
e 1.
Sum
mar
y of p
erfe
ct ra
nges
of a
uthe
ntic
and
plag
al
mod
es ac
cord
ing t
o Lu
cida
rium
, 11, 2
, 1-3
5, p
p. 3
72-9
1
Type
of m
ode
Low
est d
egre
e H
ighe
st de
gree
au
then
tic
VII
or I
8 pl
agal
V
5 o
r 6
the
mod
es, M
arch
etto
reco
gniz
es a
num
ber o
f fe
atur
es th
at
char
acte
rize
indi
vidu
al m
odes
. Fir
st, l
ike
prev
ious
theo
rist
s, M
arch
etto
ackn
owle
dges
that
each
mod
e has
a pr
imar
y ori
ent-
ing
pitc
h: fo
r mod
es I
and
II, t
his p
rim
ary o
rien
ting n
ote,
or
final
is, is
D3;
for m
odes
III a
nd IV
, E3;
for m
odes
V a
nd V
I, F3
; and
for m
odes
VII
and
VII
I, G
3. L
ike p
revi
ous a
utho
rs,
agai
n, M
arch
etto
ass
ocia
tes a
spe
cific
"pe
rfec
t" ra
nge w
ith
each
mod
e, su
ch th
at fo
r mod
es sh
arin
g the
sam
e fin
alis (
e.g.
, D
3 fo
r I a
nd II
) one
can
dist
ingu
ish hi
gher
and
low
er, o
r au-
th
entic
and p
laga
l form
s, re
spec
tivel
y, as
in T
able
1.14
Tabl
e 1.
Sum
mar
y of p
erfe
ct ra
nges
of a
uthe
ntic
and
plag
al
mod
es ac
cord
ing t
o Lu
cida
rium
, 11, 2
, 1-3
5, p
p. 3
72-9
1
Type
of m
ode
Low
est d
egre
e H
ighe
st de
gree
au
then
tic
VII
or I
8 pl
agal
V
5 o
r 6
the
mod
es, M
arch
etto
reco
gniz
es a
num
ber o
f fe
atur
es th
at
char
acte
rize
indi
vidu
al m
odes
. Fir
st, l
ike
prev
ious
theo
rist
s, M
arch
etto
ackn
owle
dges
that
each
mod
e has
a pr
imar
y ori
ent-
ing
pitc
h: fo
r mod
es I
and
II, t
his p
rim
ary o
rien
ting n
ote,
or
final
is, is
D3;
for m
odes
III a
nd IV
, E3;
for m
odes
V a
nd V
I, F3
; and
for m
odes
VII
and
VII
I, G
3. L
ike p
revi
ous a
utho
rs,
agai
n, M
arch
etto
ass
ocia
tes a
spe
cific
"pe
rfec
t" ra
nge w
ith
each
mod
e, su
ch th
at fo
r mod
es sh
arin
g the
sam
e fin
alis (
e.g.
, D
3 fo
r I a
nd II
) one
can
dist
ingu
ish hi
gher
and
low
er, o
r au-
th
entic
and p
laga
l form
s, re
spec
tivel
y, as
in T
able
1.14
Tabl
e 1.
Sum
mar
y of p
erfe
ct ra
nges
of a
uthe
ntic
and
plag
al
mod
es ac
cord
ing t
o Lu
cida
rium
, 11, 2
, 1-3
5, p
p. 3
72-9
1
Type
of m
ode
Low
est d
egre
e H
ighe
st de
gree
au
then
tic
VII
or I
8 pl
agal
V
5 o
r 6
the
mod
es, M
arch
etto
reco
gniz
es a
num
ber o
f fe
atur
es th
at
char
acte
rize
indi
vidu
al m
odes
. Fir
st, l
ike
prev
ious
theo
rist
s, M
arch
etto
ackn
owle
dges
that
each
mod
e has
a pr
imar
y ori
ent-
ing
pitc
h: fo
r mod
es I
and
II, t
his p
rim
ary o
rien
ting n
ote,
or
final
is, is
D3;
for m
odes
III a
nd IV
, E3;
for m
odes
V a
nd V
I, F3
; and
for m
odes
VII
and
VII
I, G
3. L
ike p
revi
ous a
utho
rs,
agai
n, M
arch
etto
ass
ocia
tes a
spe
cific
"pe
rfec
t" ra
nge w
ith
each
mod
e, su
ch th
at fo
r mod
es sh
arin
g the
sam
e fin
alis (
e.g.
, D
3 fo
r I a
nd II
) one
can
dist
ingu
ish hi
gher
and
low
er, o
r au-
th
entic
and p
laga
l form
s, re
spec
tivel
y, as
in T
able
1.14
Tabl
e 1.
Sum
mar
y of p
erfe
ct ra
nges
of a
uthe
ntic
and
plag
al
mod
es ac
cord
ing t
o Lu
cida
rium
, 11, 2
, 1-3
5, p
p. 3
72-9
1
Type
of m
ode
Low
est d
egre
e H
ighe
st de
gree
au
then
tic
VII
or I
8 pl
agal
V
5 o
r 6
Mar
chet
to as
soci
ates
othe
r ori
entin
g not
es w
ith ea
ch m
ode.
Im
plic
it in h
is di
scus
sion o
f the
so-c
alle
d spe
cies
stru
ctur
e of a
u-
then
tic m
odes
is a
spec
ial s
tatu
s acc
orde
d not
only
to th
efin
alis
in, f
or e
xam
ple,
mod
e I
(i.e.
, D
3),
but a
lso to
the
not
es a
fo
urth
, a fi
fth, a
nd an
octa
ve a
bove
(G3,
A3,
and
D4)
. For
a
plag
al co
unte
rpar
t, in t
his i
nsta
nce m
ode I
I, no
t onl
y is t
hefin
a-
lis (D
3) a
n ori
entin
g not
e but
also
the n
otes
G3 a
nd A
3 ab
ove,
an
d A2
belo
w. A
sim
ilar s
ituat
ion h
olds
for t
he re
mai
ning
pair
s
seve
n dia
toni
c ton
es ca
n be t
race
d as f
ar ba
ck as
the a
nony
mou
s Div
isio m
ono-
ch
ordi
, ed.
J. A
. de
la F
age,
in E
ssai
s de
diph
thtr
ogra
phie
mus
ical
e (Pa
ris:
18
64; r
epr.
Am
ster
dam
: F. A
. M. K
nuf,
1964
), 73
. The
Dia
logu
s is t
he fi
rst
trea
tise t
o di
stin
guish
b ro
tund
um (B
b) fr
om b
quad
rum
(B ).
'4
This t
able
incl
udes
only
per
fect
rang
es, le
avin
g out
an
acco
unt o
f bot
h pl
uper
fect
and
mix
ed fo
rms a
nd th
e pr
oble
mat
ic ca
ses o
f im
perf
ect m
odes
de
alt w
ith in
the t
wel
fth tr
eatis
e (Lu
cida
rium
, pp.
522
-33)
. N
ote a
lso th
at fo
r M
arch
etto
, mod
e V d
oes n
ot p
rope
rly d
esce
nd to
deg
ree V
II b
ecau
se of
the
sem
itone
that
wou
ld be
form
ed.
Mar
chet
to as
soci
ates
othe
r ori
entin
g not
es w
ith ea
ch m
ode.
Im
plic
it in h
is di
scus
sion o
f the
so-c
alle
d spe
cies
stru
ctur
e of a
u-
then
tic m
odes
is a
spec
ial s
tatu
s acc
orde
d not
only
to th
efin
alis
in, f
or e
xam
ple,
mod
e I
(i.e.
, D
3),
but a
lso to
the
not
es a
fo
urth
, a fi
fth, a
nd an
octa
ve a
bove
(G3,
A3,
and
D4)
. For
a
plag
al co
unte
rpar
t, in t
his i
nsta
nce m
ode I
I, no
t onl
y is t
hefin
a-
lis (D
3) a
n ori
entin
g not
e but
also
the n
otes
G3 a
nd A
3 ab
ove,
an
d A2
belo
w. A
sim
ilar s
ituat
ion h
olds
for t
he re
mai
ning
pair
s
seve
n dia
toni
c ton
es ca
n be t
race
d as f
ar ba
ck as
the a
nony
mou
s Div
isio m
ono-
ch
ordi
, ed.
J. A
. de
la F
age,
in E
ssai
s de
diph
thtr
ogra
phie
mus
ical
e (Pa
ris:
18
64; r
epr.
Am
ster
dam
: F. A
. M. K
nuf,
1964
), 73
. The
Dia
logu
s is t
he fi
rst
trea
tise t
o di
stin
guish
b ro
tund
um (B
b) fr
om b
quad
rum
(B ).
'4
This t
able
incl
udes
only
per
fect
rang
es, le
avin
g out
an
acco
unt o
f bot
h pl
uper
fect
and
mix
ed fo
rms a
nd th
e pr
oble
mat
ic ca
ses o
f im
perf
ect m
odes
de
alt w
ith in
the t
wel
fth tr
eatis
e (Lu
cida
rium
, pp.
522
-33)
. N
ote a
lso th
at fo
r M
arch
etto
, mod
e V d
oes n
ot p
rope
rly d
esce
nd to
deg
ree V
II b
ecau
se of
the
sem
itone
that
wou
ld be
form
ed.
Mar
chet
to as
soci
ates
othe
r ori
entin
g not
es w
ith ea
ch m
ode.
Im
plic
it in h
is di
scus
sion o
f the
so-c
alle
d spe
cies
stru
ctur
e of a
u-
then
tic m
odes
is a
spec
ial s
tatu
s acc
orde
d not
only
to th
efin
alis
in, f
or e
xam
ple,
mod
e I
(i.e.
, D
3),
but a
lso to
the
not
es a
fo
urth
, a fi
fth, a
nd an
octa
ve a
bove
(G3,
A3,
and
D4)
. For
a
plag
al co
unte
rpar
t, in t
his i
nsta
nce m
ode I
I, no
t onl
y is t
hefin
a-
lis (D
3) a
n ori
entin
g not
e but
also
the n
otes
G3 a
nd A
3 ab
ove,
an
d A2
belo
w. A
sim
ilar s
ituat
ion h
olds
for t
he re
mai
ning
pair
s
seve
n dia
toni
c ton
es ca
n be t
race
d as f
ar ba
ck as
the a
nony
mou
s Div
isio m
ono-
ch
ordi
, ed.
J. A
. de
la F
age,
in E
ssai
s de
diph
thtr
ogra
phie
mus
ical
e (Pa
ris:
18
64; r
epr.
Am
ster
dam
: F. A
. M. K
nuf,
1964
), 73
. The
Dia
logu
s is t
he fi
rst
trea
tise t
o di
stin
guish
b ro
tund
um (B
b) fr
om b
quad
rum
(B ).
'4
This t
able
incl
udes
only
per
fect
rang
es, le
avin
g out
an
acco
unt o
f bot
h pl
uper
fect
and
mix
ed fo
rms a
nd th
e pr
oble
mat
ic ca
ses o
f im
perf
ect m
odes
de
alt w
ith in
the t
wel
fth tr
eatis
e (Lu
cida
rium
, pp.
522
-33)
. N
ote a
lso th
at fo
r M
arch
etto
, mod
e V d
oes n
ot p
rope
rly d
esce
nd to
deg
ree V
II b
ecau
se of
the
sem
itone
that
wou
ld be
form
ed.
Mar
chet
to as
soci
ates
othe
r ori
entin
g not
es w
ith ea
ch m
ode.
Im
plic
it in h
is di
scus
sion o
f the
so-c
alle
d spe
cies
stru
ctur
e of a
u-
then
tic m
odes
is a
spec
ial s
tatu
s acc
orde
d not
only
to th
efin
alis
in, f
or e
xam
ple,
mod
e I
(i.e.
, D
3),
but a
lso to
the
not
es a
fo
urth
, a fi
fth, a
nd an
octa
ve a
bove
(G3,
A3,
and
D4)
. For
a
plag
al co
unte
rpar
t, in t
his i
nsta
nce m
ode I
I, no
t onl
y is t
hefin
a-
lis (D
3) a
n ori
entin
g not
e but
also
the n
otes
G3 a
nd A
3 ab
ove,
an
d A2
belo
w. A
sim
ilar s
ituat
ion h
olds
for t
he re
mai
ning
pair
s
seve
n dia
toni
c ton
es ca
n be t
race
d as f
ar ba
ck as
the a
nony
mou
s Div
isio m
ono-
ch
ordi
, ed.
J. A
. de
la F
age,
in E
ssai
s de
diph
thtr
ogra
phie
mus
ical
e (Pa
ris:
18
64; r
epr.
Am
ster
dam
: F. A
. M. K
nuf,
1964
), 73
. The
Dia
logu
s is t
he fi
rst
trea
tise t
o di
stin
guish
b ro
tund
um (B
b) fr
om b
quad
rum
(B ).
'4
This t
able
incl
udes
only
per
fect
rang
es, le
avin
g out
an
acco
unt o
f bot
h pl
uper
fect
and
mix
ed fo
rms a
nd th
e pr
oble
mat
ic ca
ses o
f im
perf
ect m
odes
de
alt w
ith in
the t
wel
fth tr
eatis
e (Lu
cida
rium
, pp.
522
-33)
. N
ote a
lso th
at fo
r M
arch
etto
, mod
e V d
oes n
ot p
rope
rly d
esce
nd to
deg
ree V
II b
ecau
se of
the
sem
itone
that
wou
ld be
form
ed.
Mar
chet
to as
soci
ates
othe
r ori
entin
g not
es w
ith ea
ch m
ode.
Im
plic
it in h
is di
scus
sion o
f the
so-c
alle
d spe
cies
stru
ctur
e of a
u-
then
tic m
odes
is a
spec
ial s
tatu
s acc
orde
d not
only
to th
efin
alis
in, f
or e
xam
ple,
mod
e I
(i.e.
, D
3),
but a
lso to
the
not
es a
fo
urth
, a fi
fth, a
nd an
octa
ve a
bove
(G3,
A3,
and
D4)
. For
a
plag
al co
unte
rpar
t, in t
his i
nsta
nce m
ode I
I, no
t onl
y is t
hefin
a-
lis (D
3) a
n ori
entin
g not
e but
also
the n
otes
G3 a
nd A
3 ab
ove,
an
d A2
belo
w. A
sim
ilar s
ituat
ion h
olds
for t
he re
mai
ning
pair
s
seve
n dia
toni
c ton
es ca
n be t
race
d as f
ar ba
ck as
the a
nony
mou
s Div
isio m
ono-
ch
ordi
, ed.
J. A
. de
la F
age,
in E
ssai
s de
diph
thtr
ogra
phie
mus
ical
e (Pa
ris:
18
64; r
epr.
Am
ster
dam
: F. A
. M. K
nuf,
1964
), 73
. The
Dia
logu
s is t
he fi
rst
trea
tise t
o di
stin
guish
b ro
tund
um (B
b) fr
om b
quad
rum
(B ).
'4
This t
able
incl
udes
only
per
fect
rang
es, le
avin
g out
an
acco
unt o
f bot
h pl
uper
fect
and
mix
ed fo
rms a
nd th
e pr
oble
mat
ic ca
ses o
f im
perf
ect m
odes
de
alt w
ith in
the t
wel
fth tr
eatis
e (Lu
cida
rium
, pp.
522
-33)
. N
ote a
lso th
at fo
r M
arch
etto
, mod
e V d
oes n
ot p
rope
rly d
esce
nd to
deg
ree V
II b
ecau
se of
the
sem
itone
that
wou
ld be
form
ed.
Mar
chet
to as
soci
ates
othe
r ori
entin
g not
es w
ith ea
ch m
ode.
Im
plic
it in h
is di
scus
sion o
f the
so-c
alle
d spe
cies
stru
ctur
e of a
u-
then
tic m
odes
is a
spec
ial s
tatu
s acc
orde
d not
only
to th
efin
alis
in, f
or e
xam
ple,
mod
e I
(i.e.
, D
3),
but a
lso to
the
not
es a
fo
urth
, a fi
fth, a
nd an
octa
ve a
bove
(G3,
A3,
and
D4)
. For
a
plag
al co
unte
rpar
t, in t
his i
nsta
nce m
ode I
I, no
t onl
y is t
hefin
a-
lis (D
3) a
n ori
entin
g not
e but
also
the n
otes
G3 a
nd A
3 ab
ove,
an
d A2
belo
w. A
sim
ilar s
ituat
ion h
olds
for t
he re
mai
ning
pair
s
seve
n dia
toni
c ton
es ca
n be t
race
d as f
ar ba
ck as
the a
nony
mou
s Div
isio m
ono-
ch
ordi
, ed.
J. A
. de
la F
age,
in E
ssai
s de
diph
thtr
ogra
phie
mus
ical
e (Pa
ris:
18
64; r
epr.
Am
ster
dam
: F. A
. M. K
nuf,
1964
), 73
. The
Dia
logu
s is t
he fi
rst
trea
tise t
o di
stin
guish
b ro
tund
um (B
b) fr
om b
quad
rum
(B ).
'4
This t
able
incl
udes
only
per
fect
rang
es, le
avin
g out
an
acco
unt o
f bot
h pl
uper
fect
and
mix
ed fo
rms a
nd th
e pr
oble
mat
ic ca
ses o
f im
perf
ect m
odes
de
alt w
ith in
the t
wel
fth tr
eatis
e (Lu
cida
rium
, pp.
522
-33)
. N
ote a
lso th
at fo
r M
arch
etto
, mod
e V d
oes n
ot p
rope
rly d
esce
nd to
deg
ree V
II b
ecau
se of
the
sem
itone
that
wou
ld be
form
ed.
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
121
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
121
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
121
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
121
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
121
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
121
Figu
re 1.
Ori
entin
g ton
es in
the e
ight
mod
es. E
achf
inal
is ap
pear
s in bo
ldfa
ce; s
econ
dary
orie
ntin
g ton
es ap
pear
in pa
rent
hese
s. Fi
gure
1. O
rien
ting t
ones
in th
e eig
ht m
odes
. Eac
hfin
alis
appe
ars in
bold
face
; sec
onda
ry or
ient
ing t
ones
appe
ar in
pare
nthe
ses.
Figu
re 1.
Ori
entin
g ton
es in
the e
ight
mod
es. E
achf
inal
is ap
pear
s in bo
ldfa
ce; s
econ
dary
orie
ntin
g ton
es ap
pear
in pa
rent
hese
s. Fi
gure
1. O
rien
ting t
ones
in th
e eig
ht m
odes
. Eac
hfin
alis
appe
ars in
bold
face
; sec
onda
ry or
ient
ing t
ones
appe
ar in
pare
nthe
ses.
Figu
re 1.
Ori
entin
g ton
es in
the e
ight
mod
es. E
achf
inal
is ap
pear
s in bo
ldfa
ce; s
econ
dary
orie
ntin
g ton
es ap
pear
in pa
rent
hese
s. Fi
gure
1. O
rien
ting t
ones
in th
e eig
ht m
odes
. Eac
hfin
alis
appe
ars in
bold
face
; sec
onda
ry or
ient
ing t
ones
appe
ar in
pare
nthe
ses.
Ori
entin
g not
es
Ori
entin
g not
es
Ori
entin
g not
es
Ori
entin
g not
es
Ori
entin
g not
es
Ori
entin
g not
es
D3 D3
D3 D3
D3 D3
D3 D3
D3 D3
D3 D3
E3
E3
E3
E3
E3
E3
E3
E3
E3
E3
E3
E3
B2
B2
B2
B2
B2
B2
(G3)
A
3
G3
(A3)
(A3)
(G3)
A
3
G3
(A3)
(A3)
(G3)
A
3
G3
(A3)
(A3)
(G3)
A
3
G3
(A3)
(A3)
(G3)
A
3
G3
(A3)
(A3)
(G3)
A
3
G3
(A3)
(A3)
F3
F3
F3
F3
F3
F3
F3
F3
F3
F3
F3
F3
C3
C3
C3
C3
C3
C3
G3
G3
G3
G3
G3
G3
G3
G3
G3
G3
G3
G3
D3
D3
D3
D3
D3
D3
D4
D4
D4
D4
D4
D4
B3
B3
B3
B3
B3
B3
E4
E4
E4
E4
E4
E4
A3
(B3)
(Bb3
) C
4
Bb3
(C4)
(C4)
D
4
C4
(D4)
A3
(B3)
(Bb3
) C
4
Bb3
(C4)
(C4)
D
4
C4
(D4)
A3
(B3)
(Bb3
) C
4
Bb3
(C4)
(C4)
D
4
C4
(D4)
A3
(B3)
(Bb3
) C
4
Bb3
(C4)
(C4)
D
4
C4
(D4)
A3
(B3)
(Bb3
) C
4
Bb3
(C4)
(C4)
D
4
C4
(D4)
A3
(B3)
(Bb3
) C
4
Bb3
(C4)
(C4)
D
4
C4
(D4)
F4
F4
F4
F4
F4
F4
G4
G4
G4
G4
G4
G4
Figu
re 2.
Inte
rval
cont
ents
of sp
ecie
s of f
ourt
hs an
d fift
hs. T
= to
ne; S
= s
emito
ne.
Figu
re 2.
Inte
rval
cont
ents
of sp
ecie
s of f
ourt
hs an
d fift
hs. T
= to
ne; S
= s
emito
ne.
Figu
re 2.
Inte
rval
cont
ents
of sp
ecie
s of f
ourt
hs an
d fift
hs. T
= to
ne; S
= s
emito
ne.
Figu
re 2.
Inte
rval
cont
ents
of sp
ecie
s of f
ourt
hs an
d fift
hs. T
= to
ne; S
= s
emito
ne.
Figu
re 2.
Inte
rval
cont
ents
of sp
ecie
s of f
ourt
hs an
d fift
hs. T
= to
ne; S
= s
emito
ne.
Figu
re 2.
Inte
rval
cont
ents
of sp
ecie
s of f
ourt
hs an
d fift
hs. T
= to
ne; S
= s
emito
ne.
Num
ber
Spec
ies o
f fou
rth
Spec
ies o
f fif
th
Num
ber
Spec
ies o
f fou
rth
Spec
ies o
f fif
th
Num
ber
Spec
ies o
f fou
rth
Spec
ies o
f fif
th
Num
ber
Spec
ies o
f fou
rth
Spec
ies o
f fif
th
Num
ber
Spec
ies o
f fou
rth
Spec
ies o
f fif
th
Num
ber
Spec
ies o
f fou
rth
Spec
ies o
f fif
th
first
seco
nd
thir
d
first
seco
nd
thir
d
first
seco
nd
thir
d
first
seco
nd
thir
d
first
seco
nd
thir
d
first
seco
nd
thir
d
D3
E3
F3
G3
T S
T
E3
F3
G3
A3
S T
T
F3
G3
A3
Bb3
T T
S
D3
E3
F3
G3
T S
T
E3
F3
G3
A3
S T
T
F3
G3
A3
Bb3
T T
S
D3
E3
F3
G3
T S
T
E3
F3
G3
A3
S T
T
F3
G3
A3
Bb3
T T
S
D3
E3
F3
G3
T S
T
E3
F3
G3
A3
S T
T
F3
G3
A3
Bb3
T T
S
D3
E3
F3
G3
T S
T
E3
F3
G3
A3
S T
T
F3
G3
A3
Bb3
T T
S
D3
E3
F3
G3
T S
T
E3
F3
G3
A3
S T
T
F3
G3
A3
Bb3
T T
S
four
th
four
th
four
th
four
th
four
th
four
th
of m
odes
; eac
h aut
hent
ic m
ode i
s ori
ente
d by i
tsfin
alis
and t
he
note
s a
perf
ect f
ourt
h, a
per
fect
fifth
, and
a p
erfe
ct o
ctav
e ab
ove;
each
plag
al m
ode i
s ori
ente
d by i
tsfin
alis a
nd th
e not
es a
perf
ect f
ourt
h an
d a
perf
ect f
ifth a
bove
, and
a pe
rfec
t fou
rth
belo
w (s
ee F
ig. 1
). Th
is in
terp
reta
tion o
f Mar
chet
to's f
orm
ulat
ion i
s bas
ed on
hi
s acc
ount
of w
hat h
e cal
ls th
e "fo
rmat
ion o
f mod
es by
spec
ies
of m
odes
; eac
h aut
hent
ic m
ode i
s ori
ente
d by i
tsfin
alis
and t
he
note
s a
perf
ect f
ourt
h, a
per
fect
fifth
, and
a p
erfe
ct o
ctav
e ab
ove;
each
plag
al m
ode i
s ori
ente
d by i
tsfin
alis a
nd th
e not
es a
perf
ect f
ourt
h an
d a
perf
ect f
ifth a
bove
, and
a pe
rfec
t fou
rth
belo
w (s
ee F
ig. 1
). Th
is in
terp
reta
tion o
f Mar
chet
to's f
orm
ulat
ion i
s bas
ed on
hi
s acc
ount
of w
hat h
e cal
ls th
e "fo
rmat
ion o
f mod
es by
spec
ies
of m
odes
; eac
h aut
hent
ic m
ode i
s ori
ente
d by i
tsfin
alis
and t
he
note
s a
perf
ect f
ourt
h, a
per
fect
fifth
, and
a p
erfe
ct o
ctav
e ab
ove;
each
plag
al m
ode i
s ori
ente
d by i
tsfin
alis a
nd th
e not
es a
perf
ect f
ourt
h an
d a
perf
ect f
ifth a
bove
, and
a pe
rfec
t fou
rth
belo
w (s
ee F
ig. 1
). Th
is in
terp
reta
tion o
f Mar
chet
to's f
orm
ulat
ion i
s bas
ed on
hi
s acc
ount
of w
hat h
e cal
ls th
e "fo
rmat
ion o
f mod
es by
spec
ies
of m
odes
; eac
h aut
hent
ic m
ode i
s ori
ente
d by i
tsfin
alis
and t
he
note
s a
perf
ect f
ourt
h, a
per
fect
fifth
, and
a p
erfe
ct o
ctav
e ab
ove;
each
plag
al m
ode i
s ori
ente
d by i
tsfin
alis a
nd th
e not
es a
perf
ect f
ourt
h an
d a
perf
ect f
ifth a
bove
, and
a pe
rfec
t fou
rth
belo
w (s
ee F
ig. 1
). Th
is in
terp
reta
tion o
f Mar
chet
to's f
orm
ulat
ion i
s bas
ed on
hi
s acc
ount
of w
hat h
e cal
ls th
e "fo
rmat
ion o
f mod
es by
spec
ies
of m
odes
; eac
h aut
hent
ic m
ode i
s ori
ente
d by i
tsfin
alis
and t
he
note
s a
perf
ect f
ourt
h, a
per
fect
fifth
, and
a p
erfe
ct o
ctav
e ab
ove;
each
plag
al m
ode i
s ori
ente
d by i
tsfin
alis a
nd th
e not
es a
perf
ect f
ourt
h an
d a
perf
ect f
ifth a
bove
, and
a pe
rfec
t fou
rth
belo
w (s
ee F
ig. 1
). Th
is in
terp
reta
tion o
f Mar
chet
to's f
orm
ulat
ion i
s bas
ed on
hi
s acc
ount
of w
hat h
e cal
ls th
e "fo
rmat
ion o
f mod
es by
spec
ies
of m
odes
; eac
h aut
hent
ic m
ode i
s ori
ente
d by i
tsfin
alis
and t
he
note
s a
perf
ect f
ourt
h, a
per
fect
fifth
, and
a p
erfe
ct o
ctav
e ab
ove;
each
plag
al m
ode i
s ori
ente
d by i
tsfin
alis a
nd th
e not
es a
perf
ect f
ourt
h an
d a
perf
ect f
ifth a
bove
, and
a pe
rfec
t fou
rth
belo
w (s
ee F
ig. 1
). Th
is in
terp
reta
tion o
f Mar
chet
to's f
orm
ulat
ion i
s bas
ed on
hi
s acc
ount
of w
hat h
e cal
ls th
e "fo
rmat
ion o
f mod
es by
spec
ies
D3
E3
F3
G3
A3
T S
T T
E3
F3
G3
A3
B3
S T
T T
F3
G3
A3
B3
C4
T T
T S
G3
A3
B3
C4
D4
T T
S T
D3
E3
F3
G3
A3
T S
T T
E3
F3
G3
A3
B3
S T
T T
F3
G3
A3
B3
C4
T T
T S
G3
A3
B3
C4
D4
T T
S T
D3
E3
F3
G3
A3
T S
T T
E3
F3
G3
A3
B3
S T
T T
F3
G3
A3
B3
C4
T T
T S
G3
A3
B3
C4
D4
T T
S T
D3
E3
F3
G3
A3
T S
T T
E3
F3
G3
A3
B3
S T
T T
F3
G3
A3
B3
C4
T T
T S
G3
A3
B3
C4
D4
T T
S T
D3
E3
F3
G3
A3
T S
T T
E3
F3
G3
A3
B3
S T
T T
F3
G3
A3
B3
C4
T T
T S
G3
A3
B3
C4
D4
T T
S T
D3
E3
F3
G3
A3
T S
T T
E3
F3
G3
A3
B3
S T
T T
F3
G3
A3
B3
C4
T T
T S
G3
A3
B3
C4
D4
T T
S T
[of f
ourt
hs an
d fif
ths]
."15
The
idea
of s
peci
es of
four
ths a
nd
fifth
s is c
entr
al to
Mar
chet
to's a
ccou
nt, b
ut u
nfor
tuna
tely
the
term
spec
ies a
s use
d by
Mar
chet
to em
bodi
es se
vera
l diff
eren
t, th
ough
clos
ely
rela
ted,
mea
ning
s. Su
ffice
it to
rem
ark a
t thi
s po
int t
hat e
ach s
peci
es ha
s: (a
) a di
stin
ctiv
e arr
ange
men
t (cor
n-
[of f
ourt
hs an
d fif
ths]
."15
The
idea
of s
peci
es of
four
ths a
nd
fifth
s is c
entr
al to
Mar
chet
to's a
ccou
nt, b
ut u
nfor
tuna
tely
the
term
spec
ies a
s use
d by
Mar
chet
to em
bodi
es se
vera
l diff
eren
t, th
ough
clos
ely
rela
ted,
mea
ning
s. Su
ffice
it to
rem
ark a
t thi
s po
int t
hat e
ach s
peci
es ha
s: (a
) a di
stin
ctiv
e arr
ange
men
t (cor
n-
[of f
ourt
hs an
d fif
ths]
."15
The
idea
of s
peci
es of
four
ths a
nd
fifth
s is c
entr
al to
Mar
chet
to's a
ccou
nt, b
ut u
nfor
tuna
tely
the
term
spec
ies a
s use
d by
Mar
chet
to em
bodi
es se
vera
l diff
eren
t, th
ough
clos
ely
rela
ted,
mea
ning
s. Su
ffice
it to
rem
ark a
t thi
s po
int t
hat e
ach s
peci
es ha
s: (a
) a di
stin
ctiv
e arr
ange
men
t (cor
n-
[of f
ourt
hs an
d fif
ths]
."15
The
idea
of s
peci
es of
four
ths a
nd
fifth
s is c
entr
al to
Mar
chet
to's a
ccou
nt, b
ut u
nfor
tuna
tely
the
term
spec
ies a
s use
d by
Mar
chet
to em
bodi
es se
vera
l diff
eren
t, th
ough
clos
ely
rela
ted,
mea
ning
s. Su
ffice
it to
rem
ark a
t thi
s po
int t
hat e
ach s
peci
es ha
s: (a
) a di
stin
ctiv
e arr
ange
men
t (cor
n-
[of f
ourt
hs an
d fif
ths]
."15
The
idea
of s
peci
es of
four
ths a
nd
fifth
s is c
entr
al to
Mar
chet
to's a
ccou
nt, b
ut u
nfor
tuna
tely
the
term
spec
ies a
s use
d by
Mar
chet
to em
bodi
es se
vera
l diff
eren
t, th
ough
clos
ely
rela
ted,
mea
ning
s. Su
ffice
it to
rem
ark a
t thi
s po
int t
hat e
ach s
peci
es ha
s: (a
) a di
stin
ctiv
e arr
ange
men
t (cor
n-
[of f
ourt
hs an
d fif
ths]
."15
The
idea
of s
peci
es of
four
ths a
nd
fifth
s is c
entr
al to
Mar
chet
to's a
ccou
nt, b
ut u
nfor
tuna
tely
the
term
spec
ies a
s use
d by
Mar
chet
to em
bodi
es se
vera
l diff
eren
t, th
ough
clos
ely
rela
ted,
mea
ning
s. Su
ffice
it to
rem
ark a
t thi
s po
int t
hat e
ach s
peci
es ha
s: (a
) a di
stin
ctiv
e arr
ange
men
t (cor
n-
15Lu
cida
rium
, 11, 4
, pp.
394-
519.
15
Luci
dari
um, 11
, 4, p
p. 39
4-51
9.
15Lu
cida
rium
, 11, 4
, pp.
394-
519.
15
Luci
dari
um, 11
, 4, p
p. 39
4-51
9.
15Lu
cida
rium
, 11, 4
, pp.
394-
519.
15
Luci
dari
um, 11
, 4, p
p. 39
4-51
9.
Mod
e M
ode
Mod
e M
ode
Mod
e M
ode
A2
A2
A2
A2
A2
A2
I II
III
IV
VI
VII
VII
I V
III
I II
III
IV
VI
VII
VII
I V
III
I II
III
IV
VI
VII
VII
I V
III
I II
III
IV
VI
VII
VII
I V
III
I II
III
IV
VI
VII
VII
I V
III
I II
III
IV
VI
VII
VII
I V
III
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
122
Mus
ic Th
eory
Spec
trum
12
2 M
usic
Theo
ry Sp
ectr
um
122
Mus
ic Th
eory
Spec
trum
12
2 M
usic
Theo
ry Sp
ectr
um
122
Mus
ic Th
eory
Spec
trum
12
2 M
usic
Theo
ry Sp
ectr
um
Figu
re 3.
Oth
er pr
oper
loca
tions
for s
peci
es of
four
ths a
nd fif
ths (
cf. F
ig. 2
, abo
ve)
Figu
re 3.
Oth
er pr
oper
loca
tions
for s
peci
es of
four
ths a
nd fif
ths (
cf. F
ig. 2
, abo
ve)
Figu
re 3.
Oth
er pr
oper
loca
tions
for s
peci
es of
four
ths a
nd fif
ths (
cf. F
ig. 2
, abo
ve)
Figu
re 3.
Oth
er pr
oper
loca
tions
for s
peci
es of
four
ths a
nd fif
ths (
cf. F
ig. 2
, abo
ve)
Figu
re 3.
Oth
er pr
oper
loca
tions
for s
peci
es of
four
ths a
nd fif
ths (
cf. F
ig. 2
, abo
ve)
Figu
re 3.
Oth
er pr
oper
loca
tions
for s
peci
es of
four
ths a
nd fif
ths (
cf. F
ig. 2
, abo
ve)
Num
ber
Spec
ies o
f fou
rth
Spec
ies o
f fift
h N
umbe
r Sp
ecie
s of f
ourt
h Sp
ecie
s of f
ifth
Num
ber
Spec
ies o
f fou
rth
Spec
ies o
f fift
h N
umbe
r Sp
ecie
s of f
ourt
h Sp
ecie
s of f
ifth
Num
ber
Spec
ies o
f fou
rth
Spec
ies o
f fift
h N
umbe
r Sp
ecie
s of f
ourt
h Sp
ecie
s of f
ifth
first
seco
nd
thir
d
first
seco
nd
thir
d
first
seco
nd
thir
d
first
seco
nd
thir
d
first
seco
nd
thir
d
first
seco
nd
thir
d
A2
B2
C3
D3
A3
B3
C4
D4
T S
T
B2
C3
D3
E3
S T
T
C3
D3
E3
F3
G3
A3
B3
C4
T T
S
A2
B2
C3
D3
A3
B3
C4
D4
T S
T
B2
C3
D3
E3
S T
T
C3
D3
E3
F3
G3
A3
B3
C4
T T
S
A2
B2
C3
D3
A3
B3
C4
D4
T S
T
B2
C3
D3
E3
S T
T
C3
D3
E3
F3
G3
A3
B3
C4
T T
S
A2
B2
C3
D3
A3
B3
C4
D4
T S
T
B2
C3
D3
E3
S T
T
C3
D3
E3
F3
G3
A3
B3
C4
T T
S
A2
B2
C3
D3
A3
B3
C4
D4
T S
T
B2
C3
D3
E3
S T
T
C3
D3
E3
F3
G3
A3
B3
C4
T T
S
A2
B2
C3
D3
A3
B3
C4
D4
T S
T
B2
C3
D3
E3
S T
T
C3
D3
E3
F3
G3
A3
B3
C4
T T
S
F3
G3
A3
Bb3
C4
T T
S T
F3
G3
A3
Bb3
C4
T T
S T
F3
G3
A3
Bb3
C4
T T
S T
F3
G3
A3
Bb3
C4
T T
S T
F3
G3
A3
Bb3
C4
T T
S T
F3
G3
A3
Bb3
C4
T T
S T
posit
io) o
f ton
es an
d sem
itone
s as r
epre
sent
ed in
Fig
ure 2
, and
(b
) a lo
catio
n (lo
catio
) tha
t is e
ither
pro
per (
prop
er) o
r im
- pr
oper
(im
prop
er).1
6 Th
e spe
cies
desc
ribe
d in
Figu
re 2
are p
rope
rly l
ocat
ed. O
n th
e oth
er ha
nd, a
s an
inst
ance
of th
e fir
st sp
ecie
s of f
ifth,
the
set o
f not
es G
3, A
, B I,
C, D
has
an im
prop
er lo
catio
n. Fu
rthe
r,
and m
ost im
port
antly
, the h
ighe
st an
d low
est n
otes
of p
rope
rly
loca
ted s
peci
es co
rres
pond
to th
e ori
entin
g not
es o
f mod
es in
th
eir p
rope
r loc
atio
ns. F
or ex
ampl
e, D
3 an
d G3
are t
he lo
wer
an
d upp
er no
tes o
f a pr
oper
ly lo
cate
d fir
st sp
ecie
s of f
ourt
h and
ar
e also
orie
ntin
g not
es fo
r mod
es I,
II, a
nd V
III;
D3
and A
3 ar
e the
bot
tom
and t
op n
otes
of a
prop
erly
loca
ted f
irst
spec
ies
of fi
fth an
d also
orie
ntin
g not
es fo
r mod
es I a
nd II
. In t
his w
ay,
thro
ugh t
he id
eas
of c
ompo
sitio
n, lo
catio
n, p
ropr
iety
(i.e
.,
16Fo
r Mar
chet
to's u
se of
the t
erm
s com
posit
io an
d loc
atio
, see
Luc
idar
ium
, 11
, 4, 7
9-80
, pp
. 430
-31.
The
term
com
posit
io is
use
d ex
tens
ivel
y in
the
Tona
le Sa
ncti B
erna
rdi (c
f. G
iimpe
l, Zur
Inte
rpre
tatio
n der
Ton
us-D
efin
ition
, pa
ssim
).
posit
io) o
f ton
es an
d sem
itone
s as r
epre
sent
ed in
Fig
ure 2
, and
(b
) a lo
catio
n (lo
catio
) tha
t is e
ither
pro
per (
prop
er) o
r im
- pr
oper
(im
prop
er).1
6 Th
e spe
cies
desc
ribe
d in
Figu
re 2
are p
rope
rly l
ocat
ed. O
n th
e oth
er ha
nd, a
s an
inst
ance
of th
e fir
st sp
ecie
s of f
ifth,
the
set o
f not
es G
3, A
, B I,
C, D
has
an im
prop
er lo
catio
n. Fu
rthe
r,
and m
ost im
port
antly
, the h
ighe
st an
d low
est n
otes
of p
rope
rly
loca
ted s
peci
es co
rres
pond
to th
e ori
entin
g not
es o
f mod
es in
th
eir p
rope
r loc
atio
ns. F
or ex
ampl
e, D
3 an
d G3
are t
he lo
wer
an
d upp
er no
tes o
f a pr
oper
ly lo
cate
d fir
st sp
ecie
s of f
ourt
h and
ar
e also
orie
ntin
g not
es fo
r mod
es I,
II, a
nd V
III;
D3
and A
3 ar
e the
bot
tom
and t
op n
otes
of a
prop
erly
loca
ted f
irst
spec
ies
of fi
fth an
d also
orie
ntin
g not
es fo
r mod
es I a
nd II
. In t
his w
ay,
thro
ugh t
he id
eas
of c
ompo
sitio
n, lo
catio
n, p
ropr
iety
(i.e
.,
16Fo
r Mar
chet
to's u
se of
the t
erm
s com
posit
io an
d loc
atio
, see
Luc
idar
ium
, 11
, 4, 7
9-80
, pp
. 430
-31.
The
term
com
posit
io is
use
d ex
tens
ivel
y in
the
Tona
le Sa
ncti B
erna
rdi (c
f. G
iimpe
l, Zur
Inte
rpre
tatio
n der
Ton
us-D
efin
ition
, pa
ssim
).
posit
io) o
f ton
es an
d sem
itone
s as r
epre
sent
ed in
Fig
ure 2
, and
(b
) a lo
catio
n (lo
catio
) tha
t is e
ither
pro
per (
prop
er) o
r im
- pr
oper
(im
prop
er).1
6 Th
e spe
cies
desc
ribe
d in
Figu
re 2
are p
rope
rly l
ocat
ed. O
n th
e oth
er ha
nd, a
s an
inst
ance
of th
e fir
st sp
ecie
s of f
ifth,
the
set o
f not
es G
3, A
, B I,
C, D
has
an im
prop
er lo
catio
n. Fu
rthe
r,
and m
ost im
port
antly
, the h
ighe
st an
d low
est n
otes
of p
rope
rly
loca
ted s
peci
es co
rres
pond
to th
e ori
entin
g not
es o
f mod
es in
th
eir p
rope
r loc
atio
ns. F
or ex
ampl
e, D
3 an
d G3
are t
he lo
wer
an
d upp
er no
tes o
f a pr
oper
ly lo
cate
d fir
st sp
ecie
s of f
ourt
h and
ar
e also
orie
ntin
g not
es fo
r mod
es I,
II, a
nd V
III;
D3
and A
3 ar
e the
bot
tom
and t
op n
otes
of a
prop
erly
loca
ted f
irst
spec
ies
of fi
fth an
d also
orie
ntin
g not
es fo
r mod
es I a
nd II
. In t
his w
ay,
thro
ugh t
he id
eas
of c
ompo
sitio
n, lo
catio
n, p
ropr
iety
(i.e
.,
16Fo
r Mar
chet
to's u
se of
the t
erm
s com
posit
io an
d loc
atio
, see
Luc
idar
ium
, 11
, 4, 7
9-80
, pp
. 430
-31.
The
term
com
posit
io is
use
d ex
tens
ivel
y in
the
Tona
le Sa
ncti B
erna
rdi (c
f. G
iimpe
l, Zur
Inte
rpre
tatio
n der
Ton
us-D
efin
ition
, pa
ssim
).
posit
io) o
f ton
es an
d sem
itone
s as r
epre
sent
ed in
Fig
ure 2
, and
(b
) a lo
catio
n (lo
catio
) tha
t is e
ither
pro
per (
prop
er) o
r im
- pr
oper
(im
prop
er).1
6 Th
e spe
cies
desc
ribe
d in
Figu
re 2
are p
rope
rly l
ocat
ed. O
n th
e oth
er ha
nd, a
s an
inst
ance
of th
e fir
st sp
ecie
s of f
ifth,
the
set o
f not
es G
3, A
, B I,
C, D
has
an im
prop
er lo
catio
n. Fu
rthe
r,
and m
ost im
port
antly
, the h
ighe
st an
d low
est n
otes
of p
rope
rly
loca
ted s
peci
es co
rres
pond
to th
e ori
entin
g not
es o
f mod
es in
th
eir p
rope
r loc
atio
ns. F
or ex
ampl
e, D
3 an
d G3
are t
he lo
wer
an
d upp
er no
tes o
f a pr
oper
ly lo
cate
d fir
st sp
ecie
s of f
ourt
h and
ar
e also
orie
ntin
g not
es fo
r mod
es I,
II, a
nd V
III;
D3
and A
3 ar
e the
bot
tom
and t
op n
otes
of a
prop
erly
loca
ted f
irst
spec
ies
of fi
fth an
d also
orie
ntin
g not
es fo
r mod
es I a
nd II
. In t
his w
ay,
thro
ugh t
he id
eas
of c
ompo
sitio
n, lo
catio
n, p
ropr
iety
(i.e
.,
16Fo
r Mar
chet
to's u
se of
the t
erm
s com
posit
io an
d loc
atio
, see
Luc
idar
ium
, 11
, 4, 7
9-80
, pp
. 430
-31.
The
term
com
posit
io is
use
d ex
tens
ivel
y in
the
Tona
le Sa
ncti B
erna
rdi (c
f. G
iimpe
l, Zur
Inte
rpre
tatio
n der
Ton
us-D
efin
ition
, pa
ssim
).
posit
io) o
f ton
es an
d sem
itone
s as r
epre
sent
ed in
Fig
ure 2
, and
(b
) a lo
catio
n (lo
catio
) tha
t is e
ither
pro
per (
prop
er) o
r im
- pr
oper
(im
prop
er).1
6 Th
e spe
cies
desc
ribe
d in
Figu
re 2
are p
rope
rly l
ocat
ed. O
n th
e oth
er ha
nd, a
s an
inst
ance
of th
e fir
st sp
ecie
s of f
ifth,
the
set o
f not
es G
3, A
, B I,
C, D
has
an im
prop
er lo
catio
n. Fu
rthe
r,
and m
ost im
port
antly
, the h
ighe
st an
d low
est n
otes
of p
rope
rly
loca
ted s
peci
es co
rres
pond
to th
e ori
entin
g not
es o
f mod
es in
th
eir p
rope
r loc
atio
ns. F
or ex
ampl
e, D
3 an
d G3
are t
he lo
wer
an
d upp
er no
tes o
f a pr
oper
ly lo
cate
d fir
st sp
ecie
s of f
ourt
h and
ar
e also
orie
ntin
g not
es fo
r mod
es I,
II, a
nd V
III;
D3
and A
3 ar
e the
bot
tom
and t
op n
otes
of a
prop
erly
loca
ted f
irst
spec
ies
of fi
fth an
d also
orie
ntin
g not
es fo
r mod
es I a
nd II
. In t
his w
ay,
thro
ugh t
he id
eas
of c
ompo
sitio
n, lo
catio
n, p
ropr
iety
(i.e
.,
16Fo
r Mar
chet
to's u
se of
the t
erm
s com
posit
io an
d loc
atio
, see
Luc
idar
ium
, 11
, 4, 7
9-80
, pp
. 430
-31.
The
term
com
posit
io is
use
d ex
tens
ivel
y in
the
Tona
le Sa
ncti B
erna
rdi (c
f. G
iimpe
l, Zur
Inte
rpre
tatio
n der
Ton
us-D
efin
ition
, pa
ssim
).
posit
io) o
f ton
es an
d sem
itone
s as r
epre
sent
ed in
Fig
ure 2
, and
(b
) a lo
catio
n (lo
catio
) tha
t is e
ither
pro
per (
prop
er) o
r im
- pr
oper
(im
prop
er).1
6 Th
e spe
cies
desc
ribe
d in
Figu
re 2
are p
rope
rly l
ocat
ed. O
n th
e oth
er ha
nd, a
s an
inst
ance
of th
e fir
st sp
ecie
s of f
ifth,
the
set o
f not
es G
3, A
, B I,
C, D
has
an im
prop
er lo
catio
n. Fu
rthe
r,
and m
ost im
port
antly
, the h
ighe
st an
d low
est n
otes
of p
rope
rly
loca
ted s
peci
es co
rres
pond
to th
e ori
entin
g not
es o
f mod
es in
th
eir p
rope
r loc
atio
ns. F
or ex
ampl
e, D
3 an
d G3
are t
he lo
wer
an
d upp
er no
tes o
f a pr
oper
ly lo
cate
d fir
st sp
ecie
s of f
ourt
h and
ar
e also
orie
ntin
g not
es fo
r mod
es I,
II, a
nd V
III;
D3
and A
3 ar
e the
bot
tom
and t
op n
otes
of a
prop
erly
loca
ted f
irst
spec
ies
of fi
fth an
d also
orie
ntin
g not
es fo
r mod
es I a
nd II
. In t
his w
ay,
thro
ugh t
he id
eas
of c
ompo
sitio
n, lo
catio
n, p
ropr
iety
(i.e
.,
16Fo
r Mar
chet
to's u
se of
the t
erm
s com
posit
io an
d loc
atio
, see
Luc
idar
ium
, 11
, 4, 7
9-80
, pp
. 430
-31.
The
term
com
posit
io is
use
d ex
tens
ivel
y in
the
Tona
le Sa
ncti B
erna
rdi (c
f. G
iimpe
l, Zur
Inte
rpre
tatio
n der
Ton
us-D
efin
ition
, pa
ssim
).
prop
er-n
ess)
, and
orie
ntat
ion,
one c
an di
scer
n how
the v
ario
us
mod
es ca
n be c
onsid
ered
to b
e mad
e up o
f spe
cies
(see
Fig
. 3).
Wha
t hap
pens
whe
n a
spec
ial n
ote
in a
mel
ody
coin
cide
s w
ith a
n or
ient
ing n
ote
in o
ne o
f the
mod
es?
This
ques
tion,
th
ough
neve
r exp
licitl
y pos
ed a
s suc
h by M
arch
etto
, see
ms t
o un
derl
ie hi
s len
gthy
disc
ussio
n of w
hat h
e des
crib
es as
"in
ter-
ru
ptio
ns of
the f
irst
spec
ies o
f fift
h and
[bot
h] ho
w an
d in
wha
t m
odes
[suc
h] in
terr
upte
d [sp
ecie
s] oc
cur p
rope
rly.
"17 Th
is pa
s-
sage
repr
esen
ts M
arch
etto
's mos
t inte
nsiv
e acc
ount
of re
latio
n-
ship
s bet
wee
n m
elod
ic p
rogr
essio
n and
com
mix
ture
. Acc
ord-
in
gly,
I sh
all d
evot
e co
nsid
erab
le sp
ace t
o th
e con
tent
s of t
his
sect
ion.
Inte
rrup
tions
of a
Spe
cies
M
arch
etto
unde
rtak
es hi
s disc
ussio
n of w
hat h
e te
rms "
in-
terr
uptio
ns" in
an
appa
rent
ly sy
stem
atic
way
. The
syst
em th
at
prop
er-n
ess)
, and
orie
ntat
ion,
one c
an di
scer
n how
the v
ario
us
mod
es ca
n be c
onsid
ered
to b
e mad
e up o
f spe
cies
(see
Fig
. 3).
Wha
t hap
pens
whe
n a
spec
ial n
ote
in a
mel
ody
coin
cide
s w
ith a
n or
ient
ing n
ote
in o
ne o
f the
mod
es?
This
ques
tion,
th
ough
neve
r exp
licitl
y pos
ed a
s suc
h by M
arch
etto
, see
ms t
o un
derl
ie hi
s len
gthy
disc
ussio
n of w
hat h
e des
crib
es as
"in
ter-
ru
ptio
ns of
the f
irst
spec
ies o
f fift
h and
[bot
h] ho
w an
d in
wha
t m
odes
[suc
h] in
terr
upte
d [sp
ecie
s] oc
cur p
rope
rly.
"17 Th
is pa
s-
sage
repr
esen
ts M
arch
etto
's mos
t inte
nsiv
e acc
ount
of re
latio
n-
ship
s bet
wee
n m
elod
ic p
rogr
essio
n and
com
mix
ture
. Acc
ord-
in
gly,
I sh
all d
evot
e co
nsid
erab
le sp
ace t
o th
e con
tent
s of t
his
sect
ion.
Inte
rrup
tions
of a
Spe
cies
M
arch
etto
unde
rtak
es hi
s disc
ussio
n of w
hat h
e te
rms "
in-
terr
uptio
ns" in
an
appa
rent
ly sy
stem
atic
way
. The
syst
em th
at
prop
er-n
ess)
, and
orie
ntat
ion,
one c
an di
scer
n how
the v
ario
us
mod
es ca
n be c
onsid
ered
to b
e mad
e up o
f spe
cies
(see
Fig
. 3).
Wha
t hap
pens
whe
n a
spec
ial n
ote
in a
mel
ody
coin
cide
s w
ith a
n or
ient
ing n
ote
in o
ne o
f the
mod
es?
This
ques
tion,
th
ough
neve
r exp
licitl
y pos
ed a
s suc
h by M
arch
etto
, see
ms t
o un
derl
ie hi
s len
gthy
disc
ussio
n of w
hat h
e des
crib
es as
"in
ter-
ru
ptio
ns of
the f
irst
spec
ies o
f fift
h and
[bot
h] ho
w an
d in
wha
t m
odes
[suc
h] in
terr
upte
d [sp
ecie
s] oc
cur p
rope
rly.
"17 Th
is pa
s-
sage
repr
esen
ts M
arch
etto
's mos
t inte
nsiv
e acc
ount
of re
latio
n-
ship
s bet
wee
n m
elod
ic p
rogr
essio
n and
com
mix
ture
. Acc
ord-
in
gly,
I sh
all d
evot
e co
nsid
erab
le sp
ace t
o th
e con
tent
s of t
his
sect
ion.
Inte
rrup
tions
of a
Spe
cies
M
arch
etto
unde
rtak
es hi
s disc
ussio
n of w
hat h
e te
rms "
in-
terr
uptio
ns" in
an
appa
rent
ly sy
stem
atic
way
. The
syst
em th
at
prop
er-n
ess)
, and
orie
ntat
ion,
one c
an di
scer
n how
the v
ario
us
mod
es ca
n be c
onsid
ered
to b
e mad
e up o
f spe
cies
(see
Fig
. 3).
Wha
t hap
pens
whe
n a
spec
ial n
ote
in a
mel
ody
coin
cide
s w
ith a
n or
ient
ing n
ote
in o
ne o
f the
mod
es?
This
ques
tion,
th
ough
neve
r exp
licitl
y pos
ed a
s suc
h by M
arch
etto
, see
ms t
o un
derl
ie hi
s len
gthy
disc
ussio
n of w
hat h
e des
crib
es as
"in
ter-
ru
ptio
ns of
the f
irst
spec
ies o
f fift
h and
[bot
h] ho
w an
d in
wha
t m
odes
[suc
h] in
terr
upte
d [sp
ecie
s] oc
cur p
rope
rly.
"17 Th
is pa
s-
sage
repr
esen
ts M
arch
etto
's mos
t inte
nsiv
e acc
ount
of re
latio
n-
ship
s bet
wee
n m
elod
ic p
rogr
essio
n and
com
mix
ture
. Acc
ord-
in
gly,
I sh
all d
evot
e co
nsid
erab
le sp
ace t
o th
e con
tent
s of t
his
sect
ion.
Inte
rrup
tions
of a
Spe
cies
M
arch
etto
unde
rtak
es hi
s disc
ussio
n of w
hat h
e te
rms "
in-
terr
uptio
ns" in
an
appa
rent
ly sy
stem
atic
way
. The
syst
em th
at
prop
er-n
ess)
, and
orie
ntat
ion,
one c
an di
scer
n how
the v
ario
us
mod
es ca
n be c
onsid
ered
to b
e mad
e up o
f spe
cies
(see
Fig
. 3).
Wha
t hap
pens
whe
n a
spec
ial n
ote
in a
mel
ody
coin
cide
s w
ith a
n or
ient
ing n
ote
in o
ne o
f the
mod
es?
This
ques
tion,
th
ough
neve
r exp
licitl
y pos
ed a
s suc
h by M
arch
etto
, see
ms t
o un
derl
ie hi
s len
gthy
disc
ussio
n of w
hat h
e des
crib
es as
"in
ter-
ru
ptio
ns of
the f
irst
spec
ies o
f fift
h and
[bot
h] ho
w an
d in
wha
t m
odes
[suc
h] in
terr
upte
d [sp
ecie
s] oc
cur p
rope
rly.
"17 Th
is pa
s-
sage
repr
esen
ts M
arch
etto
's mos
t inte
nsiv
e acc
ount
of re
latio
n-
ship
s bet
wee
n m
elod
ic p
rogr
essio
n and
com
mix
ture
. Acc
ord-
in
gly,
I sh
all d
evot
e co
nsid
erab
le sp
ace t
o th
e con
tent
s of t
his
sect
ion.
Inte
rrup
tions
of a
Spe
cies
M
arch
etto
unde
rtak
es hi
s disc
ussio
n of w
hat h
e te
rms "
in-
terr
uptio
ns" in
an
appa
rent
ly sy
stem
atic
way
. The
syst
em th
at
prop
er-n
ess)
, and
orie
ntat
ion,
one c
an di
scer
n how
the v
ario
us
mod
es ca
n be c
onsid
ered
to b
e mad
e up o
f spe
cies
(see
Fig
. 3).
Wha
t hap
pens
whe
n a
spec
ial n
ote
in a
mel
ody
coin
cide
s w
ith a
n or
ient
ing n
ote
in o
ne o
f the
mod
es?
This
ques
tion,
th
ough
neve
r exp
licitl
y pos
ed a
s suc
h by M
arch
etto
, see
ms t
o un
derl
ie hi
s len
gthy
disc
ussio
n of w
hat h
e des
crib
es as
"in
ter-
ru
ptio
ns of
the f
irst
spec
ies o
f fift
h and
[bot
h] ho
w an
d in
wha
t m
odes
[suc
h] in
terr
upte
d [sp
ecie
s] oc
cur p
rope
rly.
"17 Th
is pa
s-
sage
repr
esen
ts M
arch
etto
's mos
t inte
nsiv
e acc
ount
of re
latio
n-
ship
s bet
wee
n m
elod
ic p
rogr
essio
n and
com
mix
ture
. Acc
ord-
in
gly,
I sh
all d
evot
e co
nsid
erab
le sp
ace t
o th
e con
tent
s of t
his
sect
ion.
Inte
rrup
tions
of a
Spe
cies
M
arch
etto
unde
rtak
es hi
s disc
ussio
n of w
hat h
e te
rms "
in-
terr
uptio
ns" in
an
appa
rent
ly sy
stem
atic
way
. The
syst
em th
at
17Lu
cida
rium
, 11, 4
, 231
-50,
pp.
508-
19.
17Lu
cida
rium
, 11, 4
, 231
-50,
pp.
508-
19.
17Lu
cida
rium
, 11, 4
, 231
-50,
pp.
508-
19.
17Lu
cida
rium
, 11, 4
, 231
-50,
pp.
508-
19.
17Lu
cida
rium
, 11, 4
, 231
-50,
pp.
508-
19.
17Lu
cida
rium
, 11, 4
, 231
-50,
pp.
508-
19.
four
th
four
th
four
th
four
th
four
th
four
th
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
123
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
123
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
123
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
123
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
123
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
123
seem
s to
unde
rlie
his a
ccou
nt co
nsist
s of d
ealin
g with
all
the
com
bina
tions
of fi
ve, f
our,
thre
e, o
r tw
o of
the f
ive n
otes
of a
pr
oper
ly lo
cate
d fir
st sp
ecie
s of f
ifth (
i.e.,
D3,
E3,
F3,
G3,
and
A
3) w
here
by th
e low
est a
nd hi
ghes
t not
es (i
.e.,
D3
and A
3) a
re
incl
uded
in ea
ch co
mbi
natio
n. Th
e sen
se in
whi
ch th
ese c
ombi
- na
tions
of n
otes
can b
e con
sider
ed in
terr
uptio
ns of
the f
irst
spe-
ci
es of
fifth
is th
at ea
ch re
pres
ents
a fir
st sp
ecie
s of f
ifth o
ut o
f w
hich
hav
e be
en le
ft ze
ro, o
ne, t
wo,
or
thre
e not
es, r
espe
c-
tivel
y. In
this
way
, if th
e rem
aini
ng no
tes a
re pr
esen
ted m
elod
i- ca
lly, t
he sc
alar
or st
epw
ise or
deri
ng of
the f
ive n
otes
in a
spe-
ci
es o
f fift
h is i
nter
rupt
ed by
vari
ous o
miss
ions
(inc
ludi
ng th
e in
stan
ce in
whi
ch th
ere
are n
o om
issio
ns, i
.e.,
whe
re a
ll fiv
e no
tes
are
pres
ente
d).1
8 Mor
eove
r, th
e or
ient
ing
note
s of
a
prop
erly
loca
ted f
irst
spec
ies o
f fift
h (i.e
., D
3 an
d A3)
are
com
- m
on to
each
of th
e int
erru
ptio
ns. T
hus,
Mar
chet
to's s
yste
mat
ic
appr
oach
give
s rise
-in m
athe
mat
ical
nota
tion-
to 3
C3 +
3C
2 +
3C1
+ 3C
o =
1 +
3 +
3 +
1 =
8 co
mbi
natio
ns i
n al
l. If
one
at
tach
es M
arch
etto
's num
bers
for t
he re
sulti
ng in
terr
uptio
ns to
th
e eig
ht co
mbi
natio
ns ju
st de
scri
bed,
Tabl
e 2 re
sults
.19
In ea
ch of
his
acco
unts
of th
e eig
ht in
terr
uptio
ns of
the f
irst
sp
ecie
s of f
ifth,
Mar
chet
to (a
) des
crib
es in
wor
ds th
e int
erva
ls th
at a
ppea
r mel
odic
ally
in th
e in
terr
uptio
n, (b
) spe
cifie
s the
m
ode(
s) in
whi
ch su
ch an
inte
rrup
tion is
prop
er or
not,
and (
c)
prov
ides
a m
usic
al ex
ampl
e (or
two)
embo
dyin
g the
inte
rrup
- tio
n. M
arch
etto
's ver
bal d
escr
iptio
n of i
nter
rupt
ions
is co
uche
d in
term
s of t
he co
nsec
utiv
e mzi
odic
inte
rval
s that
appe
ar in
the
inte
rrup
tion.
For e
xam
ple,
he d
escr
ibes
the f
ourt
h int
erru
ptio
n
'8Th
us M
arch
etto
's use
of th
e ter
m in
terr
uptio
, whi
ch ot
herw
ise w
ould
sug-
ge
st a
n om
issio
n of
at l
east
one
note
, is p
oten
tially
misl
eadi
ng, b
ut co
nsist
ent
with
the m
oder
n not
ion o
f the
nul
l set
. 19
This i
s the
num
beri
ng em
ploy
ed in
MS
Mila
n, B
iblio
teca
Am
bros
iana
, D
.5 in
feri
ore,
fols.
52-
77v,
whi
ch be
caus
e of i
ts co
mpl
eten
ess a
nd ap
pare
ntly
ea
rly d
ate,
Her
linge
r jus
tifia
bly u
ses a
s the
bas
ic te
xt fo
r his
editi
on of
the L
uci-
dari
um. O
ther
sour
ces i
n th
e man
uscr
ipt tr
aditi
on ha
ve ot
her o
rder
ings
of th
e in
terr
uptio
ns. U
nles
s ot
herw
ise in
dica
ted,
ref
eren
ces
to t
he L
ucid
ariu
m
thro
ugho
ut th
is st
udy a
re ba
sed o
n th
e Mila
nese
man
uscr
ipt.
seem
s to
unde
rlie
his a
ccou
nt co
nsist
s of d
ealin
g with
all
the
com
bina
tions
of fi
ve, f
our,
thre
e, o
r tw
o of
the f
ive n
otes
of a
pr
oper
ly lo
cate
d fir
st sp
ecie
s of f
ifth (
i.e.,
D3,
E3,
F3,
G3,
and
A
3) w
here
by th
e low
est a
nd hi
ghes
t not
es (i
.e.,
D3
and A
3) a
re
incl
uded
in ea
ch co
mbi
natio
n. Th
e sen
se in
whi
ch th
ese c
ombi
- na
tions
of n
otes
can b
e con
sider
ed in
terr
uptio
ns of
the f
irst
spe-
ci
es of
fifth
is th
at ea
ch re
pres
ents
a fir
st sp
ecie
s of f
ifth o
ut o
f w
hich
hav
e be
en le
ft ze
ro, o
ne, t
wo,
or
thre
e not
es, r
espe
c-
tivel
y. In
this
way
, if th
e rem
aini
ng no
tes a
re pr
esen
ted m
elod
i- ca
lly, t
he sc
alar
or st
epw
ise or
deri
ng of
the f
ive n
otes
in a
spe-
ci
es o
f fift
h is i
nter
rupt
ed by
vari
ous o
miss
ions
(inc
ludi
ng th
e in
stan
ce in
whi
ch th
ere
are n
o om
issio
ns, i
.e.,
whe
re a
ll fiv
e no
tes
are
pres
ente
d).1
8 Mor
eove
r, th
e or
ient
ing
note
s of
a
prop
erly
loca
ted f
irst
spec
ies o
f fift
h (i.e
., D
3 an
d A3)
are
com
- m
on to
each
of th
e int
erru
ptio
ns. T
hus,
Mar
chet
to's s
yste
mat
ic
appr
oach
give
s rise
-in m
athe
mat
ical
nota
tion-
to 3
C3 +
3C
2 +
3C1
+ 3C
o =
1 +
3 +
3 +
1 =
8 co
mbi
natio
ns i
n al
l. If
one
at
tach
es M
arch
etto
's num
bers
for t
he re
sulti
ng in
terr
uptio
ns to
th
e eig
ht co
mbi
natio
ns ju
st de
scri
bed,
Tabl
e 2 re
sults
.19
In ea
ch of
his
acco
unts
of th
e eig
ht in
terr
uptio
ns of
the f
irst
sp
ecie
s of f
ifth,
Mar
chet
to (a
) des
crib
es in
wor
ds th
e int
erva
ls th
at a
ppea
r mel
odic
ally
in th
e in
terr
uptio
n, (b
) spe
cifie
s the
m
ode(
s) in
whi
ch su
ch an
inte
rrup
tion is
prop
er or
not,
and (
c)
prov
ides
a m
usic
al ex
ampl
e (or
two)
embo
dyin
g the
inte
rrup
- tio
n. M
arch
etto
's ver
bal d
escr
iptio
n of i
nter
rupt
ions
is co
uche
d in
term
s of t
he co
nsec
utiv
e mzi
odic
inte
rval
s that
appe
ar in
the
inte
rrup
tion.
For e
xam
ple,
he d
escr
ibes
the f
ourt
h int
erru
ptio
n
'8Th
us M
arch
etto
's use
of th
e ter
m in
terr
uptio
, whi
ch ot
herw
ise w
ould
sug-
ge
st a
n om
issio
n of
at l
east
one
note
, is p
oten
tially
misl
eadi
ng, b
ut co
nsist
ent
with
the m
oder
n not
ion o
f the
nul
l set
. 19
This i
s the
num
beri
ng em
ploy
ed in
MS
Mila
n, B
iblio
teca
Am
bros
iana
, D
.5 in
feri
ore,
fols.
52-
77v,
whi
ch be
caus
e of i
ts co
mpl
eten
ess a
nd ap
pare
ntly
ea
rly d
ate,
Her
linge
r jus
tifia
bly u
ses a
s the
bas
ic te
xt fo
r his
editi
on of
the L
uci-
dari
um. O
ther
sour
ces i
n th
e man
uscr
ipt tr
aditi
on ha
ve ot
her o
rder
ings
of th
e in
terr
uptio
ns. U
nles
s ot
herw
ise in
dica
ted,
ref
eren
ces
to t
he L
ucid
ariu
m
thro
ugho
ut th
is st
udy a
re ba
sed o
n th
e Mila
nese
man
uscr
ipt.
seem
s to
unde
rlie
his a
ccou
nt co
nsist
s of d
ealin
g with
all
the
com
bina
tions
of fi
ve, f
our,
thre
e, o
r tw
o of
the f
ive n
otes
of a
pr
oper
ly lo
cate
d fir
st sp
ecie
s of f
ifth (
i.e.,
D3,
E3,
F3,
G3,
and
A
3) w
here
by th
e low
est a
nd hi
ghes
t not
es (i
.e.,
D3
and A
3) a
re
incl
uded
in ea
ch co
mbi
natio
n. Th
e sen
se in
whi
ch th
ese c
ombi
- na
tions
of n
otes
can b
e con
sider
ed in
terr
uptio
ns of
the f
irst
spe-
ci
es of
fifth
is th
at ea
ch re
pres
ents
a fir
st sp
ecie
s of f
ifth o
ut o
f w
hich
hav
e be
en le
ft ze
ro, o
ne, t
wo,
or
thre
e not
es, r
espe
c-
tivel
y. In
this
way
, if th
e rem
aini
ng no
tes a
re pr
esen
ted m
elod
i- ca
lly, t
he sc
alar
or st
epw
ise or
deri
ng of
the f
ive n
otes
in a
spe-
ci
es o
f fift
h is i
nter
rupt
ed by
vari
ous o
miss
ions
(inc
ludi
ng th
e in
stan
ce in
whi
ch th
ere
are n
o om
issio
ns, i
.e.,
whe
re a
ll fiv
e no
tes
are
pres
ente
d).1
8 Mor
eove
r, th
e or
ient
ing
note
s of
a
prop
erly
loca
ted f
irst
spec
ies o
f fift
h (i.e
., D
3 an
d A3)
are
com
- m
on to
each
of th
e int
erru
ptio
ns. T
hus,
Mar
chet
to's s
yste
mat
ic
appr
oach
give
s rise
-in m
athe
mat
ical
nota
tion-
to 3
C3 +
3C
2 +
3C1
+ 3C
o =
1 +
3 +
3 +
1 =
8 co
mbi
natio
ns i
n al
l. If
one
at
tach
es M
arch
etto
's num
bers
for t
he re
sulti
ng in
terr
uptio
ns to
th
e eig
ht co
mbi
natio
ns ju
st de
scri
bed,
Tabl
e 2 re
sults
.19
In ea
ch of
his
acco
unts
of th
e eig
ht in
terr
uptio
ns of
the f
irst
sp
ecie
s of f
ifth,
Mar
chet
to (a
) des
crib
es in
wor
ds th
e int
erva
ls th
at a
ppea
r mel
odic
ally
in th
e in
terr
uptio
n, (b
) spe
cifie
s the
m
ode(
s) in
whi
ch su
ch an
inte
rrup
tion is
prop
er or
not,
and (
c)
prov
ides
a m
usic
al ex
ampl
e (or
two)
embo
dyin
g the
inte
rrup
- tio
n. M
arch
etto
's ver
bal d
escr
iptio
n of i
nter
rupt
ions
is co
uche
d in
term
s of t
he co
nsec
utiv
e mzi
odic
inte
rval
s that
appe
ar in
the
inte
rrup
tion.
For e
xam
ple,
he d
escr
ibes
the f
ourt
h int
erru
ptio
n
'8Th
us M
arch
etto
's use
of th
e ter
m in
terr
uptio
, whi
ch ot
herw
ise w
ould
sug-
ge
st a
n om
issio
n of
at l
east
one
note
, is p
oten
tially
misl
eadi
ng, b
ut co
nsist
ent
with
the m
oder
n not
ion o
f the
nul
l set
. 19
This i
s the
num
beri
ng em
ploy
ed in
MS
Mila
n, B
iblio
teca
Am
bros
iana
, D
.5 in
feri
ore,
fols.
52-
77v,
whi
ch be
caus
e of i
ts co
mpl
eten
ess a
nd ap
pare
ntly
ea
rly d
ate,
Her
linge
r jus
tifia
bly u
ses a
s the
bas
ic te
xt fo
r his
editi
on of
the L
uci-
dari
um. O
ther
sour
ces i
n th
e man
uscr
ipt tr
aditi
on ha
ve ot
her o
rder
ings
of th
e in
terr
uptio
ns. U
nles
s ot
herw
ise in
dica
ted,
ref
eren
ces
to t
he L
ucid
ariu
m
thro
ugho
ut th
is st
udy a
re ba
sed o
n th
e Mila
nese
man
uscr
ipt.
seem
s to
unde
rlie
his a
ccou
nt co
nsist
s of d
ealin
g with
all
the
com
bina
tions
of fi
ve, f
our,
thre
e, o
r tw
o of
the f
ive n
otes
of a
pr
oper
ly lo
cate
d fir
st sp
ecie
s of f
ifth (
i.e.,
D3,
E3,
F3,
G3,
and
A
3) w
here
by th
e low
est a
nd hi
ghes
t not
es (i
.e.,
D3
and A
3) a
re
incl
uded
in ea
ch co
mbi
natio
n. Th
e sen
se in
whi
ch th
ese c
ombi
- na
tions
of n
otes
can b
e con
sider
ed in
terr
uptio
ns of
the f
irst
spe-
ci
es of
fifth
is th
at ea
ch re
pres
ents
a fir
st sp
ecie
s of f
ifth o
ut o
f w
hich
hav
e be
en le
ft ze
ro, o
ne, t
wo,
or
thre
e not
es, r
espe
c-
tivel
y. In
this
way
, if th
e rem
aini
ng no
tes a
re pr
esen
ted m
elod
i- ca
lly, t
he sc
alar
or st
epw
ise or
deri
ng of
the f
ive n
otes
in a
spe-
ci
es o
f fift
h is i
nter
rupt
ed by
vari
ous o
miss
ions
(inc
ludi
ng th
e in
stan
ce in
whi
ch th
ere
are n
o om
issio
ns, i
.e.,
whe
re a
ll fiv
e no
tes
are
pres
ente
d).1
8 Mor
eove
r, th
e or
ient
ing
note
s of
a
prop
erly
loca
ted f
irst
spec
ies o
f fift
h (i.e
., D
3 an
d A3)
are
com
- m
on to
each
of th
e int
erru
ptio
ns. T
hus,
Mar
chet
to's s
yste
mat
ic
appr
oach
give
s rise
-in m
athe
mat
ical
nota
tion-
to 3
C3 +
3C
2 +
3C1
+ 3C
o =
1 +
3 +
3 +
1 =
8 co
mbi
natio
ns i
n al
l. If
one
at
tach
es M
arch
etto
's num
bers
for t
he re
sulti
ng in
terr
uptio
ns to
th
e eig
ht co
mbi
natio
ns ju
st de
scri
bed,
Tabl
e 2 re
sults
.19
In ea
ch of
his
acco
unts
of th
e eig
ht in
terr
uptio
ns of
the f
irst
sp
ecie
s of f
ifth,
Mar
chet
to (a
) des
crib
es in
wor
ds th
e int
erva
ls th
at a
ppea
r mel
odic
ally
in th
e in
terr
uptio
n, (b
) spe
cifie
s the
m
ode(
s) in
whi
ch su
ch an
inte
rrup
tion is
prop
er or
not,
and (
c)
prov
ides
a m
usic
al ex
ampl
e (or
two)
embo
dyin
g the
inte
rrup
- tio
n. M
arch
etto
's ver
bal d
escr
iptio
n of i
nter
rupt
ions
is co
uche
d in
term
s of t
he co
nsec
utiv
e mzi
odic
inte
rval
s that
appe
ar in
the
inte
rrup
tion.
For e
xam
ple,
he d
escr
ibes
the f
ourt
h int
erru
ptio
n
'8Th
us M
arch
etto
's use
of th
e ter
m in
terr
uptio
, whi
ch ot
herw
ise w
ould
sug-
ge
st a
n om
issio
n of
at l
east
one
note
, is p
oten
tially
misl
eadi
ng, b
ut co
nsist
ent
with
the m
oder
n not
ion o
f the
nul
l set
. 19
This i
s the
num
beri
ng em
ploy
ed in
MS
Mila
n, B
iblio
teca
Am
bros
iana
, D
.5 in
feri
ore,
fols.
52-
77v,
whi
ch be
caus
e of i
ts co
mpl
eten
ess a
nd ap
pare
ntly
ea
rly d
ate,
Her
linge
r jus
tifia
bly u
ses a
s the
bas
ic te
xt fo
r his
editi
on of
the L
uci-
dari
um. O
ther
sour
ces i
n th
e man
uscr
ipt tr
aditi
on ha
ve ot
her o
rder
ings
of th
e in
terr
uptio
ns. U
nles
s ot
herw
ise in
dica
ted,
ref
eren
ces
to t
he L
ucid
ariu
m
thro
ugho
ut th
is st
udy a
re ba
sed o
n th
e Mila
nese
man
uscr
ipt.
seem
s to
unde
rlie
his a
ccou
nt co
nsist
s of d
ealin
g with
all
the
com
bina
tions
of fi
ve, f
our,
thre
e, o
r tw
o of
the f
ive n
otes
of a
pr
oper
ly lo
cate
d fir
st sp
ecie
s of f
ifth (
i.e.,
D3,
E3,
F3,
G3,
and
A
3) w
here
by th
e low
est a
nd hi
ghes
t not
es (i
.e.,
D3
and A
3) a
re
incl
uded
in ea
ch co
mbi
natio
n. Th
e sen
se in
whi
ch th
ese c
ombi
- na
tions
of n
otes
can b
e con
sider
ed in
terr
uptio
ns of
the f
irst
spe-
ci
es of
fifth
is th
at ea
ch re
pres
ents
a fir
st sp
ecie
s of f
ifth o
ut o
f w
hich
hav
e be
en le
ft ze
ro, o
ne, t
wo,
or
thre
e not
es, r
espe
c-
tivel
y. In
this
way
, if th
e rem
aini
ng no
tes a
re pr
esen
ted m
elod
i- ca
lly, t
he sc
alar
or st
epw
ise or
deri
ng of
the f
ive n
otes
in a
spe-
ci
es o
f fift
h is i
nter
rupt
ed by
vari
ous o
miss
ions
(inc
ludi
ng th
e in
stan
ce in
whi
ch th
ere
are n
o om
issio
ns, i
.e.,
whe
re a
ll fiv
e no
tes
are
pres
ente
d).1
8 Mor
eove
r, th
e or
ient
ing
note
s of
a
prop
erly
loca
ted f
irst
spec
ies o
f fift
h (i.e
., D
3 an
d A3)
are
com
- m
on to
each
of th
e int
erru
ptio
ns. T
hus,
Mar
chet
to's s
yste
mat
ic
appr
oach
give
s rise
-in m
athe
mat
ical
nota
tion-
to 3
C3 +
3C
2 +
3C1
+ 3C
o =
1 +
3 +
3 +
1 =
8 co
mbi
natio
ns i
n al
l. If
one
at
tach
es M
arch
etto
's num
bers
for t
he re
sulti
ng in
terr
uptio
ns to
th
e eig
ht co
mbi
natio
ns ju
st de
scri
bed,
Tabl
e 2 re
sults
.19
In ea
ch of
his
acco
unts
of th
e eig
ht in
terr
uptio
ns of
the f
irst
sp
ecie
s of f
ifth,
Mar
chet
to (a
) des
crib
es in
wor
ds th
e int
erva
ls th
at a
ppea
r mel
odic
ally
in th
e in
terr
uptio
n, (b
) spe
cifie
s the
m
ode(
s) in
whi
ch su
ch an
inte
rrup
tion is
prop
er or
not,
and (
c)
prov
ides
a m
usic
al ex
ampl
e (or
two)
embo
dyin
g the
inte
rrup
- tio
n. M
arch
etto
's ver
bal d
escr
iptio
n of i
nter
rupt
ions
is co
uche
d in
term
s of t
he co
nsec
utiv
e mzi
odic
inte
rval
s that
appe
ar in
the
inte
rrup
tion.
For e
xam
ple,
he d
escr
ibes
the f
ourt
h int
erru
ptio
n
'8Th
us M
arch
etto
's use
of th
e ter
m in
terr
uptio
, whi
ch ot
herw
ise w
ould
sug-
ge
st a
n om
issio
n of
at l
east
one
note
, is p
oten
tially
misl
eadi
ng, b
ut co
nsist
ent
with
the m
oder
n not
ion o
f the
nul
l set
. 19
This i
s the
num
beri
ng em
ploy
ed in
MS
Mila
n, B
iblio
teca
Am
bros
iana
, D
.5 in
feri
ore,
fols.
52-
77v,
whi
ch be
caus
e of i
ts co
mpl
eten
ess a
nd ap
pare
ntly
ea
rly d
ate,
Her
linge
r jus
tifia
bly u
ses a
s the
bas
ic te
xt fo
r his
editi
on of
the L
uci-
dari
um. O
ther
sour
ces i
n th
e man
uscr
ipt tr
aditi
on ha
ve ot
her o
rder
ings
of th
e in
terr
uptio
ns. U
nles
s ot
herw
ise in
dica
ted,
ref
eren
ces
to t
he L
ucid
ariu
m
thro
ugho
ut th
is st
udy a
re ba
sed o
n th
e Mila
nese
man
uscr
ipt.
seem
s to
unde
rlie
his a
ccou
nt co
nsist
s of d
ealin
g with
all
the
com
bina
tions
of fi
ve, f
our,
thre
e, o
r tw
o of
the f
ive n
otes
of a
pr
oper
ly lo
cate
d fir
st sp
ecie
s of f
ifth (
i.e.,
D3,
E3,
F3,
G3,
and
A
3) w
here
by th
e low
est a
nd hi
ghes
t not
es (i
.e.,
D3
and A
3) a
re
incl
uded
in ea
ch co
mbi
natio
n. Th
e sen
se in
whi
ch th
ese c
ombi
- na
tions
of n
otes
can b
e con
sider
ed in
terr
uptio
ns of
the f
irst
spe-
ci
es of
fifth
is th
at ea
ch re
pres
ents
a fir
st sp
ecie
s of f
ifth o
ut o
f w
hich
hav
e be
en le
ft ze
ro, o
ne, t
wo,
or
thre
e not
es, r
espe
c-
tivel
y. In
this
way
, if th
e rem
aini
ng no
tes a
re pr
esen
ted m
elod
i- ca
lly, t
he sc
alar
or st
epw
ise or
deri
ng of
the f
ive n
otes
in a
spe-
ci
es o
f fift
h is i
nter
rupt
ed by
vari
ous o
miss
ions
(inc
ludi
ng th
e in
stan
ce in
whi
ch th
ere
are n
o om
issio
ns, i
.e.,
whe
re a
ll fiv
e no
tes
are
pres
ente
d).1
8 Mor
eove
r, th
e or
ient
ing
note
s of
a
prop
erly
loca
ted f
irst
spec
ies o
f fift
h (i.e
., D
3 an
d A3)
are
com
- m
on to
each
of th
e int
erru
ptio
ns. T
hus,
Mar
chet
to's s
yste
mat
ic
appr
oach
give
s rise
-in m
athe
mat
ical
nota
tion-
to 3
C3 +
3C
2 +
3C1
+ 3C
o =
1 +
3 +
3 +
1 =
8 co
mbi
natio
ns i
n al
l. If
one
at
tach
es M
arch
etto
's num
bers
for t
he re
sulti
ng in
terr
uptio
ns to
th
e eig
ht co
mbi
natio
ns ju
st de
scri
bed,
Tabl
e 2 re
sults
.19
In ea
ch of
his
acco
unts
of th
e eig
ht in
terr
uptio
ns of
the f
irst
sp
ecie
s of f
ifth,
Mar
chet
to (a
) des
crib
es in
wor
ds th
e int
erva
ls th
at a
ppea
r mel
odic
ally
in th
e in
terr
uptio
n, (b
) spe
cifie
s the
m
ode(
s) in
whi
ch su
ch an
inte
rrup
tion is
prop
er or
not,
and (
c)
prov
ides
a m
usic
al ex
ampl
e (or
two)
embo
dyin
g the
inte
rrup
- tio
n. M
arch
etto
's ver
bal d
escr
iptio
n of i
nter
rupt
ions
is co
uche
d in
term
s of t
he co
nsec
utiv
e mzi
odic
inte
rval
s that
appe
ar in
the
inte
rrup
tion.
For e
xam
ple,
he d
escr
ibes
the f
ourt
h int
erru
ptio
n
'8Th
us M
arch
etto
's use
of th
e ter
m in
terr
uptio
, whi
ch ot
herw
ise w
ould
sug-
ge
st a
n om
issio
n of
at l
east
one
note
, is p
oten
tially
misl
eadi
ng, b
ut co
nsist
ent
with
the m
oder
n not
ion o
f the
nul
l set
. 19
This i
s the
num
beri
ng em
ploy
ed in
MS
Mila
n, B
iblio
teca
Am
bros
iana
, D
.5 in
feri
ore,
fols.
52-
77v,
whi
ch be
caus
e of i
ts co
mpl
eten
ess a
nd ap
pare
ntly
ea
rly d
ate,
Her
linge
r jus
tifia
bly u
ses a
s the
bas
ic te
xt fo
r his
editi
on of
the L
uci-
dari
um. O
ther
sour
ces i
n th
e man
uscr
ipt tr
aditi
on ha
ve ot
her o
rder
ings
of th
e in
terr
uptio
ns. U
nles
s ot
herw
ise in
dica
ted,
ref
eren
ces
to t
he L
ucid
ariu
m
thro
ugho
ut th
is st
udy a
re ba
sed o
n th
e Mila
nese
man
uscr
ipt.
Tabl
e 2. T
he ei
ght i
nter
rupt
ions
of a
pro
perl
y loca
ted f
irst
spe-
ci
es of
fifth
(mid
dle C
= C
4)
Tabl
e 2. T
he ei
ght i
nter
rupt
ions
of a
pro
perl
y loca
ted f
irst
spe-
ci
es of
fifth
(mid
dle C
= C
4)
Tabl
e 2. T
he ei
ght i
nter
rupt
ions
of a
pro
perl
y loca
ted f
irst
spe-
ci
es of
fifth
(mid
dle C
= C
4)
Tabl
e 2. T
he ei
ght i
nter
rupt
ions
of a
pro
perl
y loca
ted f
irst
spe-
ci
es of
fifth
(mid
dle C
= C
4)
Tabl
e 2. T
he ei
ght i
nter
rupt
ions
of a
pro
perl
y loca
ted f
irst
spe-
ci
es of
fifth
(mid
dle C
= C
4)
Tabl
e 2. T
he ei
ght i
nter
rupt
ions
of a
pro
perl
y loca
ted f
irst
spe-
ci
es of
fifth
(mid
dle C
= C
4)
Com
bina
tions
D
3 E3
F3
D
3 E3
F3
D
3 E3
D
3 F3
D
3 E3
D
3 F3
D
3 D
3
Com
bina
tions
D
3 E3
F3
D
3 E3
F3
D
3 E3
D
3 F3
D
3 E3
D
3 F3
D
3 D
3
Com
bina
tions
D
3 E3
F3
D
3 E3
F3
D
3 E3
D
3 F3
D
3 E3
D
3 F3
D
3 D
3
Com
bina
tions
D
3 E3
F3
D
3 E3
F3
D
3 E3
D
3 F3
D
3 E3
D
3 F3
D
3 D
3
Com
bina
tions
D
3 E3
F3
D
3 E3
F3
D
3 E3
D
3 F3
D
3 E3
D
3 F3
D
3 D
3
Com
bina
tions
D
3 E3
F3
D
3 E3
F3
D
3 E3
D
3 F3
D
3 E3
D
3 F3
D
3 D
3
Mar
chet
to's n
umbe
ring
M
arch
etto
's num
beri
ng
Mar
chet
to's n
umbe
ring
M
arch
etto
's num
beri
ng
Mar
chet
to's n
umbe
ring
M
arch
etto
's num
beri
ng
G3
A3
A3
G3
A3
G3
A3
A3
A3
G3
A3
A3
G3
A3
A3
G3
A3
G3
A3
A3
A3
G3
A3
A3
G3
A3
A3
G3
A3
G3
A3
A3
A3
G3
A3
A3
G3
A3
A3
G3
A3
G3
A3
A3
A3
G3
A3
A3
G3
A3
A3
G3
A3
G3
A3
A3
A3
G3
A3
A3
G3
A3
A3
G3
A3
G3
A3
A3
A3
G3
A3
A3
1 6 3 7 2 5 4 8 1 6 3 7 2 5 4 8 1 6 3 7 2 5 4 8 1 6 3 7 2 5 4 8 1 6 3 7 2 5 4 8 1 6 3 7 2 5 4 8
as co
nsist
ing o
f a pe
rfec
t four
th an
d a m
ajor
seco
nd. T
his v
erba
l de
scri
ptio
n cor
resp
onds
to th
e unf
oldi
ng of
the i
nter
rupt
ion in
th
e mel
odic
prog
ress
ion D
3-G
3-A
3-G
3-D
3,
whi
ch se
rves
as
his m
usic
al ex
ampl
e of
the
inte
rrup
tion (
see
Ex. 6
, bel
ow).
Hen
ce, h
is co
ncep
tion
of th
e in
terr
uptio
ns' in
terv
allic
orde
r-
ings
see
ms
to b
e-in
th
e te
rmin
olog
y of
mod
ern
mus
ic
theo
ry-te
mpo
ral
(rat
her t
han
mer
ely c
onte
nt-b
ased
) in n
a-
ture
and
capa
ble o
f ret
rogr
ade p
rese
ntat
ion.
In h
is ex
ampl
es,
he g
ener
ally
pres
ents
bot
h w
hat m
ight
be
term
ed a
"ri
sing-
or
igin
al" f
orm
and a
"fa
lling
-ret
rogr
ade"
form
of th
e int
erru
p-
tion
(e.g
., fo
r th
e fo
urth
inte
rrup
tion d
escr
ibed
abov
e, h
e pr
esen
ts th
e m
elod
ic fi
gure
s D3-
G3-
A3,
an
d A
3-G
3-D
3,
resp
ectiv
ely-
the
A3'
s co
inci
de in
a s
ingl
e not
e). W
hen
he
pres
ents
both
form
s, he
cons
isten
tly pr
esen
ts th
e not
es in
thei
r ri
sing f
orm
befo
re h
e pre
sent
s the
m in
thei
r fal
ling f
orm
. If h
e pr
esen
ts on
ly on
e for
m of
an in
terr
uptio
n, it is
risin
g rat
her th
an
falli
ng. A
nd w
hen
he d
escr
ibes
the i
nter
rupt
ions
in w
ords
, he
cons
isten
tly m
entio
ns th
e int
erva
ls in r
ising
orde
r rat
her th
an in
fa
lling
orde
r. A
ll of
this
is sy
mpt
omat
ic of
the i
mpl
icit p
rim
acy
that
he a
ccor
ds to
risin
g fig
ures
. Inde
ed, t
hrou
ghou
t the L
uci-
dari
um ri
sing f
igur
es ar
e ass
ocia
ted w
ith be
ginn
ings
of p
assa
ges
and f
allin
g fig
ures
with
ends
of p
assa
ges.
as co
nsist
ing o
f a pe
rfec
t four
th an
d a m
ajor
seco
nd. T
his v
erba
l de
scri
ptio
n cor
resp
onds
to th
e unf
oldi
ng of
the i
nter
rupt
ion in
th
e mel
odic
prog
ress
ion D
3-G
3-A
3-G
3-D
3,
whi
ch se
rves
as
his m
usic
al ex
ampl
e of
the
inte
rrup
tion (
see
Ex. 6
, bel
ow).
Hen
ce, h
is co
ncep
tion
of th
e in
terr
uptio
ns' in
terv
allic
orde
r-
ings
see
ms
to b
e-in
th
e te
rmin
olog
y of
mod
ern
mus
ic
theo
ry-te
mpo
ral
(rat
her t
han
mer
ely c
onte
nt-b
ased
) in n
a-
ture
and
capa
ble o
f ret
rogr
ade p
rese
ntat
ion.
In h
is ex
ampl
es,
he g
ener
ally
pres
ents
bot
h w
hat m
ight
be
term
ed a
"ri
sing-
or
igin
al" f
orm
and a
"fa
lling
-ret
rogr
ade"
form
of th
e int
erru
p-
tion
(e.g
., fo
r th
e fo
urth
inte
rrup
tion d
escr
ibed
abov
e, h
e pr
esen
ts th
e m
elod
ic fi
gure
s D3-
G3-
A3,
an
d A
3-G
3-D
3,
resp
ectiv
ely-
the
A3'
s co
inci
de in
a s
ingl
e not
e). W
hen
he
pres
ents
both
form
s, he
cons
isten
tly pr
esen
ts th
e not
es in
thei
r ri
sing f
orm
befo
re h
e pre
sent
s the
m in
thei
r fal
ling f
orm
. If h
e pr
esen
ts on
ly on
e for
m of
an in
terr
uptio
n, it is
risin
g rat
her th
an
falli
ng. A
nd w
hen
he d
escr
ibes
the i
nter
rupt
ions
in w
ords
, he
cons
isten
tly m
entio
ns th
e int
erva
ls in r
ising
orde
r rat
her th
an in
fa
lling
orde
r. A
ll of
this
is sy
mpt
omat
ic of
the i
mpl
icit p
rim
acy
that
he a
ccor
ds to
risin
g fig
ures
. Inde
ed, t
hrou
ghou
t the L
uci-
dari
um ri
sing f
igur
es ar
e ass
ocia
ted w
ith be
ginn
ings
of p
assa
ges
and f
allin
g fig
ures
with
ends
of p
assa
ges.
as co
nsist
ing o
f a pe
rfec
t four
th an
d a m
ajor
seco
nd. T
his v
erba
l de
scri
ptio
n cor
resp
onds
to th
e unf
oldi
ng of
the i
nter
rupt
ion in
th
e mel
odic
prog
ress
ion D
3-G
3-A
3-G
3-D
3,
whi
ch se
rves
as
his m
usic
al ex
ampl
e of
the
inte
rrup
tion (
see
Ex. 6
, bel
ow).
Hen
ce, h
is co
ncep
tion
of th
e in
terr
uptio
ns' in
terv
allic
orde
r-
ings
see
ms
to b
e-in
th
e te
rmin
olog
y of
mod
ern
mus
ic
theo
ry-te
mpo
ral
(rat
her t
han
mer
ely c
onte
nt-b
ased
) in n
a-
ture
and
capa
ble o
f ret
rogr
ade p
rese
ntat
ion.
In h
is ex
ampl
es,
he g
ener
ally
pres
ents
bot
h w
hat m
ight
be
term
ed a
"ri
sing-
or
igin
al" f
orm
and a
"fa
lling
-ret
rogr
ade"
form
of th
e int
erru
p-
tion
(e.g
., fo
r th
e fo
urth
inte
rrup
tion d
escr
ibed
abov
e, h
e pr
esen
ts th
e m
elod
ic fi
gure
s D3-
G3-
A3,
an
d A
3-G
3-D
3,
resp
ectiv
ely-
the
A3'
s co
inci
de in
a s
ingl
e not
e). W
hen
he
pres
ents
both
form
s, he
cons
isten
tly pr
esen
ts th
e not
es in
thei
r ri
sing f
orm
befo
re h
e pre
sent
s the
m in
thei
r fal
ling f
orm
. If h
e pr
esen
ts on
ly on
e for
m of
an in
terr
uptio
n, it is
risin
g rat
her th
an
falli
ng. A
nd w
hen
he d
escr
ibes
the i
nter
rupt
ions
in w
ords
, he
cons
isten
tly m
entio
ns th
e int
erva
ls in r
ising
orde
r rat
her th
an in
fa
lling
orde
r. A
ll of
this
is sy
mpt
omat
ic of
the i
mpl
icit p
rim
acy
that
he a
ccor
ds to
risin
g fig
ures
. Inde
ed, t
hrou
ghou
t the L
uci-
dari
um ri
sing f
igur
es ar
e ass
ocia
ted w
ith be
ginn
ings
of p
assa
ges
and f
allin
g fig
ures
with
ends
of p
assa
ges.
as co
nsist
ing o
f a pe
rfec
t four
th an
d a m
ajor
seco
nd. T
his v
erba
l de
scri
ptio
n cor
resp
onds
to th
e unf
oldi
ng of
the i
nter
rupt
ion in
th
e mel
odic
prog
ress
ion D
3-G
3-A
3-G
3-D
3,
whi
ch se
rves
as
his m
usic
al ex
ampl
e of
the
inte
rrup
tion (
see
Ex. 6
, bel
ow).
Hen
ce, h
is co
ncep
tion
of th
e in
terr
uptio
ns' in
terv
allic
orde
r-
ings
see
ms
to b
e-in
th
e te
rmin
olog
y of
mod
ern
mus
ic
theo
ry-te
mpo
ral
(rat
her t
han
mer
ely c
onte
nt-b
ased
) in n
a-
ture
and
capa
ble o
f ret
rogr
ade p
rese
ntat
ion.
In h
is ex
ampl
es,
he g
ener
ally
pres
ents
bot
h w
hat m
ight
be
term
ed a
"ri
sing-
or
igin
al" f
orm
and a
"fa
lling
-ret
rogr
ade"
form
of th
e int
erru
p-
tion
(e.g
., fo
r th
e fo
urth
inte
rrup
tion d
escr
ibed
abov
e, h
e pr
esen
ts th
e m
elod
ic fi
gure
s D3-
G3-
A3,
an
d A
3-G
3-D
3,
resp
ectiv
ely-
the
A3'
s co
inci
de in
a s
ingl
e not
e). W
hen
he
pres
ents
both
form
s, he
cons
isten
tly pr
esen
ts th
e not
es in
thei
r ri
sing f
orm
befo
re h
e pre
sent
s the
m in
thei
r fal
ling f
orm
. If h
e pr
esen
ts on
ly on
e for
m of
an in
terr
uptio
n, it is
risin
g rat
her th
an
falli
ng. A
nd w
hen
he d
escr
ibes
the i
nter
rupt
ions
in w
ords
, he
cons
isten
tly m
entio
ns th
e int
erva
ls in r
ising
orde
r rat
her th
an in
fa
lling
orde
r. A
ll of
this
is sy
mpt
omat
ic of
the i
mpl
icit p
rim
acy
that
he a
ccor
ds to
risin
g fig
ures
. Inde
ed, t
hrou
ghou
t the L
uci-
dari
um ri
sing f
igur
es ar
e ass
ocia
ted w
ith be
ginn
ings
of p
assa
ges
and f
allin
g fig
ures
with
ends
of p
assa
ges.
as co
nsist
ing o
f a pe
rfec
t four
th an
d a m
ajor
seco
nd. T
his v
erba
l de
scri
ptio
n cor
resp
onds
to th
e unf
oldi
ng of
the i
nter
rupt
ion in
th
e mel
odic
prog
ress
ion D
3-G
3-A
3-G
3-D
3,
whi
ch se
rves
as
his m
usic
al ex
ampl
e of
the
inte
rrup
tion (
see
Ex. 6
, bel
ow).
Hen
ce, h
is co
ncep
tion
of th
e in
terr
uptio
ns' in
terv
allic
orde
r-
ings
see
ms
to b
e-in
th
e te
rmin
olog
y of
mod
ern
mus
ic
theo
ry-te
mpo
ral
(rat
her t
han
mer
ely c
onte
nt-b
ased
) in n
a-
ture
and
capa
ble o
f ret
rogr
ade p
rese
ntat
ion.
In h
is ex
ampl
es,
he g
ener
ally
pres
ents
bot
h w
hat m
ight
be
term
ed a
"ri
sing-
or
igin
al" f
orm
and a
"fa
lling
-ret
rogr
ade"
form
of th
e int
erru
p-
tion
(e.g
., fo
r th
e fo
urth
inte
rrup
tion d
escr
ibed
abov
e, h
e pr
esen
ts th
e m
elod
ic fi
gure
s D3-
G3-
A3,
an
d A
3-G
3-D
3,
resp
ectiv
ely-
the
A3'
s co
inci
de in
a s
ingl
e not
e). W
hen
he
pres
ents
both
form
s, he
cons
isten
tly pr
esen
ts th
e not
es in
thei
r ri
sing f
orm
befo
re h
e pre
sent
s the
m in
thei
r fal
ling f
orm
. If h
e pr
esen
ts on
ly on
e for
m of
an in
terr
uptio
n, it is
risin
g rat
her th
an
falli
ng. A
nd w
hen
he d
escr
ibes
the i
nter
rupt
ions
in w
ords
, he
cons
isten
tly m
entio
ns th
e int
erva
ls in r
ising
orde
r rat
her th
an in
fa
lling
orde
r. A
ll of
this
is sy
mpt
omat
ic of
the i
mpl
icit p
rim
acy
that
he a
ccor
ds to
risin
g fig
ures
. Inde
ed, t
hrou
ghou
t the L
uci-
dari
um ri
sing f
igur
es ar
e ass
ocia
ted w
ith be
ginn
ings
of p
assa
ges
and f
allin
g fig
ures
with
ends
of p
assa
ges.
as co
nsist
ing o
f a pe
rfec
t four
th an
d a m
ajor
seco
nd. T
his v
erba
l de
scri
ptio
n cor
resp
onds
to th
e unf
oldi
ng of
the i
nter
rupt
ion in
th
e mel
odic
prog
ress
ion D
3-G
3-A
3-G
3-D
3,
whi
ch se
rves
as
his m
usic
al ex
ampl
e of
the
inte
rrup
tion (
see
Ex. 6
, bel
ow).
Hen
ce, h
is co
ncep
tion
of th
e in
terr
uptio
ns' in
terv
allic
orde
r-
ings
see
ms
to b
e-in
th
e te
rmin
olog
y of
mod
ern
mus
ic
theo
ry-te
mpo
ral
(rat
her t
han
mer
ely c
onte
nt-b
ased
) in n
a-
ture
and
capa
ble o
f ret
rogr
ade p
rese
ntat
ion.
In h
is ex
ampl
es,
he g
ener
ally
pres
ents
bot
h w
hat m
ight
be
term
ed a
"ri
sing-
or
igin
al" f
orm
and a
"fa
lling
-ret
rogr
ade"
form
of th
e int
erru
p-
tion
(e.g
., fo
r th
e fo
urth
inte
rrup
tion d
escr
ibed
abov
e, h
e pr
esen
ts th
e m
elod
ic fi
gure
s D3-
G3-
A3,
an
d A
3-G
3-D
3,
resp
ectiv
ely-
the
A3'
s co
inci
de in
a s
ingl
e not
e). W
hen
he
pres
ents
both
form
s, he
cons
isten
tly pr
esen
ts th
e not
es in
thei
r ri
sing f
orm
befo
re h
e pre
sent
s the
m in
thei
r fal
ling f
orm
. If h
e pr
esen
ts on
ly on
e for
m of
an in
terr
uptio
n, it is
risin
g rat
her th
an
falli
ng. A
nd w
hen
he d
escr
ibes
the i
nter
rupt
ions
in w
ords
, he
cons
isten
tly m
entio
ns th
e int
erva
ls in r
ising
orde
r rat
her th
an in
fa
lling
orde
r. A
ll of
this
is sy
mpt
omat
ic of
the i
mpl
icit p
rim
acy
that
he a
ccor
ds to
risin
g fig
ures
. Inde
ed, t
hrou
ghou
t the L
uci-
dari
um ri
sing f
igur
es ar
e ass
ocia
ted w
ith be
ginn
ings
of p
assa
ges
and f
allin
g fig
ures
with
ends
of p
assa
ges.
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
124
Mus
ic Th
eory
Spec
trum
12
4 M
usic
Theo
ry Sp
ectr
um
124
Mus
ic Th
eory
Spec
trum
12
4 M
usic
Theo
ry Sp
ectr
um
124
Mus
ic Th
eory
Spec
trum
12
4 M
usic
Theo
ry Sp
ectr
um
As w
as po
inte
d out
abo
ve, M
arch
etto
spec
ifies
for e
ach
in-
terr
uptio
n the
mod
e(s)
in w
hich
it ap
pear
s pro
perl
y or n
ot. T
o co
nvey
the n
otio
n of a
prop
er ap
pear
ance
, Mar
chet
to ge
nera
lly
uses
the a
dver
b pro
prie
(pro
perl
y). T
o ind
icat
e an
"im
prop
er"
appe
aran
ce, h
e ge
nera
lly us
es th
e ad
ject
ive c
omm
ixta
(com
- m
ixed
). Th
e sig
nific
ance
of a
com
mix
ed in
terr
uptio
n see
ms t
o be
that
it im
plie
s a m
ode d
iffer
ent fr
om th
e mod
e im
plie
d by
the l
arge
r mel
ody i
n whi
ch it
mig
ht be
embe
dded
. For
exam
ple,
an
inte
rrup
tion th
at is
prop
er in
the f
irst
mod
e mig
ht ap
pear
as
a mel
odic
pass
age w
ithin
a la
rger
mel
ody t
hat h
as, a
part
from
th
e pa
ssag
e in
ques
tion,
a fo
urth
- or
sixth
-mod
e cha
ract
er.
Thus
, the
embe
dded
pass
age c
an b
e co
nsid
ered
to e
mbo
dy a
sort
of m
odal
"mod
ulat
ion"
(or w
hat I
wou
ld pr
efer
to te
rm a
com
mix
ture
) with
rega
rd to
the m
odal
impl
icat
ions
of th
e mel
- od
y tha
t sur
roun
ds it.
How
ever
, Mar
chet
to, in
his
mus
ical
ex-
ampl
es, d
oes n
ot ge
nera
lly pr
esen
t suc
h com
mix
ed pa
ssag
es in
a
larg
er m
elod
ic co
ntex
t. Pe
rhap
s thi
s is f
or re
ason
s of e
con-
om
y, fo
r to d
o so s
yste
mat
ical
ly wou
ld ha
ve in
volv
ed pr
ovid
ing
eigh
t exa
mpl
es-o
ne f
or ea
ch of
the e
ight
mod
es-fo
r ea
ch of
th
e eig
ht in
terr
uptio
ns (i.
e., 8
* 8 =
64 e
xam
ples
). A
s no
ted
abov
e, M
arch
etto
gene
rally
empl
oys t
he te
rms
prop
rie a
nd co
mm
ixta
to d
enot
e int
erru
ptio
ns th
at ar
e pro
per
to th
e sur
roun
ding
mod
ality
or di
scre
pant
with
it, re
spec
tivel
y.
He u
ses o
ther
term
s as w
ell: s
empe
r (alw
ays)
, saep
e (of
ten)
, ali-
qu
ando
(som
etim
es), a
nd ra
ro (r
arel
y). E
ach o
f the
se ad
verb
s co
nvey
s the
mea
ning
of a
deg
ree o
f reg
ular
ity or
nor
mal
cy by
m
eans
of th
e not
ion
of fr
eque
ncy o
r rat
e of o
ccur
renc
e. T
his
mig
ht se
em to
impl
y tha
t Mar
chet
to ar
rive
d at h
is ap
plic
atio
n of
thes
e ter
ms b
y an
empi
rica
l stud
y of c
hant
mel
odie
s.20 H
ow-
ever
, whe
n M
arch
etto
wri
tes t
hat a
giv
en in
terr
uptio
n is
"al-
20Ti
ncto
ris la
ter a
sser
ts th
at su
ch w
as th
e cas
e, fo
r ini
tials,
whe
n he w
rite
s th
at "m
oreo
ver th
ere w
ere s
ome p
eopl
e who
, afte
r the
y had
exam
ined
all t
he
initi
als in
sim
ple G
eorg
ian c
hant
with
the g
reat
est c
are,
assig
ned t
o ea
ch m
ode
a cer
tain
num
ber o
f ini
tials"
(fuer
unt au
tem
nonn
ulli q
uipo
stqu
am om
niap
rin-
ci
pia s
impl
icis
cant
us G
rego
rian
i sum
ma c
um d
ilige
ntia
pers
ecru
tati fu
issen
t,
As w
as po
inte
d out
abo
ve, M
arch
etto
spec
ifies
for e
ach
in-
terr
uptio
n the
mod
e(s)
in w
hich
it ap
pear
s pro
perl
y or n
ot. T
o co
nvey
the n
otio
n of a
prop
er ap
pear
ance
, Mar
chet
to ge
nera
lly
uses
the a
dver
b pro
prie
(pro
perl
y). T
o ind
icat
e an
"im
prop
er"
appe
aran
ce, h
e ge
nera
lly us
es th
e ad
ject
ive c
omm
ixta
(com
- m
ixed
). Th
e sig
nific
ance
of a
com
mix
ed in
terr
uptio
n see
ms t
o be
that
it im
plie
s a m
ode d
iffer
ent fr
om th
e mod
e im
plie
d by
the l
arge
r mel
ody i
n whi
ch it
mig
ht be
embe
dded
. For
exam
ple,
an
inte
rrup
tion th
at is
prop
er in
the f
irst
mod
e mig
ht ap
pear
as
a mel
odic
pass
age w
ithin
a la
rger
mel
ody t
hat h
as, a
part
from
th
e pa
ssag
e in
ques
tion,
a fo
urth
- or
sixth
-mod
e cha
ract
er.
Thus
, the
embe
dded
pass
age c
an b
e co
nsid
ered
to e
mbo
dy a
sort
of m
odal
"mod
ulat
ion"
(or w
hat I
wou
ld pr
efer
to te
rm a
com
mix
ture
) with
rega
rd to
the m
odal
impl
icat
ions
of th
e mel
- od
y tha
t sur
roun
ds it.
How
ever
, Mar
chet
to, in
his
mus
ical
ex-
ampl
es, d
oes n
ot ge
nera
lly pr
esen
t suc
h com
mix
ed pa
ssag
es in
a
larg
er m
elod
ic co
ntex
t. Pe
rhap
s thi
s is f
or re
ason
s of e
con-
om
y, fo
r to d
o so s
yste
mat
ical
ly wou
ld ha
ve in
volv
ed pr
ovid
ing
eigh
t exa
mpl
es-o
ne f
or ea
ch of
the e
ight
mod
es-fo
r ea
ch of
th
e eig
ht in
terr
uptio
ns (i.
e., 8
* 8 =
64 e
xam
ples
). A
s no
ted
abov
e, M
arch
etto
gene
rally
empl
oys t
he te
rms
prop
rie a
nd co
mm
ixta
to d
enot
e int
erru
ptio
ns th
at ar
e pro
per
to th
e sur
roun
ding
mod
ality
or di
scre
pant
with
it, re
spec
tivel
y.
He u
ses o
ther
term
s as w
ell: s
empe
r (alw
ays)
, saep
e (of
ten)
, ali-
qu
ando
(som
etim
es), a
nd ra
ro (r
arel
y). E
ach o
f the
se ad
verb
s co
nvey
s the
mea
ning
of a
deg
ree o
f reg
ular
ity or
nor
mal
cy by
m
eans
of th
e not
ion
of fr
eque
ncy o
r rat
e of o
ccur
renc
e. T
his
mig
ht se
em to
impl
y tha
t Mar
chet
to ar
rive
d at h
is ap
plic
atio
n of
thes
e ter
ms b
y an
empi
rica
l stud
y of c
hant
mel
odie
s.20 H
ow-
ever
, whe
n M
arch
etto
wri
tes t
hat a
giv
en in
terr
uptio
n is
"al-
20Ti
ncto
ris la
ter a
sser
ts th
at su
ch w
as th
e cas
e, fo
r ini
tials,
whe
n he w
rite
s th
at "m
oreo
ver th
ere w
ere s
ome p
eopl
e who
, afte
r the
y had
exam
ined
all t
he
initi
als in
sim
ple G
eorg
ian c
hant
with
the g
reat
est c
are,
assig
ned t
o ea
ch m
ode
a cer
tain
num
ber o
f ini
tials"
(fuer
unt au
tem
nonn
ulli q
uipo
stqu
am om
niap
rin-
ci
pia s
impl
icis
cant
us G
rego
rian
i sum
ma c
um d
ilige
ntia
pers
ecru
tati fu
issen
t,
As w
as po
inte
d out
abo
ve, M
arch
etto
spec
ifies
for e
ach
in-
terr
uptio
n the
mod
e(s)
in w
hich
it ap
pear
s pro
perl
y or n
ot. T
o co
nvey
the n
otio
n of a
prop
er ap
pear
ance
, Mar
chet
to ge
nera
lly
uses
the a
dver
b pro
prie
(pro
perl
y). T
o ind
icat
e an
"im
prop
er"
appe
aran
ce, h
e ge
nera
lly us
es th
e ad
ject
ive c
omm
ixta
(com
- m
ixed
). Th
e sig
nific
ance
of a
com
mix
ed in
terr
uptio
n see
ms t
o be
that
it im
plie
s a m
ode d
iffer
ent fr
om th
e mod
e im
plie
d by
the l
arge
r mel
ody i
n whi
ch it
mig
ht be
embe
dded
. For
exam
ple,
an
inte
rrup
tion th
at is
prop
er in
the f
irst
mod
e mig
ht ap
pear
as
a mel
odic
pass
age w
ithin
a la
rger
mel
ody t
hat h
as, a
part
from
th
e pa
ssag
e in
ques
tion,
a fo
urth
- or
sixth
-mod
e cha
ract
er.
Thus
, the
embe
dded
pass
age c
an b
e co
nsid
ered
to e
mbo
dy a
sort
of m
odal
"mod
ulat
ion"
(or w
hat I
wou
ld pr
efer
to te
rm a
com
mix
ture
) with
rega
rd to
the m
odal
impl
icat
ions
of th
e mel
- od
y tha
t sur
roun
ds it.
How
ever
, Mar
chet
to, in
his
mus
ical
ex-
ampl
es, d
oes n
ot ge
nera
lly pr
esen
t suc
h com
mix
ed pa
ssag
es in
a
larg
er m
elod
ic co
ntex
t. Pe
rhap
s thi
s is f
or re
ason
s of e
con-
om
y, fo
r to d
o so s
yste
mat
ical
ly wou
ld ha
ve in
volv
ed pr
ovid
ing
eigh
t exa
mpl
es-o
ne f
or ea
ch of
the e
ight
mod
es-fo
r ea
ch of
th
e eig
ht in
terr
uptio
ns (i.
e., 8
* 8 =
64 e
xam
ples
). A
s no
ted
abov
e, M
arch
etto
gene
rally
empl
oys t
he te
rms
prop
rie a
nd co
mm
ixta
to d
enot
e int
erru
ptio
ns th
at ar
e pro
per
to th
e sur
roun
ding
mod
ality
or di
scre
pant
with
it, re
spec
tivel
y.
He u
ses o
ther
term
s as w
ell: s
empe
r (alw
ays)
, saep
e (of
ten)
, ali-
qu
ando
(som
etim
es), a
nd ra
ro (r
arel
y). E
ach o
f the
se ad
verb
s co
nvey
s the
mea
ning
of a
deg
ree o
f reg
ular
ity or
nor
mal
cy by
m
eans
of th
e not
ion
of fr
eque
ncy o
r rat
e of o
ccur
renc
e. T
his
mig
ht se
em to
impl
y tha
t Mar
chet
to ar
rive
d at h
is ap
plic
atio
n of
thes
e ter
ms b
y an
empi
rica
l stud
y of c
hant
mel
odie
s.20 H
ow-
ever
, whe
n M
arch
etto
wri
tes t
hat a
giv
en in
terr
uptio
n is
"al-
20Ti
ncto
ris la
ter a
sser
ts th
at su
ch w
as th
e cas
e, fo
r ini
tials,
whe
n he w
rite
s th
at "m
oreo
ver th
ere w
ere s
ome p
eopl
e who
, afte
r the
y had
exam
ined
all t
he
initi
als in
sim
ple G
eorg
ian c
hant
with
the g
reat
est c
are,
assig
ned t
o ea
ch m
ode
a cer
tain
num
ber o
f ini
tials"
(fuer
unt au
tem
nonn
ulli q
uipo
stqu
am om
niap
rin-
ci
pia s
impl
icis
cant
us G
rego
rian
i sum
ma c
um d
ilige
ntia
pers
ecru
tati fu
issen
t,
As w
as po
inte
d out
abo
ve, M
arch
etto
spec
ifies
for e
ach
in-
terr
uptio
n the
mod
e(s)
in w
hich
it ap
pear
s pro
perl
y or n
ot. T
o co
nvey
the n
otio
n of a
prop
er ap
pear
ance
, Mar
chet
to ge
nera
lly
uses
the a
dver
b pro
prie
(pro
perl
y). T
o ind
icat
e an
"im
prop
er"
appe
aran
ce, h
e ge
nera
lly us
es th
e ad
ject
ive c
omm
ixta
(com
- m
ixed
). Th
e sig
nific
ance
of a
com
mix
ed in
terr
uptio
n see
ms t
o be
that
it im
plie
s a m
ode d
iffer
ent fr
om th
e mod
e im
plie
d by
the l
arge
r mel
ody i
n whi
ch it
mig
ht be
embe
dded
. For
exam
ple,
an
inte
rrup
tion th
at is
prop
er in
the f
irst
mod
e mig
ht ap
pear
as
a mel
odic
pass
age w
ithin
a la
rger
mel
ody t
hat h
as, a
part
from
th
e pa
ssag
e in
ques
tion,
a fo
urth
- or
sixth
-mod
e cha
ract
er.
Thus
, the
embe
dded
pass
age c
an b
e co
nsid
ered
to e
mbo
dy a
sort
of m
odal
"mod
ulat
ion"
(or w
hat I
wou
ld pr
efer
to te
rm a
com
mix
ture
) with
rega
rd to
the m
odal
impl
icat
ions
of th
e mel
- od
y tha
t sur
roun
ds it.
How
ever
, Mar
chet
to, in
his
mus
ical
ex-
ampl
es, d
oes n
ot ge
nera
lly pr
esen
t suc
h com
mix
ed pa
ssag
es in
a
larg
er m
elod
ic co
ntex
t. Pe
rhap
s thi
s is f
or re
ason
s of e
con-
om
y, fo
r to d
o so s
yste
mat
ical
ly wou
ld ha
ve in
volv
ed pr
ovid
ing
eigh
t exa
mpl
es-o
ne f
or ea
ch of
the e
ight
mod
es-fo
r ea
ch of
th
e eig
ht in
terr
uptio
ns (i.
e., 8
* 8 =
64 e
xam
ples
). A
s no
ted
abov
e, M
arch
etto
gene
rally
empl
oys t
he te
rms
prop
rie a
nd co
mm
ixta
to d
enot
e int
erru
ptio
ns th
at ar
e pro
per
to th
e sur
roun
ding
mod
ality
or di
scre
pant
with
it, re
spec
tivel
y.
He u
ses o
ther
term
s as w
ell: s
empe
r (alw
ays)
, saep
e (of
ten)
, ali-
qu
ando
(som
etim
es), a
nd ra
ro (r
arel
y). E
ach o
f the
se ad
verb
s co
nvey
s the
mea
ning
of a
deg
ree o
f reg
ular
ity or
nor
mal
cy by
m
eans
of th
e not
ion
of fr
eque
ncy o
r rat
e of o
ccur
renc
e. T
his
mig
ht se
em to
impl
y tha
t Mar
chet
to ar
rive
d at h
is ap
plic
atio
n of
thes
e ter
ms b
y an
empi
rica
l stud
y of c
hant
mel
odie
s.20 H
ow-
ever
, whe
n M
arch
etto
wri
tes t
hat a
giv
en in
terr
uptio
n is
"al-
20Ti
ncto
ris la
ter a
sser
ts th
at su
ch w
as th
e cas
e, fo
r ini
tials,
whe
n he w
rite
s th
at "m
oreo
ver th
ere w
ere s
ome p
eopl
e who
, afte
r the
y had
exam
ined
all t
he
initi
als in
sim
ple G
eorg
ian c
hant
with
the g
reat
est c
are,
assig
ned t
o ea
ch m
ode
a cer
tain
num
ber o
f ini
tials"
(fuer
unt au
tem
nonn
ulli q
uipo
stqu
am om
niap
rin-
ci
pia s
impl
icis
cant
us G
rego
rian
i sum
ma c
um d
ilige
ntia
pers
ecru
tati fu
issen
t,
As w
as po
inte
d out
abo
ve, M
arch
etto
spec
ifies
for e
ach
in-
terr
uptio
n the
mod
e(s)
in w
hich
it ap
pear
s pro
perl
y or n
ot. T
o co
nvey
the n
otio
n of a
prop
er ap
pear
ance
, Mar
chet
to ge
nera
lly
uses
the a
dver
b pro
prie
(pro
perl
y). T
o ind
icat
e an
"im
prop
er"
appe
aran
ce, h
e ge
nera
lly us
es th
e ad
ject
ive c
omm
ixta
(com
- m
ixed
). Th
e sig
nific
ance
of a
com
mix
ed in
terr
uptio
n see
ms t
o be
that
it im
plie
s a m
ode d
iffer
ent fr
om th
e mod
e im
plie
d by
the l
arge
r mel
ody i
n whi
ch it
mig
ht be
embe
dded
. For
exam
ple,
an
inte
rrup
tion th
at is
prop
er in
the f
irst
mod
e mig
ht ap
pear
as
a mel
odic
pass
age w
ithin
a la
rger
mel
ody t
hat h
as, a
part
from
th
e pa
ssag
e in
ques
tion,
a fo
urth
- or
sixth
-mod
e cha
ract
er.
Thus
, the
embe
dded
pass
age c
an b
e co
nsid
ered
to e
mbo
dy a
sort
of m
odal
"mod
ulat
ion"
(or w
hat I
wou
ld pr
efer
to te
rm a
com
mix
ture
) with
rega
rd to
the m
odal
impl
icat
ions
of th
e mel
- od
y tha
t sur
roun
ds it.
How
ever
, Mar
chet
to, in
his
mus
ical
ex-
ampl
es, d
oes n
ot ge
nera
lly pr
esen
t suc
h com
mix
ed pa
ssag
es in
a
larg
er m
elod
ic co
ntex
t. Pe
rhap
s thi
s is f
or re
ason
s of e
con-
om
y, fo
r to d
o so s
yste
mat
ical
ly wou
ld ha
ve in
volv
ed pr
ovid
ing
eigh
t exa
mpl
es-o
ne f
or ea
ch of
the e
ight
mod
es-fo
r ea
ch of
th
e eig
ht in
terr
uptio
ns (i.
e., 8
* 8 =
64 e
xam
ples
). A
s no
ted
abov
e, M
arch
etto
gene
rally
empl
oys t
he te
rms
prop
rie a
nd co
mm
ixta
to d
enot
e int
erru
ptio
ns th
at ar
e pro
per
to th
e sur
roun
ding
mod
ality
or di
scre
pant
with
it, re
spec
tivel
y.
He u
ses o
ther
term
s as w
ell: s
empe
r (alw
ays)
, saep
e (of
ten)
, ali-
qu
ando
(som
etim
es), a
nd ra
ro (r
arel
y). E
ach o
f the
se ad
verb
s co
nvey
s the
mea
ning
of a
deg
ree o
f reg
ular
ity or
nor
mal
cy by
m
eans
of th
e not
ion
of fr
eque
ncy o
r rat
e of o
ccur
renc
e. T
his
mig
ht se
em to
impl
y tha
t Mar
chet
to ar
rive
d at h
is ap
plic
atio
n of
thes
e ter
ms b
y an
empi
rica
l stud
y of c
hant
mel
odie
s.20 H
ow-
ever
, whe
n M
arch
etto
wri
tes t
hat a
giv
en in
terr
uptio
n is
"al-
20Ti
ncto
ris la
ter a
sser
ts th
at su
ch w
as th
e cas
e, fo
r ini
tials,
whe
n he w
rite
s th
at "m
oreo
ver th
ere w
ere s
ome p
eopl
e who
, afte
r the
y had
exam
ined
all t
he
initi
als in
sim
ple G
eorg
ian c
hant
with
the g
reat
est c
are,
assig
ned t
o ea
ch m
ode
a cer
tain
num
ber o
f ini
tials"
(fuer
unt au
tem
nonn
ulli q
uipo
stqu
am om
niap
rin-
ci
pia s
impl
icis
cant
us G
rego
rian
i sum
ma c
um d
ilige
ntia
pers
ecru
tati fu
issen
t,
As w
as po
inte
d out
abo
ve, M
arch
etto
spec
ifies
for e
ach
in-
terr
uptio
n the
mod
e(s)
in w
hich
it ap
pear
s pro
perl
y or n
ot. T
o co
nvey
the n
otio
n of a
prop
er ap
pear
ance
, Mar
chet
to ge
nera
lly
uses
the a
dver
b pro
prie
(pro
perl
y). T
o ind
icat
e an
"im
prop
er"
appe
aran
ce, h
e ge
nera
lly us
es th
e ad
ject
ive c
omm
ixta
(com
- m
ixed
). Th
e sig
nific
ance
of a
com
mix
ed in
terr
uptio
n see
ms t
o be
that
it im
plie
s a m
ode d
iffer
ent fr
om th
e mod
e im
plie
d by
the l
arge
r mel
ody i
n whi
ch it
mig
ht be
embe
dded
. For
exam
ple,
an
inte
rrup
tion th
at is
prop
er in
the f
irst
mod
e mig
ht ap
pear
as
a mel
odic
pass
age w
ithin
a la
rger
mel
ody t
hat h
as, a
part
from
th
e pa
ssag
e in
ques
tion,
a fo
urth
- or
sixth
-mod
e cha
ract
er.
Thus
, the
embe
dded
pass
age c
an b
e co
nsid
ered
to e
mbo
dy a
sort
of m
odal
"mod
ulat
ion"
(or w
hat I
wou
ld pr
efer
to te
rm a
com
mix
ture
) with
rega
rd to
the m
odal
impl
icat
ions
of th
e mel
- od
y tha
t sur
roun
ds it.
How
ever
, Mar
chet
to, in
his
mus
ical
ex-
ampl
es, d
oes n
ot ge
nera
lly pr
esen
t suc
h com
mix
ed pa
ssag
es in
a
larg
er m
elod
ic co
ntex
t. Pe
rhap
s thi
s is f
or re
ason
s of e
con-
om
y, fo
r to d
o so s
yste
mat
ical
ly wou
ld ha
ve in
volv
ed pr
ovid
ing
eigh
t exa
mpl
es-o
ne f
or ea
ch of
the e
ight
mod
es-fo
r ea
ch of
th
e eig
ht in
terr
uptio
ns (i.
e., 8
* 8 =
64 e
xam
ples
). A
s no
ted
abov
e, M
arch
etto
gene
rally
empl
oys t
he te
rms
prop
rie a
nd co
mm
ixta
to d
enot
e int
erru
ptio
ns th
at ar
e pro
per
to th
e sur
roun
ding
mod
ality
or di
scre
pant
with
it, re
spec
tivel
y.
He u
ses o
ther
term
s as w
ell: s
empe
r (alw
ays)
, saep
e (of
ten)
, ali-
qu
ando
(som
etim
es), a
nd ra
ro (r
arel
y). E
ach o
f the
se ad
verb
s co
nvey
s the
mea
ning
of a
deg
ree o
f reg
ular
ity or
nor
mal
cy by
m
eans
of th
e not
ion
of fr
eque
ncy o
r rat
e of o
ccur
renc
e. T
his
mig
ht se
em to
impl
y tha
t Mar
chet
to ar
rive
d at h
is ap
plic
atio
n of
thes
e ter
ms b
y an
empi
rica
l stud
y of c
hant
mel
odie
s.20 H
ow-
ever
, whe
n M
arch
etto
wri
tes t
hat a
giv
en in
terr
uptio
n is
"al-
20Ti
ncto
ris la
ter a
sser
ts th
at su
ch w
as th
e cas
e, fo
r ini
tials,
whe
n he w
rite
s th
at "m
oreo
ver th
ere w
ere s
ome p
eopl
e who
, afte
r the
y had
exam
ined
all t
he
initi
als in
sim
ple G
eorg
ian c
hant
with
the g
reat
est c
are,
assig
ned t
o ea
ch m
ode
a cer
tain
num
ber o
f ini
tials"
(fuer
unt au
tem
nonn
ulli q
uipo
stqu
am om
niap
rin-
ci
pia s
impl
icis
cant
us G
rego
rian
i sum
ma c
um d
ilige
ntia
pers
ecru
tati fu
issen
t,
way
s" in
the f
irst
mod
e, h
e can
not m
ean t
hat i
t alw
ays a
ppea
rs
in a
larg
er fir
st-m
ode c
onte
xt. T
his w
ould
be an
empi
rica
l stat
e-
men
t and
, sin
ce m
odes
can
be c
omm
ixed
, a fa
lse on
e at
that
. R
athe
r, he
mus
t mea
n tha
t suc
h an i
nter
rupt
ion a
lway
s impl
ies
the f
irst
mod
e or a
lway
s is co
nsist
ent w
ith a f
irst
-mod
e con
text
- a
form
al o
r st
ruct
ural
stat
emen
t. M
arch
etto
's di
stin
ctio
ns
amon
g deg
rees
of p
ropr
iety
thus
corr
espo
nd no
t to
an em
piri
- ca
l, fre
quen
cy-b
ased
scal
ing,
desp
ite th
e ter
ms h
e cho
oses
, but
ra
ther
to d
iffer
ence
s in
the
degr
ees t
o w
hich
vari
ous m
odes
se
em to
be i
mpl
ied b
y giv
en m
elod
ic su
cces
sions
. Acc
ordi
ngly
, se
mpe
r mig
ht b
e tr
ansla
ted a
s "d
efin
itely
(im
plyi
ng a
give
n m
ode)
," sa
epe a
s "ra
ther
(impl
icat
ive o
f a g
iven
mod
e),"
ali-
qu
ando
as "
som
ewha
t (im
plic
ativ
e of a
give
n mod
e),"
and r
aro
as "
wea
kly (
impl
icat
ive o
f a gi
ven m
ode)
."21
Su
ch a s
calin
g is a
dmitt
edly
rath
er va
gue a
nd ca
lls in
to qu
es-
tion
(esp
ecia
lly in
the
inst
ance
s of t
he a
dver
bs ra
ther
, som
e-
wha
t, and
wea
kly)
just
whe
re th
e cut
off p
oint
is to
be m
ade b
e-
twee
n pr
oper
and
com
mix
ed, w
hich
oth
erw
ise a
ppea
r to
re
pres
ent d
iscre
te ca
tego
ries
. Whe
n he d
oes n
ot di
stin
guish
be-
twee
n var
ious
degr
ees o
f im
plic
atio
n, on
e can
only
gues
s, al
beit
in a
pos
sibly
educ
ated
way
, wha
t sor
t of h
iera
rchy
he m
ight
ha
ve ha
d in m
ind.
Inde
ed, t
here
are s
ome i
nsta
nces
whe
re M
ar-
chet
to do
es n
ot d
escr
ibe a
give
n mod
e as i
mpl
ied b
y a gi
ven i
n-
terr
uptio
n alth
ough
one
wou
ld ex
pect
him
to ta
ke n
ote
of it
. H
owev
er, o
ne sh
ould
obse
rve t
hat d
espi
te th
e int
ensit
y of M
ar-
chet
to's t
reat
men
t of i
nter
rupt
ions
, he is
quite
laco
nic i
n his
dis-
cu
ssio
n of i
ndiv
idua
l case
s. Fu
rthe
rmor
e, on
e mus
t rem
embe
r
cuili
bet to
no su
apri
ncip
ia ce
rto n
umer
o red
dide
runt
), in L
iber
de N
atur
a et P
ro-
prie
tate
Tono
rum
, ed. E
dmon
d de C
ouss
emak
er, in
Scri
ptor
es de
Mus
ica M
edii
Aev
i (Pa
ris:
1876
; rep
r. H
ildes
heim
: Geo
rg O
lms,
1963
; 4 vo
ls.) 4
:27,
and A
l- be
rt Se
ay, e
d., J
ohan
nis T
inct
oris,
Ope
ra T
heor
etic
a, in
Cor
pus S
crip
toru
m de
M
usic
a, 22
(Rom
e: A
mer
ican
Inst
itute
of M
usic
olog
y, 19
75, 2
vols.
) 1:8
2, al
so
tran
slate
d in A
lber
t Sea
y, tr
ans.,
Con
cern
ing th
e Nat
ure a
nd Pr
opri
ety o
f Ton
es
(Col
orad
o Spr
ings
: Col
orad
o Col
lege
Mus
ic Pr
ess,
1967
), 20-
21.
2"In
othe
r pas
sage
s of t
he L
ucid
ariu
m, th
ese a
dver
bs ca
n be p
rofit
ably
as-
signe
d the
ir no
rmal
, freq
uenc
y-ba
sed m
eani
ngs.
way
s" in
the f
irst
mod
e, h
e can
not m
ean t
hat i
t alw
ays a
ppea
rs
in a
larg
er fir
st-m
ode c
onte
xt. T
his w
ould
be an
empi
rica
l stat
e-
men
t and
, sin
ce m
odes
can
be c
omm
ixed
, a fa
lse on
e at
that
. R
athe
r, he
mus
t mea
n tha
t suc
h an i
nter
rupt
ion a
lway
s impl
ies
the f
irst
mod
e or a
lway
s is co
nsist
ent w
ith a f
irst
-mod
e con
text
- a
form
al o
r st
ruct
ural
stat
emen
t. M
arch
etto
's di
stin
ctio
ns
amon
g deg
rees
of p
ropr
iety
thus
corr
espo
nd no
t to
an em
piri
- ca
l, fre
quen
cy-b
ased
scal
ing,
desp
ite th
e ter
ms h
e cho
oses
, but
ra
ther
to d
iffer
ence
s in
the
degr
ees t
o w
hich
vari
ous m
odes
se
em to
be i
mpl
ied b
y giv
en m
elod
ic su
cces
sions
. Acc
ordi
ngly
, se
mpe
r mig
ht b
e tr
ansla
ted a
s "d
efin
itely
(im
plyi
ng a
give
n m
ode)
," sa
epe a
s "ra
ther
(impl
icat
ive o
f a g
iven
mod
e),"
ali-
qu
ando
as "
som
ewha
t (im
plic
ativ
e of a
give
n mod
e),"
and r
aro
as "
wea
kly (
impl
icat
ive o
f a gi
ven m
ode)
."21
Su
ch a s
calin
g is a
dmitt
edly
rath
er va
gue a
nd ca
lls in
to qu
es-
tion
(esp
ecia
lly in
the
inst
ance
s of t
he a
dver
bs ra
ther
, som
e-
wha
t, and
wea
kly)
just
whe
re th
e cut
off p
oint
is to
be m
ade b
e-
twee
n pr
oper
and
com
mix
ed, w
hich
oth
erw
ise a
ppea
r to
re
pres
ent d
iscre
te ca
tego
ries
. Whe
n he d
oes n
ot di
stin
guish
be-
twee
n var
ious
degr
ees o
f im
plic
atio
n, on
e can
only
gues
s, al
beit
in a
pos
sibly
educ
ated
way
, wha
t sor
t of h
iera
rchy
he m
ight
ha
ve ha
d in m
ind.
Inde
ed, t
here
are s
ome i
nsta
nces
whe
re M
ar-
chet
to do
es n
ot d
escr
ibe a
give
n mod
e as i
mpl
ied b
y a gi
ven i
n-
terr
uptio
n alth
ough
one
wou
ld ex
pect
him
to ta
ke n
ote
of it
. H
owev
er, o
ne sh
ould
obse
rve t
hat d
espi
te th
e int
ensit
y of M
ar-
chet
to's t
reat
men
t of i
nter
rupt
ions
, he is
quite
laco
nic i
n his
dis-
cu
ssio
n of i
ndiv
idua
l case
s. Fu
rthe
rmor
e, on
e mus
t rem
embe
r
cuili
bet to
no su
apri
ncip
ia ce
rto n
umer
o red
dide
runt
), in L
iber
de N
atur
a et P
ro-
prie
tate
Tono
rum
, ed. E
dmon
d de C
ouss
emak
er, in
Scri
ptor
es de
Mus
ica M
edii
Aev
i (Pa
ris:
1876
; rep
r. H
ildes
heim
: Geo
rg O
lms,
1963
; 4 vo
ls.) 4
:27,
and A
l- be
rt Se
ay, e
d., J
ohan
nis T
inct
oris,
Ope
ra T
heor
etic
a, in
Cor
pus S
crip
toru
m de
M
usic
a, 22
(Rom
e: A
mer
ican
Inst
itute
of M
usic
olog
y, 19
75, 2
vols.
) 1:8
2, al
so
tran
slate
d in A
lber
t Sea
y, tr
ans.,
Con
cern
ing th
e Nat
ure a
nd Pr
opri
ety o
f Ton
es
(Col
orad
o Spr
ings
: Col
orad
o Col
lege
Mus
ic Pr
ess,
1967
), 20-
21.
2"In
othe
r pas
sage
s of t
he L
ucid
ariu
m, th
ese a
dver
bs ca
n be p
rofit
ably
as-
signe
d the
ir no
rmal
, freq
uenc
y-ba
sed m
eani
ngs.
way
s" in
the f
irst
mod
e, h
e can
not m
ean t
hat i
t alw
ays a
ppea
rs
in a
larg
er fir
st-m
ode c
onte
xt. T
his w
ould
be an
empi
rica
l stat
e-
men
t and
, sin
ce m
odes
can
be c
omm
ixed
, a fa
lse on
e at
that
. R
athe
r, he
mus
t mea
n tha
t suc
h an i
nter
rupt
ion a
lway
s impl
ies
the f
irst
mod
e or a
lway
s is co
nsist
ent w
ith a f
irst
-mod
e con
text
- a
form
al o
r st
ruct
ural
stat
emen
t. M
arch
etto
's di
stin
ctio
ns
amon
g deg
rees
of p
ropr
iety
thus
corr
espo
nd no
t to
an em
piri
- ca
l, fre
quen
cy-b
ased
scal
ing,
desp
ite th
e ter
ms h
e cho
oses
, but
ra
ther
to d
iffer
ence
s in
the
degr
ees t
o w
hich
vari
ous m
odes
se
em to
be i
mpl
ied b
y giv
en m
elod
ic su
cces
sions
. Acc
ordi
ngly
, se
mpe
r mig
ht b
e tr
ansla
ted a
s "d
efin
itely
(im
plyi
ng a
give
n m
ode)
," sa
epe a
s "ra
ther
(impl
icat
ive o
f a g
iven
mod
e),"
ali-
qu
ando
as "
som
ewha
t (im
plic
ativ
e of a
give
n mod
e),"
and r
aro
as "
wea
kly (
impl
icat
ive o
f a gi
ven m
ode)
."21
Su
ch a s
calin
g is a
dmitt
edly
rath
er va
gue a
nd ca
lls in
to qu
es-
tion
(esp
ecia
lly in
the
inst
ance
s of t
he a
dver
bs ra
ther
, som
e-
wha
t, and
wea
kly)
just
whe
re th
e cut
off p
oint
is to
be m
ade b
e-
twee
n pr
oper
and
com
mix
ed, w
hich
oth
erw
ise a
ppea
r to
re
pres
ent d
iscre
te ca
tego
ries
. Whe
n he d
oes n
ot di
stin
guish
be-
twee
n var
ious
degr
ees o
f im
plic
atio
n, on
e can
only
gues
s, al
beit
in a
pos
sibly
educ
ated
way
, wha
t sor
t of h
iera
rchy
he m
ight
ha
ve ha
d in m
ind.
Inde
ed, t
here
are s
ome i
nsta
nces
whe
re M
ar-
chet
to do
es n
ot d
escr
ibe a
give
n mod
e as i
mpl
ied b
y a gi
ven i
n-
terr
uptio
n alth
ough
one
wou
ld ex
pect
him
to ta
ke n
ote
of it
. H
owev
er, o
ne sh
ould
obse
rve t
hat d
espi
te th
e int
ensit
y of M
ar-
chet
to's t
reat
men
t of i
nter
rupt
ions
, he is
quite
laco
nic i
n his
dis-
cu
ssio
n of i
ndiv
idua
l case
s. Fu
rthe
rmor
e, on
e mus
t rem
embe
r
cuili
bet to
no su
apri
ncip
ia ce
rto n
umer
o red
dide
runt
), in L
iber
de N
atur
a et P
ro-
prie
tate
Tono
rum
, ed. E
dmon
d de C
ouss
emak
er, in
Scri
ptor
es de
Mus
ica M
edii
Aev
i (Pa
ris:
1876
; rep
r. H
ildes
heim
: Geo
rg O
lms,
1963
; 4 vo
ls.) 4
:27,
and A
l- be
rt Se
ay, e
d., J
ohan
nis T
inct
oris,
Ope
ra T
heor
etic
a, in
Cor
pus S
crip
toru
m de
M
usic
a, 22
(Rom
e: A
mer
ican
Inst
itute
of M
usic
olog
y, 19
75, 2
vols.
) 1:8
2, al
so
tran
slate
d in A
lber
t Sea
y, tr
ans.,
Con
cern
ing th
e Nat
ure a
nd Pr
opri
ety o
f Ton
es
(Col
orad
o Spr
ings
: Col
orad
o Col
lege
Mus
ic Pr
ess,
1967
), 20-
21.
2"In
othe
r pas
sage
s of t
he L
ucid
ariu
m, th
ese a
dver
bs ca
n be p
rofit
ably
as-
signe
d the
ir no
rmal
, freq
uenc
y-ba
sed m
eani
ngs.
way
s" in
the f
irst
mod
e, h
e can
not m
ean t
hat i
t alw
ays a
ppea
rs
in a
larg
er fir
st-m
ode c
onte
xt. T
his w
ould
be an
empi
rica
l stat
e-
men
t and
, sin
ce m
odes
can
be c
omm
ixed
, a fa
lse on
e at
that
. R
athe
r, he
mus
t mea
n tha
t suc
h an i
nter
rupt
ion a
lway
s impl
ies
the f
irst
mod
e or a
lway
s is co
nsist
ent w
ith a f
irst
-mod
e con
text
- a
form
al o
r st
ruct
ural
stat
emen
t. M
arch
etto
's di
stin
ctio
ns
amon
g deg
rees
of p
ropr
iety
thus
corr
espo
nd no
t to
an em
piri
- ca
l, fre
quen
cy-b
ased
scal
ing,
desp
ite th
e ter
ms h
e cho
oses
, but
ra
ther
to d
iffer
ence
s in
the
degr
ees t
o w
hich
vari
ous m
odes
se
em to
be i
mpl
ied b
y giv
en m
elod
ic su
cces
sions
. Acc
ordi
ngly
, se
mpe
r mig
ht b
e tr
ansla
ted a
s "d
efin
itely
(im
plyi
ng a
give
n m
ode)
," sa
epe a
s "ra
ther
(impl
icat
ive o
f a g
iven
mod
e),"
ali-
qu
ando
as "
som
ewha
t (im
plic
ativ
e of a
give
n mod
e),"
and r
aro
as "
wea
kly (
impl
icat
ive o
f a gi
ven m
ode)
."21
Su
ch a s
calin
g is a
dmitt
edly
rath
er va
gue a
nd ca
lls in
to qu
es-
tion
(esp
ecia
lly in
the
inst
ance
s of t
he a
dver
bs ra
ther
, som
e-
wha
t, and
wea
kly)
just
whe
re th
e cut
off p
oint
is to
be m
ade b
e-
twee
n pr
oper
and
com
mix
ed, w
hich
oth
erw
ise a
ppea
r to
re
pres
ent d
iscre
te ca
tego
ries
. Whe
n he d
oes n
ot di
stin
guish
be-
twee
n var
ious
degr
ees o
f im
plic
atio
n, on
e can
only
gues
s, al
beit
in a
pos
sibly
educ
ated
way
, wha
t sor
t of h
iera
rchy
he m
ight
ha
ve ha
d in m
ind.
Inde
ed, t
here
are s
ome i
nsta
nces
whe
re M
ar-
chet
to do
es n
ot d
escr
ibe a
give
n mod
e as i
mpl
ied b
y a gi
ven i
n-
terr
uptio
n alth
ough
one
wou
ld ex
pect
him
to ta
ke n
ote
of it
. H
owev
er, o
ne sh
ould
obse
rve t
hat d
espi
te th
e int
ensit
y of M
ar-
chet
to's t
reat
men
t of i
nter
rupt
ions
, he is
quite
laco
nic i
n his
dis-
cu
ssio
n of i
ndiv
idua
l case
s. Fu
rthe
rmor
e, on
e mus
t rem
embe
r
cuili
bet to
no su
apri
ncip
ia ce
rto n
umer
o red
dide
runt
), in L
iber
de N
atur
a et P
ro-
prie
tate
Tono
rum
, ed. E
dmon
d de C
ouss
emak
er, in
Scri
ptor
es de
Mus
ica M
edii
Aev
i (Pa
ris:
1876
; rep
r. H
ildes
heim
: Geo
rg O
lms,
1963
; 4 vo
ls.) 4
:27,
and A
l- be
rt Se
ay, e
d., J
ohan
nis T
inct
oris,
Ope
ra T
heor
etic
a, in
Cor
pus S
crip
toru
m de
M
usic
a, 22
(Rom
e: A
mer
ican
Inst
itute
of M
usic
olog
y, 19
75, 2
vols.
) 1:8
2, al
so
tran
slate
d in A
lber
t Sea
y, tr
ans.,
Con
cern
ing th
e Nat
ure a
nd Pr
opri
ety o
f Ton
es
(Col
orad
o Spr
ings
: Col
orad
o Col
lege
Mus
ic Pr
ess,
1967
), 20-
21.
2"In
othe
r pas
sage
s of t
he L
ucid
ariu
m, th
ese a
dver
bs ca
n be p
rofit
ably
as-
signe
d the
ir no
rmal
, freq
uenc
y-ba
sed m
eani
ngs.
way
s" in
the f
irst
mod
e, h
e can
not m
ean t
hat i
t alw
ays a
ppea
rs
in a
larg
er fir
st-m
ode c
onte
xt. T
his w
ould
be an
empi
rica
l stat
e-
men
t and
, sin
ce m
odes
can
be c
omm
ixed
, a fa
lse on
e at
that
. R
athe
r, he
mus
t mea
n tha
t suc
h an i
nter
rupt
ion a
lway
s impl
ies
the f
irst
mod
e or a
lway
s is co
nsist
ent w
ith a f
irst
-mod
e con
text
- a
form
al o
r st
ruct
ural
stat
emen
t. M
arch
etto
's di
stin
ctio
ns
amon
g deg
rees
of p
ropr
iety
thus
corr
espo
nd no
t to
an em
piri
- ca
l, fre
quen
cy-b
ased
scal
ing,
desp
ite th
e ter
ms h
e cho
oses
, but
ra
ther
to d
iffer
ence
s in
the
degr
ees t
o w
hich
vari
ous m
odes
se
em to
be i
mpl
ied b
y giv
en m
elod
ic su
cces
sions
. Acc
ordi
ngly
, se
mpe
r mig
ht b
e tr
ansla
ted a
s "d
efin
itely
(im
plyi
ng a
give
n m
ode)
," sa
epe a
s "ra
ther
(impl
icat
ive o
f a g
iven
mod
e),"
ali-
qu
ando
as "
som
ewha
t (im
plic
ativ
e of a
give
n mod
e),"
and r
aro
as "
wea
kly (
impl
icat
ive o
f a gi
ven m
ode)
."21
Su
ch a s
calin
g is a
dmitt
edly
rath
er va
gue a
nd ca
lls in
to qu
es-
tion
(esp
ecia
lly in
the
inst
ance
s of t
he a
dver
bs ra
ther
, som
e-
wha
t, and
wea
kly)
just
whe
re th
e cut
off p
oint
is to
be m
ade b
e-
twee
n pr
oper
and
com
mix
ed, w
hich
oth
erw
ise a
ppea
r to
re
pres
ent d
iscre
te ca
tego
ries
. Whe
n he d
oes n
ot di
stin
guish
be-
twee
n var
ious
degr
ees o
f im
plic
atio
n, on
e can
only
gues
s, al
beit
in a
pos
sibly
educ
ated
way
, wha
t sor
t of h
iera
rchy
he m
ight
ha
ve ha
d in m
ind.
Inde
ed, t
here
are s
ome i
nsta
nces
whe
re M
ar-
chet
to do
es n
ot d
escr
ibe a
give
n mod
e as i
mpl
ied b
y a gi
ven i
n-
terr
uptio
n alth
ough
one
wou
ld ex
pect
him
to ta
ke n
ote
of it
. H
owev
er, o
ne sh
ould
obse
rve t
hat d
espi
te th
e int
ensit
y of M
ar-
chet
to's t
reat
men
t of i
nter
rupt
ions
, he is
quite
laco
nic i
n his
dis-
cu
ssio
n of i
ndiv
idua
l case
s. Fu
rthe
rmor
e, on
e mus
t rem
embe
r
cuili
bet to
no su
apri
ncip
ia ce
rto n
umer
o red
dide
runt
), in L
iber
de N
atur
a et P
ro-
prie
tate
Tono
rum
, ed. E
dmon
d de C
ouss
emak
er, in
Scri
ptor
es de
Mus
ica M
edii
Aev
i (Pa
ris:
1876
; rep
r. H
ildes
heim
: Geo
rg O
lms,
1963
; 4 vo
ls.) 4
:27,
and A
l- be
rt Se
ay, e
d., J
ohan
nis T
inct
oris,
Ope
ra T
heor
etic
a, in
Cor
pus S
crip
toru
m de
M
usic
a, 22
(Rom
e: A
mer
ican
Inst
itute
of M
usic
olog
y, 19
75, 2
vols.
) 1:8
2, al
so
tran
slate
d in A
lber
t Sea
y, tr
ans.,
Con
cern
ing th
e Nat
ure a
nd Pr
opri
ety o
f Ton
es
(Col
orad
o Spr
ings
: Col
orad
o Col
lege
Mus
ic Pr
ess,
1967
), 20-
21.
2"In
othe
r pas
sage
s of t
he L
ucid
ariu
m, th
ese a
dver
bs ca
n be p
rofit
ably
as-
signe
d the
ir no
rmal
, freq
uenc
y-ba
sed m
eani
ngs.
way
s" in
the f
irst
mod
e, h
e can
not m
ean t
hat i
t alw
ays a
ppea
rs
in a
larg
er fir
st-m
ode c
onte
xt. T
his w
ould
be an
empi
rica
l stat
e-
men
t and
, sin
ce m
odes
can
be c
omm
ixed
, a fa
lse on
e at
that
. R
athe
r, he
mus
t mea
n tha
t suc
h an i
nter
rupt
ion a
lway
s impl
ies
the f
irst
mod
e or a
lway
s is co
nsist
ent w
ith a f
irst
-mod
e con
text
- a
form
al o
r st
ruct
ural
stat
emen
t. M
arch
etto
's di
stin
ctio
ns
amon
g deg
rees
of p
ropr
iety
thus
corr
espo
nd no
t to
an em
piri
- ca
l, fre
quen
cy-b
ased
scal
ing,
desp
ite th
e ter
ms h
e cho
oses
, but
ra
ther
to d
iffer
ence
s in
the
degr
ees t
o w
hich
vari
ous m
odes
se
em to
be i
mpl
ied b
y giv
en m
elod
ic su
cces
sions
. Acc
ordi
ngly
, se
mpe
r mig
ht b
e tr
ansla
ted a
s "d
efin
itely
(im
plyi
ng a
give
n m
ode)
," sa
epe a
s "ra
ther
(impl
icat
ive o
f a g
iven
mod
e),"
ali-
qu
ando
as "
som
ewha
t (im
plic
ativ
e of a
give
n mod
e),"
and r
aro
as "
wea
kly (
impl
icat
ive o
f a gi
ven m
ode)
."21
Su
ch a s
calin
g is a
dmitt
edly
rath
er va
gue a
nd ca
lls in
to qu
es-
tion
(esp
ecia
lly in
the
inst
ance
s of t
he a
dver
bs ra
ther
, som
e-
wha
t, and
wea
kly)
just
whe
re th
e cut
off p
oint
is to
be m
ade b
e-
twee
n pr
oper
and
com
mix
ed, w
hich
oth
erw
ise a
ppea
r to
re
pres
ent d
iscre
te ca
tego
ries
. Whe
n he d
oes n
ot di
stin
guish
be-
twee
n var
ious
degr
ees o
f im
plic
atio
n, on
e can
only
gues
s, al
beit
in a
pos
sibly
educ
ated
way
, wha
t sor
t of h
iera
rchy
he m
ight
ha
ve ha
d in m
ind.
Inde
ed, t
here
are s
ome i
nsta
nces
whe
re M
ar-
chet
to do
es n
ot d
escr
ibe a
give
n mod
e as i
mpl
ied b
y a gi
ven i
n-
terr
uptio
n alth
ough
one
wou
ld ex
pect
him
to ta
ke n
ote
of it
. H
owev
er, o
ne sh
ould
obse
rve t
hat d
espi
te th
e int
ensit
y of M
ar-
chet
to's t
reat
men
t of i
nter
rupt
ions
, he is
quite
laco
nic i
n his
dis-
cu
ssio
n of i
ndiv
idua
l case
s. Fu
rthe
rmor
e, on
e mus
t rem
embe
r
cuili
bet to
no su
apri
ncip
ia ce
rto n
umer
o red
dide
runt
), in L
iber
de N
atur
a et P
ro-
prie
tate
Tono
rum
, ed. E
dmon
d de C
ouss
emak
er, in
Scri
ptor
es de
Mus
ica M
edii
Aev
i (Pa
ris:
1876
; rep
r. H
ildes
heim
: Geo
rg O
lms,
1963
; 4 vo
ls.) 4
:27,
and A
l- be
rt Se
ay, e
d., J
ohan
nis T
inct
oris,
Ope
ra T
heor
etic
a, in
Cor
pus S
crip
toru
m de
M
usic
a, 22
(Rom
e: A
mer
ican
Inst
itute
of M
usic
olog
y, 19
75, 2
vols.
) 1:8
2, al
so
tran
slate
d in A
lber
t Sea
y, tr
ans.,
Con
cern
ing th
e Nat
ure a
nd Pr
opri
ety o
f Ton
es
(Col
orad
o Spr
ings
: Col
orad
o Col
lege
Mus
ic Pr
ess,
1967
), 20-
21.
2"In
othe
r pas
sage
s of t
he L
ucid
ariu
m, th
ese a
dver
bs ca
n be p
rofit
ably
as-
signe
d the
ir no
rmal
, freq
uenc
y-ba
sed m
eani
ngs.
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
125
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
125
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
125
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
125
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
125
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
125
that
this
sect
ion
of th
e Lu
cida
rium
seem
s to
be th
e fir
st ex
- te
nded
trea
tmen
t of a
rath
er no
vel a
ppro
ach t
o m
odal
theo
ry.
Acc
ordi
ngly
, one
can
unde
rsta
nd w
hy M
arch
etto
, in w
hat a
p-
pear
s to
be a
n ex
plor
ator
y for
mul
atio
n, m
ight
have
neg
lect
ed
cert
ain p
oint
s rat
her t
han p
rese
ntin
g a co
mpl
etel
y wor
ked o
ut
acco
unt.
Mar
chet
to's
mus
ical
exam
ples
clar
ify an
d co
rrob
orat
e his
verb
al ac
coun
ts of
the v
ario
us in
terr
uptio
ns' m
elod
ic in
terv
al
cont
ents
. How
ever
, in
line w
ith th
e lac
onic
natu
re of
this
pas-
sa
ge, h
e pro
vide
s no
expl
anat
ions
of th
e con
nect
ions
betw
een
(a) h
is ve
rbal
des
crip
tions
and
mus
ical
exam
ples
, and
(b) h
is sp
ecifi
catio
ns of
vari
ous d
egre
es of
mod
al pr
opri
ety.
One
mus
t, th
en, i
nfer
such
expl
anat
ions
from
the p
assa
ge as
a w
hole
, and
ho
pe to
arr
ive a
t an
acco
unt t
hat i
s max
imal
ly co
nsist
ent w
ith
wha
t he e
xplic
itly w
rite
s. In
arr
ivin
g at t
he fo
llow
ing
inte
rpre
tatio
n of
Mar
chet
to's
pass
age o
n in
terr
uptio
ns, I
have
infe
rred
that
, for
Mar
chet
to,
spec
ial n
otes
in a
mel
odic
prog
ress
ion c
an im
ply g
iven
mod
es
acco
rdin
g to
a num
ber o
f cri
teri
a. Th
ese a
re as
follo
ws:
(1) a
ll th
e no
tes i
n th
e m
elod
ic p
rogr
essio
n, w
heth
er sp
ecia
l or n
ot,
mus
t app
ear w
ithin
the
prop
er pe
rfec
t ran
ge of
the
mod
e in
qu
estio
n; (2
) a gi
ven m
ode c
an be
impl
ied o
nly i
f one
or m
ore
mel
odic
ally
spec
ial n
otes
coin
cide
with
one
or m
ore o
rien
ting
note
s of t
he m
ode;
(3) i
f tw
o su
ch sp
ecia
l not
es co
inci
de w
ith
one o
r mor
e ori
entin
g not
es of
a gi
ven m
ode,
that
mod
e is m
ore
stro
ngly
impl
ied t
han a
mod
e tha
t mig
ht be
impl
ied b
y onl
y one
sp
ecia
l not
e-sim
ilarl
y fo
r th
ree
note
s vi
s-a-
vis t
wo,
and
so
fort
h; (4
) if t
wo m
elod
ical
ly sp
ecia
l not
es (c
orre
spon
ding
to d
if-
fere
nt pi
tche
s) ar
e rel
ativ
ely c
lose
r to
each
othe
r in
time t
han
are t
he m
embe
rs of
anot
her p
air o
f spe
cial
note
s, th
e mor
e tem
- po
rally
prox
imat
e not
es im
ply a
give
n mod
e mor
e str
ongl
y tha
n do
the m
ore t
empo
rally
rem
ote n
otes
;22 (5
) if t
wo
mel
odic
ally
that
this
sect
ion
of th
e Lu
cida
rium
seem
s to
be th
e fir
st ex
- te
nded
trea
tmen
t of a
rath
er no
vel a
ppro
ach t
o m
odal
theo
ry.
Acc
ordi
ngly
, one
can
unde
rsta
nd w
hy M
arch
etto
, in w
hat a
p-
pear
s to
be a
n ex
plor
ator
y for
mul
atio
n, m
ight
have
neg
lect
ed
cert
ain p
oint
s rat
her t
han p
rese
ntin
g a co
mpl
etel
y wor
ked o
ut
acco
unt.
Mar
chet
to's
mus
ical
exam
ples
clar
ify an
d co
rrob
orat
e his
verb
al ac
coun
ts of
the v
ario
us in
terr
uptio
ns' m
elod
ic in
terv
al
cont
ents
. How
ever
, in
line w
ith th
e lac
onic
natu
re of
this
pas-
sa
ge, h
e pro
vide
s no
expl
anat
ions
of th
e con
nect
ions
betw
een
(a) h
is ve
rbal
des
crip
tions
and
mus
ical
exam
ples
, and
(b) h
is sp
ecifi
catio
ns of
vari
ous d
egre
es of
mod
al pr
opri
ety.
One
mus
t, th
en, i
nfer
such
expl
anat
ions
from
the p
assa
ge as
a w
hole
, and
ho
pe to
arr
ive a
t an
acco
unt t
hat i
s max
imal
ly co
nsist
ent w
ith
wha
t he e
xplic
itly w
rite
s. In
arr
ivin
g at t
he fo
llow
ing
inte
rpre
tatio
n of
Mar
chet
to's
pass
age o
n in
terr
uptio
ns, I
have
infe
rred
that
, for
Mar
chet
to,
spec
ial n
otes
in a
mel
odic
prog
ress
ion c
an im
ply g
iven
mod
es
acco
rdin
g to
a num
ber o
f cri
teri
a. Th
ese a
re as
follo
ws:
(1) a
ll th
e no
tes i
n th
e m
elod
ic p
rogr
essio
n, w
heth
er sp
ecia
l or n
ot,
mus
t app
ear w
ithin
the
prop
er pe
rfec
t ran
ge of
the
mod
e in
qu
estio
n; (2
) a gi
ven m
ode c
an be
impl
ied o
nly i
f one
or m
ore
mel
odic
ally
spec
ial n
otes
coin
cide
with
one
or m
ore o
rien
ting
note
s of t
he m
ode;
(3) i
f tw
o su
ch sp
ecia
l not
es co
inci
de w
ith
one o
r mor
e ori
entin
g not
es of
a gi
ven m
ode,
that
mod
e is m
ore
stro
ngly
impl
ied t
han a
mod
e tha
t mig
ht be
impl
ied b
y onl
y one
sp
ecia
l not
e-sim
ilarl
y fo
r th
ree
note
s vi
s-a-
vis t
wo,
and
so
fort
h; (4
) if t
wo m
elod
ical
ly sp
ecia
l not
es (c
orre
spon
ding
to d
if-
fere
nt pi
tche
s) ar
e rel
ativ
ely c
lose
r to
each
othe
r in
time t
han
are t
he m
embe
rs of
anot
her p
air o
f spe
cial
note
s, th
e mor
e tem
- po
rally
prox
imat
e not
es im
ply a
give
n mod
e mor
e str
ongl
y tha
n do
the m
ore t
empo
rally
rem
ote n
otes
;22 (5
) if t
wo
mel
odic
ally
that
this
sect
ion
of th
e Lu
cida
rium
seem
s to
be th
e fir
st ex
- te
nded
trea
tmen
t of a
rath
er no
vel a
ppro
ach t
o m
odal
theo
ry.
Acc
ordi
ngly
, one
can
unde
rsta
nd w
hy M
arch
etto
, in w
hat a
p-
pear
s to
be a
n ex
plor
ator
y for
mul
atio
n, m
ight
have
neg
lect
ed
cert
ain p
oint
s rat
her t
han p
rese
ntin
g a co
mpl
etel
y wor
ked o
ut
acco
unt.
Mar
chet
to's
mus
ical
exam
ples
clar
ify an
d co
rrob
orat
e his
verb
al ac
coun
ts of
the v
ario
us in
terr
uptio
ns' m
elod
ic in
terv
al
cont
ents
. How
ever
, in
line w
ith th
e lac
onic
natu
re of
this
pas-
sa
ge, h
e pro
vide
s no
expl
anat
ions
of th
e con
nect
ions
betw
een
(a) h
is ve
rbal
des
crip
tions
and
mus
ical
exam
ples
, and
(b) h
is sp
ecifi
catio
ns of
vari
ous d
egre
es of
mod
al pr
opri
ety.
One
mus
t, th
en, i
nfer
such
expl
anat
ions
from
the p
assa
ge as
a w
hole
, and
ho
pe to
arr
ive a
t an
acco
unt t
hat i
s max
imal
ly co
nsist
ent w
ith
wha
t he e
xplic
itly w
rite
s. In
arr
ivin
g at t
he fo
llow
ing
inte
rpre
tatio
n of
Mar
chet
to's
pass
age o
n in
terr
uptio
ns, I
have
infe
rred
that
, for
Mar
chet
to,
spec
ial n
otes
in a
mel
odic
prog
ress
ion c
an im
ply g
iven
mod
es
acco
rdin
g to
a num
ber o
f cri
teri
a. Th
ese a
re as
follo
ws:
(1) a
ll th
e no
tes i
n th
e m
elod
ic p
rogr
essio
n, w
heth
er sp
ecia
l or n
ot,
mus
t app
ear w
ithin
the
prop
er pe
rfec
t ran
ge of
the
mod
e in
qu
estio
n; (2
) a gi
ven m
ode c
an be
impl
ied o
nly i
f one
or m
ore
mel
odic
ally
spec
ial n
otes
coin
cide
with
one
or m
ore o
rien
ting
note
s of t
he m
ode;
(3) i
f tw
o su
ch sp
ecia
l not
es co
inci
de w
ith
one o
r mor
e ori
entin
g not
es of
a gi
ven m
ode,
that
mod
e is m
ore
stro
ngly
impl
ied t
han a
mod
e tha
t mig
ht be
impl
ied b
y onl
y one
sp
ecia
l not
e-sim
ilarl
y fo
r th
ree
note
s vi
s-a-
vis t
wo,
and
so
fort
h; (4
) if t
wo m
elod
ical
ly sp
ecia
l not
es (c
orre
spon
ding
to d
if-
fere
nt pi
tche
s) ar
e rel
ativ
ely c
lose
r to
each
othe
r in
time t
han
are t
he m
embe
rs of
anot
her p
air o
f spe
cial
note
s, th
e mor
e tem
- po
rally
prox
imat
e not
es im
ply a
give
n mod
e mor
e str
ongl
y tha
n do
the m
ore t
empo
rally
rem
ote n
otes
;22 (5
) if t
wo
mel
odic
ally
that
this
sect
ion
of th
e Lu
cida
rium
seem
s to
be th
e fir
st ex
- te
nded
trea
tmen
t of a
rath
er no
vel a
ppro
ach t
o m
odal
theo
ry.
Acc
ordi
ngly
, one
can
unde
rsta
nd w
hy M
arch
etto
, in w
hat a
p-
pear
s to
be a
n ex
plor
ator
y for
mul
atio
n, m
ight
have
neg
lect
ed
cert
ain p
oint
s rat
her t
han p
rese
ntin
g a co
mpl
etel
y wor
ked o
ut
acco
unt.
Mar
chet
to's
mus
ical
exam
ples
clar
ify an
d co
rrob
orat
e his
verb
al ac
coun
ts of
the v
ario
us in
terr
uptio
ns' m
elod
ic in
terv
al
cont
ents
. How
ever
, in
line w
ith th
e lac
onic
natu
re of
this
pas-
sa
ge, h
e pro
vide
s no
expl
anat
ions
of th
e con
nect
ions
betw
een
(a) h
is ve
rbal
des
crip
tions
and
mus
ical
exam
ples
, and
(b) h
is sp
ecifi
catio
ns of
vari
ous d
egre
es of
mod
al pr
opri
ety.
One
mus
t, th
en, i
nfer
such
expl
anat
ions
from
the p
assa
ge as
a w
hole
, and
ho
pe to
arr
ive a
t an
acco
unt t
hat i
s max
imal
ly co
nsist
ent w
ith
wha
t he e
xplic
itly w
rite
s. In
arr
ivin
g at t
he fo
llow
ing
inte
rpre
tatio
n of
Mar
chet
to's
pass
age o
n in
terr
uptio
ns, I
have
infe
rred
that
, for
Mar
chet
to,
spec
ial n
otes
in a
mel
odic
prog
ress
ion c
an im
ply g
iven
mod
es
acco
rdin
g to
a num
ber o
f cri
teri
a. Th
ese a
re as
follo
ws:
(1) a
ll th
e no
tes i
n th
e m
elod
ic p
rogr
essio
n, w
heth
er sp
ecia
l or n
ot,
mus
t app
ear w
ithin
the
prop
er pe
rfec
t ran
ge of
the
mod
e in
qu
estio
n; (2
) a gi
ven m
ode c
an be
impl
ied o
nly i
f one
or m
ore
mel
odic
ally
spec
ial n
otes
coin
cide
with
one
or m
ore o
rien
ting
note
s of t
he m
ode;
(3) i
f tw
o su
ch sp
ecia
l not
es co
inci
de w
ith
one o
r mor
e ori
entin
g not
es of
a gi
ven m
ode,
that
mod
e is m
ore
stro
ngly
impl
ied t
han a
mod
e tha
t mig
ht be
impl
ied b
y onl
y one
sp
ecia
l not
e-sim
ilarl
y fo
r th
ree
note
s vi
s-a-
vis t
wo,
and
so
fort
h; (4
) if t
wo m
elod
ical
ly sp
ecia
l not
es (c
orre
spon
ding
to d
if-
fere
nt pi
tche
s) ar
e rel
ativ
ely c
lose
r to
each
othe
r in
time t
han
are t
he m
embe
rs of
anot
her p
air o
f spe
cial
note
s, th
e mor
e tem
- po
rally
prox
imat
e not
es im
ply a
give
n mod
e mor
e str
ongl
y tha
n do
the m
ore t
empo
rally
rem
ote n
otes
;22 (5
) if t
wo
mel
odic
ally
that
this
sect
ion
of th
e Lu
cida
rium
seem
s to
be th
e fir
st ex
- te
nded
trea
tmen
t of a
rath
er no
vel a
ppro
ach t
o m
odal
theo
ry.
Acc
ordi
ngly
, one
can
unde
rsta
nd w
hy M
arch
etto
, in w
hat a
p-
pear
s to
be a
n ex
plor
ator
y for
mul
atio
n, m
ight
have
neg
lect
ed
cert
ain p
oint
s rat
her t
han p
rese
ntin
g a co
mpl
etel
y wor
ked o
ut
acco
unt.
Mar
chet
to's
mus
ical
exam
ples
clar
ify an
d co
rrob
orat
e his
verb
al ac
coun
ts of
the v
ario
us in
terr
uptio
ns' m
elod
ic in
terv
al
cont
ents
. How
ever
, in
line w
ith th
e lac
onic
natu
re of
this
pas-
sa
ge, h
e pro
vide
s no
expl
anat
ions
of th
e con
nect
ions
betw
een
(a) h
is ve
rbal
des
crip
tions
and
mus
ical
exam
ples
, and
(b) h
is sp
ecifi
catio
ns of
vari
ous d
egre
es of
mod
al pr
opri
ety.
One
mus
t, th
en, i
nfer
such
expl
anat
ions
from
the p
assa
ge as
a w
hole
, and
ho
pe to
arr
ive a
t an
acco
unt t
hat i
s max
imal
ly co
nsist
ent w
ith
wha
t he e
xplic
itly w
rite
s. In
arr
ivin
g at t
he fo
llow
ing
inte
rpre
tatio
n of
Mar
chet
to's
pass
age o
n in
terr
uptio
ns, I
have
infe
rred
that
, for
Mar
chet
to,
spec
ial n
otes
in a
mel
odic
prog
ress
ion c
an im
ply g
iven
mod
es
acco
rdin
g to
a num
ber o
f cri
teri
a. Th
ese a
re as
follo
ws:
(1) a
ll th
e no
tes i
n th
e m
elod
ic p
rogr
essio
n, w
heth
er sp
ecia
l or n
ot,
mus
t app
ear w
ithin
the
prop
er pe
rfec
t ran
ge of
the
mod
e in
qu
estio
n; (2
) a gi
ven m
ode c
an be
impl
ied o
nly i
f one
or m
ore
mel
odic
ally
spec
ial n
otes
coin
cide
with
one
or m
ore o
rien
ting
note
s of t
he m
ode;
(3) i
f tw
o su
ch sp
ecia
l not
es co
inci
de w
ith
one o
r mor
e ori
entin
g not
es of
a gi
ven m
ode,
that
mod
e is m
ore
stro
ngly
impl
ied t
han a
mod
e tha
t mig
ht be
impl
ied b
y onl
y one
sp
ecia
l not
e-sim
ilarl
y fo
r th
ree
note
s vi
s-a-
vis t
wo,
and
so
fort
h; (4
) if t
wo m
elod
ical
ly sp
ecia
l not
es (c
orre
spon
ding
to d
if-
fere
nt pi
tche
s) ar
e rel
ativ
ely c
lose
r to
each
othe
r in
time t
han
are t
he m
embe
rs of
anot
her p
air o
f spe
cial
note
s, th
e mor
e tem
- po
rally
prox
imat
e not
es im
ply a
give
n mod
e mor
e str
ongl
y tha
n do
the m
ore t
empo
rally
rem
ote n
otes
;22 (5
) if t
wo
mel
odic
ally
that
this
sect
ion
of th
e Lu
cida
rium
seem
s to
be th
e fir
st ex
- te
nded
trea
tmen
t of a
rath
er no
vel a
ppro
ach t
o m
odal
theo
ry.
Acc
ordi
ngly
, one
can
unde
rsta
nd w
hy M
arch
etto
, in w
hat a
p-
pear
s to
be a
n ex
plor
ator
y for
mul
atio
n, m
ight
have
neg
lect
ed
cert
ain p
oint
s rat
her t
han p
rese
ntin
g a co
mpl
etel
y wor
ked o
ut
acco
unt.
Mar
chet
to's
mus
ical
exam
ples
clar
ify an
d co
rrob
orat
e his
verb
al ac
coun
ts of
the v
ario
us in
terr
uptio
ns' m
elod
ic in
terv
al
cont
ents
. How
ever
, in
line w
ith th
e lac
onic
natu
re of
this
pas-
sa
ge, h
e pro
vide
s no
expl
anat
ions
of th
e con
nect
ions
betw
een
(a) h
is ve
rbal
des
crip
tions
and
mus
ical
exam
ples
, and
(b) h
is sp
ecifi
catio
ns of
vari
ous d
egre
es of
mod
al pr
opri
ety.
One
mus
t, th
en, i
nfer
such
expl
anat
ions
from
the p
assa
ge as
a w
hole
, and
ho
pe to
arr
ive a
t an
acco
unt t
hat i
s max
imal
ly co
nsist
ent w
ith
wha
t he e
xplic
itly w
rite
s. In
arr
ivin
g at t
he fo
llow
ing
inte
rpre
tatio
n of
Mar
chet
to's
pass
age o
n in
terr
uptio
ns, I
have
infe
rred
that
, for
Mar
chet
to,
spec
ial n
otes
in a
mel
odic
prog
ress
ion c
an im
ply g
iven
mod
es
acco
rdin
g to
a num
ber o
f cri
teri
a. Th
ese a
re as
follo
ws:
(1) a
ll th
e no
tes i
n th
e m
elod
ic p
rogr
essio
n, w
heth
er sp
ecia
l or n
ot,
mus
t app
ear w
ithin
the
prop
er pe
rfec
t ran
ge of
the
mod
e in
qu
estio
n; (2
) a gi
ven m
ode c
an be
impl
ied o
nly i
f one
or m
ore
mel
odic
ally
spec
ial n
otes
coin
cide
with
one
or m
ore o
rien
ting
note
s of t
he m
ode;
(3) i
f tw
o su
ch sp
ecia
l not
es co
inci
de w
ith
one o
r mor
e ori
entin
g not
es of
a gi
ven m
ode,
that
mod
e is m
ore
stro
ngly
impl
ied t
han a
mod
e tha
t mig
ht be
impl
ied b
y onl
y one
sp
ecia
l not
e-sim
ilarl
y fo
r th
ree
note
s vi
s-a-
vis t
wo,
and
so
fort
h; (4
) if t
wo m
elod
ical
ly sp
ecia
l not
es (c
orre
spon
ding
to d
if-
fere
nt pi
tche
s) ar
e rel
ativ
ely c
lose
r to
each
othe
r in
time t
han
are t
he m
embe
rs of
anot
her p
air o
f spe
cial
note
s, th
e mor
e tem
- po
rally
prox
imat
e not
es im
ply a
give
n mod
e mor
e str
ongl
y tha
n do
the m
ore t
empo
rally
rem
ote n
otes
;22 (5
) if t
wo
mel
odic
ally
22O
ne as
sum
es, h
ere,
of c
ours
e, th
at th
e no
tes i
n ch
ant m
elod
ies a
re o
f eq
ual d
urat
ion (
exce
pt fo
r the
spec
ial c
ases
of re
peat
ed no
tes,
phra
se en
ding
s, 22
One
assu
mes
, her
e, o
f cou
rse,
that
the
note
s in
chan
t mel
odie
s are
of
equa
l dur
atio
n (ex
cept
for t
he sp
ecia
l cas
es of
repe
ated
note
s, ph
rase
endi
ngs,
22O
ne as
sum
es, h
ere,
of c
ours
e, th
at th
e no
tes i
n ch
ant m
elod
ies a
re o
f eq
ual d
urat
ion (
exce
pt fo
r the
spec
ial c
ases
of re
peat
ed no
tes,
phra
se en
ding
s, 22
One
assu
mes
, her
e, o
f cou
rse,
that
the
note
s in
chan
t mel
odie
s are
of
equa
l dur
atio
n (ex
cept
for t
he sp
ecia
l cas
es of
repe
ated
note
s, ph
rase
endi
ngs,
22O
ne as
sum
es, h
ere,
of c
ours
e, th
at th
e no
tes i
n ch
ant m
elod
ies a
re o
f eq
ual d
urat
ion (
exce
pt fo
r the
spec
ial c
ases
of re
peat
ed no
tes,
phra
se en
ding
s, 22
One
assu
mes
, her
e, o
f cou
rse,
that
the
note
s in
chan
t mel
odie
s are
of
equa
l dur
atio
n (ex
cept
for t
he sp
ecia
l cas
es of
repe
ated
note
s, ph
rase
endi
ngs,
spec
ial n
otes
are
a fif
th ap
art a
nd co
rres
pond
to th
e fin
alis
and
the f
ifth d
egre
e abo
ve th
efin
alis
in a
give
n pai
r of m
odes
(e.g
., D
3 an
d A3 v
is-a-
vis m
odes
I and
II),
the a
uthe
ntic
form
is m
ore
stro
ngly
impl
ied
than
the
plag
al fo
rm; (
6) if
two
mel
odic
ally
sp
ecia
l not
es a
re a
four
th ap
art a
nd co
rres
pond
to th
e fin
alis
and t
he fo
urth
degr
ee ab
ove t
hefin
alis
on a
give
n pai
r of m
odes
(e
.g.,
D3
and
G3
vis-
a-vi
s mod
es I
and I
I), t
he p
laga
l form
is
mor
e str
ongl
y im
plie
d tha
n the
auth
entic
form
;23 (7
) if t
wo m
e-
lodi
cally
spec
ial n
otes
are a
four
th ap
art so
that
they
mig
ht co
r-
resp
ond e
ither
to th
e fin
alis
and
the
four
th de
gree
abov
e the
fin
alis
or to
the f
inal
is an
d th
e fou
rth d
egre
e bel
ow th
e fin
alis
(e.g
., D
3 an
d G
3 vi
s-a-
vis m
odes
II a
nd V
III)
, the
mod
e in
whi
ch th
e sp
ecia
l not
e th
at w
ould
corr
espo
nd to
the f
inal
is is
mor
e str
ongl
y pre
sent
ed is
the m
ode t
hat i
s mor
e str
ongl
y im
- pl
ied;
(8) a
note
that
is b
oth a
mem
ber o
f a le
ap an
d an e
xtre
me
is m
ore s
peci
al th
an a n
ote t
hat h
as on
ly on
e of t
hese
prop
ertie
s an
d im
plie
s the
mod
e(s)
in w
hich
it is
an
orie
ntin
g not
e mor
e st
rong
ly; a
nd (9
) tw
o sp
ecia
l not
es co
rres
pond
ing to
the s
ame
pitc
h and
furt
her a
part
in ti
me a
re m
ore s
peci
al th
an no
tes t
hat
are c
lose
r tog
ethe
r in
time (
cf.,
how
ever
, cri
teri
on 4,
abo
ve).
Thes
e nin
e inf
erre
d cri
teri
a ser
ve to
mak
e fai
rly c
onsis
tent
se
nse
of M
arch
etto
's tre
atm
ent o
f int
erru
ptio
ns. In
ord
er to
de
mon
stra
te th
is po
int,
I of
fer
the
follo
win
g acc
ount
of th
e
andf
inal
es).
Such
an as
sum
ptio
n is bo
rne o
ut by
the r
est o
f the
Luc
idar
ium
and
its va
riou
s cop
ies i
n w
hich
ther
e is n
o co
nsist
ency
in li
gatio
n. M
oreo
ver,
Mar
- ch
etto
's di
stin
ctio
n bet
wee
n te
mpo
rally
mea
sure
d mus
ic an
d th
e te
mpo
rally
un
mea
sure
d sty
le of
chan
t (Luc
idar
ium
1,15
, pp.
100-
03, a
nd 10
, pp.
368-
69)
can b
e und
erst
ood i
n te
rms o
f his
notio
n tha
t mea
sure
is ba
sed o
n pr
opor
tions
of
num
bers
(locc
. cit.
) and
his t
ypic
ally
med
ieva
l vie
w th
at "t
he nu
mbe
r one
" (w
hich
wou
ld co
rres
pond
to th
e uni
t dur
atio
n in
pulsa
tile c
hant
) is n
ot re
ally
a nu
mbe
r (Lu
cida
rium
, 9, 1
, 55,
pp.
336
-37)
, fr
om w
hich
one c
an in
fer t
hat t
he
prop
ortio
n "1:
1," f
ound
betw
een t
he du
ratio
ns of
not
es in
chan
t, is n
ot re
ally
a pr
opor
tion,
so th
at ch
ant c
anno
t be
cons
ider
ed "m
easu
red"
in M
arch
etto
's se
nse.
23
The la
tter t
wo
crite
ria c
once
rn th
e di
stin
ctio
n bet
wee
n "p
rope
r" an
d "c
omm
on" s
peci
es di
scus
sed i
n Lu
cida
rium
, 11, 4
, 217
-18,
pp.
490-
93.
spec
ial n
otes
are
a fif
th ap
art a
nd co
rres
pond
to th
e fin
alis
and
the f
ifth d
egre
e abo
ve th
efin
alis
in a
give
n pai
r of m
odes
(e.g
., D
3 an
d A3 v
is-a-
vis m
odes
I and
II),
the a
uthe
ntic
form
is m
ore
stro
ngly
impl
ied
than
the
plag
al fo
rm; (
6) if
two
mel
odic
ally
sp
ecia
l not
es a
re a
four
th ap
art a
nd co
rres
pond
to th
e fin
alis
and t
he fo
urth
degr
ee ab
ove t
hefin
alis
on a
give
n pai
r of m
odes
(e
.g.,
D3
and
G3
vis-
a-vi
s mod
es I
and I
I), t
he p
laga
l form
is
mor
e str
ongl
y im
plie
d tha
n the
auth
entic
form
;23 (7
) if t
wo m
e-
lodi
cally
spec
ial n
otes
are a
four
th ap
art so
that
they
mig
ht co
r-
resp
ond e
ither
to th
e fin
alis
and
the
four
th de
gree
abov
e the
fin
alis
or to
the f
inal
is an
d th
e fou
rth d
egre
e bel
ow th
e fin
alis
(e.g
., D
3 an
d G
3 vi
s-a-
vis m
odes
II a
nd V
III)
, the
mod
e in
whi
ch th
e sp
ecia
l not
e th
at w
ould
corr
espo
nd to
the f
inal
is is
mor
e str
ongl
y pre
sent
ed is
the m
ode t
hat i
s mor
e str
ongl
y im
- pl
ied;
(8) a
note
that
is b
oth a
mem
ber o
f a le
ap an
d an e
xtre
me
is m
ore s
peci
al th
an a n
ote t
hat h
as on
ly on
e of t
hese
prop
ertie
s an
d im
plie
s the
mod
e(s)
in w
hich
it is
an
orie
ntin
g not
e mor
e st
rong
ly; a
nd (9
) tw
o sp
ecia
l not
es co
rres
pond
ing to
the s
ame
pitc
h and
furt
her a
part
in ti
me a
re m
ore s
peci
al th
an no
tes t
hat
are c
lose
r tog
ethe
r in
time (
cf.,
how
ever
, cri
teri
on 4,
abo
ve).
Thes
e nin
e inf
erre
d cri
teri
a ser
ve to
mak
e fai
rly c
onsis
tent
se
nse
of M
arch
etto
's tre
atm
ent o
f int
erru
ptio
ns. In
ord
er to
de
mon
stra
te th
is po
int,
I of
fer
the
follo
win
g acc
ount
of th
e
andf
inal
es).
Such
an as
sum
ptio
n is bo
rne o
ut by
the r
est o
f the
Luc
idar
ium
and
its va
riou
s cop
ies i
n w
hich
ther
e is n
o co
nsist
ency
in li
gatio
n. M
oreo
ver,
Mar
- ch
etto
's di
stin
ctio
n bet
wee
n te
mpo
rally
mea
sure
d mus
ic an
d th
e te
mpo
rally
un
mea
sure
d sty
le of
chan
t (Luc
idar
ium
1,15
, pp.
100-
03, a
nd 10
, pp.
368-
69)
can b
e und
erst
ood i
n te
rms o
f his
notio
n tha
t mea
sure
is ba
sed o
n pr
opor
tions
of
num
bers
(locc
. cit.
) and
his t
ypic
ally
med
ieva
l vie
w th
at "t
he nu
mbe
r one
" (w
hich
wou
ld co
rres
pond
to th
e uni
t dur
atio
n in
pulsa
tile c
hant
) is n
ot re
ally
a nu
mbe
r (Lu
cida
rium
, 9, 1
, 55,
pp.
336
-37)
, fr
om w
hich
one c
an in
fer t
hat t
he
prop
ortio
n "1:
1," f
ound
betw
een t
he du
ratio
ns of
not
es in
chan
t, is n
ot re
ally
a pr
opor
tion,
so th
at ch
ant c
anno
t be
cons
ider
ed "m
easu
red"
in M
arch
etto
's se
nse.
23
The la
tter t
wo
crite
ria c
once
rn th
e di
stin
ctio
n bet
wee
n "p
rope
r" an
d "c
omm
on" s
peci
es di
scus
sed i
n Lu
cida
rium
, 11, 4
, 217
-18,
pp.
490-
93.
spec
ial n
otes
are
a fif
th ap
art a
nd co
rres
pond
to th
e fin
alis
and
the f
ifth d
egre
e abo
ve th
efin
alis
in a
give
n pai
r of m
odes
(e.g
., D
3 an
d A3 v
is-a-
vis m
odes
I and
II),
the a
uthe
ntic
form
is m
ore
stro
ngly
impl
ied
than
the
plag
al fo
rm; (
6) if
two
mel
odic
ally
sp
ecia
l not
es a
re a
four
th ap
art a
nd co
rres
pond
to th
e fin
alis
and t
he fo
urth
degr
ee ab
ove t
hefin
alis
on a
give
n pai
r of m
odes
(e
.g.,
D3
and
G3
vis-
a-vi
s mod
es I
and I
I), t
he p
laga
l form
is
mor
e str
ongl
y im
plie
d tha
n the
auth
entic
form
;23 (7
) if t
wo m
e-
lodi
cally
spec
ial n
otes
are a
four
th ap
art so
that
they
mig
ht co
r-
resp
ond e
ither
to th
e fin
alis
and
the
four
th de
gree
abov
e the
fin
alis
or to
the f
inal
is an
d th
e fou
rth d
egre
e bel
ow th
e fin
alis
(e.g
., D
3 an
d G
3 vi
s-a-
vis m
odes
II a
nd V
III)
, the
mod
e in
whi
ch th
e sp
ecia
l not
e th
at w
ould
corr
espo
nd to
the f
inal
is is
mor
e str
ongl
y pre
sent
ed is
the m
ode t
hat i
s mor
e str
ongl
y im
- pl
ied;
(8) a
note
that
is b
oth a
mem
ber o
f a le
ap an
d an e
xtre
me
is m
ore s
peci
al th
an a n
ote t
hat h
as on
ly on
e of t
hese
prop
ertie
s an
d im
plie
s the
mod
e(s)
in w
hich
it is
an
orie
ntin
g not
e mor
e st
rong
ly; a
nd (9
) tw
o sp
ecia
l not
es co
rres
pond
ing to
the s
ame
pitc
h and
furt
her a
part
in ti
me a
re m
ore s
peci
al th
an no
tes t
hat
are c
lose
r tog
ethe
r in
time (
cf.,
how
ever
, cri
teri
on 4,
abo
ve).
Thes
e nin
e inf
erre
d cri
teri
a ser
ve to
mak
e fai
rly c
onsis
tent
se
nse
of M
arch
etto
's tre
atm
ent o
f int
erru
ptio
ns. In
ord
er to
de
mon
stra
te th
is po
int,
I of
fer
the
follo
win
g acc
ount
of th
e
andf
inal
es).
Such
an as
sum
ptio
n is bo
rne o
ut by
the r
est o
f the
Luc
idar
ium
and
its va
riou
s cop
ies i
n w
hich
ther
e is n
o co
nsist
ency
in li
gatio
n. M
oreo
ver,
Mar
- ch
etto
's di
stin
ctio
n bet
wee
n te
mpo
rally
mea
sure
d mus
ic an
d th
e te
mpo
rally
un
mea
sure
d sty
le of
chan
t (Luc
idar
ium
1,15
, pp.
100-
03, a
nd 10
, pp.
368-
69)
can b
e und
erst
ood i
n te
rms o
f his
notio
n tha
t mea
sure
is ba
sed o
n pr
opor
tions
of
num
bers
(locc
. cit.
) and
his t
ypic
ally
med
ieva
l vie
w th
at "t
he nu
mbe
r one
" (w
hich
wou
ld co
rres
pond
to th
e uni
t dur
atio
n in
pulsa
tile c
hant
) is n
ot re
ally
a nu
mbe
r (Lu
cida
rium
, 9, 1
, 55,
pp.
336
-37)
, fr
om w
hich
one c
an in
fer t
hat t
he
prop
ortio
n "1:
1," f
ound
betw
een t
he du
ratio
ns of
not
es in
chan
t, is n
ot re
ally
a pr
opor
tion,
so th
at ch
ant c
anno
t be
cons
ider
ed "m
easu
red"
in M
arch
etto
's se
nse.
23
The la
tter t
wo
crite
ria c
once
rn th
e di
stin
ctio
n bet
wee
n "p
rope
r" an
d "c
omm
on" s
peci
es di
scus
sed i
n Lu
cida
rium
, 11, 4
, 217
-18,
pp.
490-
93.
spec
ial n
otes
are
a fif
th ap
art a
nd co
rres
pond
to th
e fin
alis
and
the f
ifth d
egre
e abo
ve th
efin
alis
in a
give
n pai
r of m
odes
(e.g
., D
3 an
d A3 v
is-a-
vis m
odes
I and
II),
the a
uthe
ntic
form
is m
ore
stro
ngly
impl
ied
than
the
plag
al fo
rm; (
6) if
two
mel
odic
ally
sp
ecia
l not
es a
re a
four
th ap
art a
nd co
rres
pond
to th
e fin
alis
and t
he fo
urth
degr
ee ab
ove t
hefin
alis
on a
give
n pai
r of m
odes
(e
.g.,
D3
and
G3
vis-
a-vi
s mod
es I
and I
I), t
he p
laga
l form
is
mor
e str
ongl
y im
plie
d tha
n the
auth
entic
form
;23 (7
) if t
wo m
e-
lodi
cally
spec
ial n
otes
are a
four
th ap
art so
that
they
mig
ht co
r-
resp
ond e
ither
to th
e fin
alis
and
the
four
th de
gree
abov
e the
fin
alis
or to
the f
inal
is an
d th
e fou
rth d
egre
e bel
ow th
e fin
alis
(e.g
., D
3 an
d G
3 vi
s-a-
vis m
odes
II a
nd V
III)
, the
mod
e in
whi
ch th
e sp
ecia
l not
e th
at w
ould
corr
espo
nd to
the f
inal
is is
mor
e str
ongl
y pre
sent
ed is
the m
ode t
hat i
s mor
e str
ongl
y im
- pl
ied;
(8) a
note
that
is b
oth a
mem
ber o
f a le
ap an
d an e
xtre
me
is m
ore s
peci
al th
an a n
ote t
hat h
as on
ly on
e of t
hese
prop
ertie
s an
d im
plie
s the
mod
e(s)
in w
hich
it is
an
orie
ntin
g not
e mor
e st
rong
ly; a
nd (9
) tw
o sp
ecia
l not
es co
rres
pond
ing to
the s
ame
pitc
h and
furt
her a
part
in ti
me a
re m
ore s
peci
al th
an no
tes t
hat
are c
lose
r tog
ethe
r in
time (
cf.,
how
ever
, cri
teri
on 4,
abo
ve).
Thes
e nin
e inf
erre
d cri
teri
a ser
ve to
mak
e fai
rly c
onsis
tent
se
nse
of M
arch
etto
's tre
atm
ent o
f int
erru
ptio
ns. In
ord
er to
de
mon
stra
te th
is po
int,
I of
fer
the
follo
win
g acc
ount
of th
e
andf
inal
es).
Such
an as
sum
ptio
n is bo
rne o
ut by
the r
est o
f the
Luc
idar
ium
and
its va
riou
s cop
ies i
n w
hich
ther
e is n
o co
nsist
ency
in li
gatio
n. M
oreo
ver,
Mar
- ch
etto
's di
stin
ctio
n bet
wee
n te
mpo
rally
mea
sure
d mus
ic an
d th
e te
mpo
rally
un
mea
sure
d sty
le of
chan
t (Luc
idar
ium
1,15
, pp.
100-
03, a
nd 10
, pp.
368-
69)
can b
e und
erst
ood i
n te
rms o
f his
notio
n tha
t mea
sure
is ba
sed o
n pr
opor
tions
of
num
bers
(locc
. cit.
) and
his t
ypic
ally
med
ieva
l vie
w th
at "t
he nu
mbe
r one
" (w
hich
wou
ld co
rres
pond
to th
e uni
t dur
atio
n in
pulsa
tile c
hant
) is n
ot re
ally
a nu
mbe
r (Lu
cida
rium
, 9, 1
, 55,
pp.
336
-37)
, fr
om w
hich
one c
an in
fer t
hat t
he
prop
ortio
n "1:
1," f
ound
betw
een t
he du
ratio
ns of
not
es in
chan
t, is n
ot re
ally
a pr
opor
tion,
so th
at ch
ant c
anno
t be
cons
ider
ed "m
easu
red"
in M
arch
etto
's se
nse.
23
The la
tter t
wo
crite
ria c
once
rn th
e di
stin
ctio
n bet
wee
n "p
rope
r" an
d "c
omm
on" s
peci
es di
scus
sed i
n Lu
cida
rium
, 11, 4
, 217
-18,
pp.
490-
93.
spec
ial n
otes
are
a fif
th ap
art a
nd co
rres
pond
to th
e fin
alis
and
the f
ifth d
egre
e abo
ve th
efin
alis
in a
give
n pai
r of m
odes
(e.g
., D
3 an
d A3 v
is-a-
vis m
odes
I and
II),
the a
uthe
ntic
form
is m
ore
stro
ngly
impl
ied
than
the
plag
al fo
rm; (
6) if
two
mel
odic
ally
sp
ecia
l not
es a
re a
four
th ap
art a
nd co
rres
pond
to th
e fin
alis
and t
he fo
urth
degr
ee ab
ove t
hefin
alis
on a
give
n pai
r of m
odes
(e
.g.,
D3
and
G3
vis-
a-vi
s mod
es I
and I
I), t
he p
laga
l form
is
mor
e str
ongl
y im
plie
d tha
n the
auth
entic
form
;23 (7
) if t
wo m
e-
lodi
cally
spec
ial n
otes
are a
four
th ap
art so
that
they
mig
ht co
r-
resp
ond e
ither
to th
e fin
alis
and
the
four
th de
gree
abov
e the
fin
alis
or to
the f
inal
is an
d th
e fou
rth d
egre
e bel
ow th
e fin
alis
(e.g
., D
3 an
d G
3 vi
s-a-
vis m
odes
II a
nd V
III)
, the
mod
e in
whi
ch th
e sp
ecia
l not
e th
at w
ould
corr
espo
nd to
the f
inal
is is
mor
e str
ongl
y pre
sent
ed is
the m
ode t
hat i
s mor
e str
ongl
y im
- pl
ied;
(8) a
note
that
is b
oth a
mem
ber o
f a le
ap an
d an e
xtre
me
is m
ore s
peci
al th
an a n
ote t
hat h
as on
ly on
e of t
hese
prop
ertie
s an
d im
plie
s the
mod
e(s)
in w
hich
it is
an
orie
ntin
g not
e mor
e st
rong
ly; a
nd (9
) tw
o sp
ecia
l not
es co
rres
pond
ing to
the s
ame
pitc
h and
furt
her a
part
in ti
me a
re m
ore s
peci
al th
an no
tes t
hat
are c
lose
r tog
ethe
r in
time (
cf.,
how
ever
, cri
teri
on 4,
abo
ve).
Thes
e nin
e inf
erre
d cri
teri
a ser
ve to
mak
e fai
rly c
onsis
tent
se
nse
of M
arch
etto
's tre
atm
ent o
f int
erru
ptio
ns. In
ord
er to
de
mon
stra
te th
is po
int,
I of
fer
the
follo
win
g acc
ount
of th
e
andf
inal
es).
Such
an as
sum
ptio
n is bo
rne o
ut by
the r
est o
f the
Luc
idar
ium
and
its va
riou
s cop
ies i
n w
hich
ther
e is n
o co
nsist
ency
in li
gatio
n. M
oreo
ver,
Mar
- ch
etto
's di
stin
ctio
n bet
wee
n te
mpo
rally
mea
sure
d mus
ic an
d th
e te
mpo
rally
un
mea
sure
d sty
le of
chan
t (Luc
idar
ium
1,15
, pp.
100-
03, a
nd 10
, pp.
368-
69)
can b
e und
erst
ood i
n te
rms o
f his
notio
n tha
t mea
sure
is ba
sed o
n pr
opor
tions
of
num
bers
(locc
. cit.
) and
his t
ypic
ally
med
ieva
l vie
w th
at "t
he nu
mbe
r one
" (w
hich
wou
ld co
rres
pond
to th
e uni
t dur
atio
n in
pulsa
tile c
hant
) is n
ot re
ally
a nu
mbe
r (Lu
cida
rium
, 9, 1
, 55,
pp.
336
-37)
, fr
om w
hich
one c
an in
fer t
hat t
he
prop
ortio
n "1:
1," f
ound
betw
een t
he du
ratio
ns of
not
es in
chan
t, is n
ot re
ally
a pr
opor
tion,
so th
at ch
ant c
anno
t be
cons
ider
ed "m
easu
red"
in M
arch
etto
's se
nse.
23
The la
tter t
wo
crite
ria c
once
rn th
e di
stin
ctio
n bet
wee
n "p
rope
r" an
d "c
omm
on" s
peci
es di
scus
sed i
n Lu
cida
rium
, 11, 4
, 217
-18,
pp.
490-
93.
spec
ial n
otes
are
a fif
th ap
art a
nd co
rres
pond
to th
e fin
alis
and
the f
ifth d
egre
e abo
ve th
efin
alis
in a
give
n pai
r of m
odes
(e.g
., D
3 an
d A3 v
is-a-
vis m
odes
I and
II),
the a
uthe
ntic
form
is m
ore
stro
ngly
impl
ied
than
the
plag
al fo
rm; (
6) if
two
mel
odic
ally
sp
ecia
l not
es a
re a
four
th ap
art a
nd co
rres
pond
to th
e fin
alis
and t
he fo
urth
degr
ee ab
ove t
hefin
alis
on a
give
n pai
r of m
odes
(e
.g.,
D3
and
G3
vis-
a-vi
s mod
es I
and I
I), t
he p
laga
l form
is
mor
e str
ongl
y im
plie
d tha
n the
auth
entic
form
;23 (7
) if t
wo m
e-
lodi
cally
spec
ial n
otes
are a
four
th ap
art so
that
they
mig
ht co
r-
resp
ond e
ither
to th
e fin
alis
and
the
four
th de
gree
abov
e the
fin
alis
or to
the f
inal
is an
d th
e fou
rth d
egre
e bel
ow th
e fin
alis
(e.g
., D
3 an
d G
3 vi
s-a-
vis m
odes
II a
nd V
III)
, the
mod
e in
whi
ch th
e sp
ecia
l not
e th
at w
ould
corr
espo
nd to
the f
inal
is is
mor
e str
ongl
y pre
sent
ed is
the m
ode t
hat i
s mor
e str
ongl
y im
- pl
ied;
(8) a
note
that
is b
oth a
mem
ber o
f a le
ap an
d an e
xtre
me
is m
ore s
peci
al th
an a n
ote t
hat h
as on
ly on
e of t
hese
prop
ertie
s an
d im
plie
s the
mod
e(s)
in w
hich
it is
an
orie
ntin
g not
e mor
e st
rong
ly; a
nd (9
) tw
o sp
ecia
l not
es co
rres
pond
ing to
the s
ame
pitc
h and
furt
her a
part
in ti
me a
re m
ore s
peci
al th
an no
tes t
hat
are c
lose
r tog
ethe
r in
time (
cf.,
how
ever
, cri
teri
on 4,
abo
ve).
Thes
e nin
e inf
erre
d cri
teri
a ser
ve to
mak
e fai
rly c
onsis
tent
se
nse
of M
arch
etto
's tre
atm
ent o
f int
erru
ptio
ns. In
ord
er to
de
mon
stra
te th
is po
int,
I of
fer
the
follo
win
g acc
ount
of th
e
andf
inal
es).
Such
an as
sum
ptio
n is bo
rne o
ut by
the r
est o
f the
Luc
idar
ium
and
its va
riou
s cop
ies i
n w
hich
ther
e is n
o co
nsist
ency
in li
gatio
n. M
oreo
ver,
Mar
- ch
etto
's di
stin
ctio
n bet
wee
n te
mpo
rally
mea
sure
d mus
ic an
d th
e te
mpo
rally
un
mea
sure
d sty
le of
chan
t (Luc
idar
ium
1,15
, pp.
100-
03, a
nd 10
, pp.
368-
69)
can b
e und
erst
ood i
n te
rms o
f his
notio
n tha
t mea
sure
is ba
sed o
n pr
opor
tions
of
num
bers
(locc
. cit.
) and
his t
ypic
ally
med
ieva
l vie
w th
at "t
he nu
mbe
r one
" (w
hich
wou
ld co
rres
pond
to th
e uni
t dur
atio
n in
pulsa
tile c
hant
) is n
ot re
ally
a nu
mbe
r (Lu
cida
rium
, 9, 1
, 55,
pp.
336
-37)
, fr
om w
hich
one c
an in
fer t
hat t
he
prop
ortio
n "1:
1," f
ound
betw
een t
he du
ratio
ns of
not
es in
chan
t, is n
ot re
ally
a pr
opor
tion,
so th
at ch
ant c
anno
t be
cons
ider
ed "m
easu
red"
in M
arch
etto
's se
nse.
23
The la
tter t
wo
crite
ria c
once
rn th
e di
stin
ctio
n bet
wee
n "p
rope
r" an
d "c
omm
on" s
peci
es di
scus
sed i
n Lu
cida
rium
, 11, 4
, 217
-18,
pp.
490-
93.
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
126
Mus
ic Th
eory
Spec
trum
12
6 M
usic
Theo
ry Sp
ectr
um
126
Mus
ic Th
eory
Spec
trum
12
6 M
usic
Theo
ry Sp
ectr
um
126
Mus
ic Th
eory
Spec
trum
12
6 M
usic
Theo
ry Sp
ectr
um
eigh
t inte
rrup
tions
with
whi
ch M
arch
etto
deal
s. In
each
case
, I
pres
ent M
arch
etto
's mel
odic
exam
ple w
ith th
e ad
ditio
n of x
's an
dy's
over
the r
elev
ant sp
ecia
l not
es, h
is ve
rbal
acco
unt o
f the
re
lativ
e pr
oper
ties o
f th
e m
elod
ic p
rogr
essio
n fo
r va
riou
s m
odes
, and
an ex
plan
atio
n of h
is ac
coun
t as w
ell a
s any
anom
a-
lies t
hat m
ight
appe
ar in
it, w
heth
er ex
plic
itly o
r im
plic
itly.
Exam
ple 3
. Int
erru
ptio
n la:
"Pr
oper
ly in
mod
e 1
[whi
ch ha
s D
3, (G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
ha
s D3,
G3,
C4,
and (
D4)
as o
rien
ting t
ones
]." H
ere a
nd in
fol-
low
ing e
xam
ple c
aptio
ns, o
rien
ting to
nes c
orre
spon
ding
to sp
e-
cial
not
es in
exa
mpl
es ar
e giv
en in
bol
dfac
e; or
ient
ing t
ones
at
ypic
al of
a gi
ven a
uthe
ntic
or pl
agel
mod
e are
plac
ed in
pare
n-
thes
es.
eigh
t inte
rrup
tions
with
whi
ch M
arch
etto
deal
s. In
each
case
, I
pres
ent M
arch
etto
's mel
odic
exam
ple w
ith th
e ad
ditio
n of x
's an
dy's
over
the r
elev
ant sp
ecia
l not
es, h
is ve
rbal
acco
unt o
f the
re
lativ
e pr
oper
ties o
f th
e m
elod
ic p
rogr
essio
n fo
r va
riou
s m
odes
, and
an ex
plan
atio
n of h
is ac
coun
t as w
ell a
s any
anom
a-
lies t
hat m
ight
appe
ar in
it, w
heth
er ex
plic
itly o
r im
plic
itly.
Exam
ple 3
. Int
erru
ptio
n la:
"Pr
oper
ly in
mod
e 1
[whi
ch ha
s D
3, (G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
ha
s D3,
G3,
C4,
and (
D4)
as o
rien
ting t
ones
]." H
ere a
nd in
fol-
low
ing e
xam
ple c
aptio
ns, o
rien
ting to
nes c
orre
spon
ding
to sp
e-
cial
not
es in
exa
mpl
es ar
e giv
en in
bol
dfac
e; or
ient
ing t
ones
at
ypic
al of
a gi
ven a
uthe
ntic
or pl
agel
mod
e are
plac
ed in
pare
n-
thes
es.
eigh
t inte
rrup
tions
with
whi
ch M
arch
etto
deal
s. In
each
case
, I
pres
ent M
arch
etto
's mel
odic
exam
ple w
ith th
e ad
ditio
n of x
's an
dy's
over
the r
elev
ant sp
ecia
l not
es, h
is ve
rbal
acco
unt o
f the
re
lativ
e pr
oper
ties o
f th
e m
elod
ic p
rogr
essio
n fo
r va
riou
s m
odes
, and
an ex
plan
atio
n of h
is ac
coun
t as w
ell a
s any
anom
a-
lies t
hat m
ight
appe
ar in
it, w
heth
er ex
plic
itly o
r im
plic
itly.
Exam
ple 3
. Int
erru
ptio
n la:
"Pr
oper
ly in
mod
e 1
[whi
ch ha
s D
3, (G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
ha
s D3,
G3,
C4,
and (
D4)
as o
rien
ting t
ones
]." H
ere a
nd in
fol-
low
ing e
xam
ple c
aptio
ns, o
rien
ting to
nes c
orre
spon
ding
to sp
e-
cial
not
es in
exa
mpl
es ar
e giv
en in
bol
dfac
e; or
ient
ing t
ones
at
ypic
al of
a gi
ven a
uthe
ntic
or pl
agel
mod
e are
plac
ed in
pare
n-
thes
es.
eigh
t inte
rrup
tions
with
whi
ch M
arch
etto
deal
s. In
each
case
, I
pres
ent M
arch
etto
's mel
odic
exam
ple w
ith th
e ad
ditio
n of x
's an
dy's
over
the r
elev
ant sp
ecia
l not
es, h
is ve
rbal
acco
unt o
f the
re
lativ
e pr
oper
ties o
f th
e m
elod
ic p
rogr
essio
n fo
r va
riou
s m
odes
, and
an ex
plan
atio
n of h
is ac
coun
t as w
ell a
s any
anom
a-
lies t
hat m
ight
appe
ar in
it, w
heth
er ex
plic
itly o
r im
plic
itly.
Exam
ple 3
. Int
erru
ptio
n la:
"Pr
oper
ly in
mod
e 1
[whi
ch ha
s D
3, (G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
ha
s D3,
G3,
C4,
and (
D4)
as o
rien
ting t
ones
]." H
ere a
nd in
fol-
low
ing e
xam
ple c
aptio
ns, o
rien
ting to
nes c
orre
spon
ding
to sp
e-
cial
not
es in
exa
mpl
es ar
e giv
en in
bol
dfac
e; or
ient
ing t
ones
at
ypic
al of
a gi
ven a
uthe
ntic
or pl
agel
mod
e are
plac
ed in
pare
n-
thes
es.
eigh
t inte
rrup
tions
with
whi
ch M
arch
etto
deal
s. In
each
case
, I
pres
ent M
arch
etto
's mel
odic
exam
ple w
ith th
e ad
ditio
n of x
's an
dy's
over
the r
elev
ant sp
ecia
l not
es, h
is ve
rbal
acco
unt o
f the
re
lativ
e pr
oper
ties o
f th
e m
elod
ic p
rogr
essio
n fo
r va
riou
s m
odes
, and
an ex
plan
atio
n of h
is ac
coun
t as w
ell a
s any
anom
a-
lies t
hat m
ight
appe
ar in
it, w
heth
er ex
plic
itly o
r im
plic
itly.
Exam
ple 3
. Int
erru
ptio
n la:
"Pr
oper
ly in
mod
e 1
[whi
ch ha
s D
3, (G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
ha
s D3,
G3,
C4,
and (
D4)
as o
rien
ting t
ones
]." H
ere a
nd in
fol-
low
ing e
xam
ple c
aptio
ns, o
rien
ting to
nes c
orre
spon
ding
to sp
e-
cial
not
es in
exa
mpl
es ar
e giv
en in
bol
dfac
e; or
ient
ing t
ones
at
ypic
al of
a gi
ven a
uthe
ntic
or pl
agel
mod
e are
plac
ed in
pare
n-
thes
es.
eigh
t inte
rrup
tions
with
whi
ch M
arch
etto
deal
s. In
each
case
, I
pres
ent M
arch
etto
's mel
odic
exam
ple w
ith th
e ad
ditio
n of x
's an
dy's
over
the r
elev
ant sp
ecia
l not
es, h
is ve
rbal
acco
unt o
f the
re
lativ
e pr
oper
ties o
f th
e m
elod
ic p
rogr
essio
n fo
r va
riou
s m
odes
, and
an ex
plan
atio
n of h
is ac
coun
t as w
ell a
s any
anom
a-
lies t
hat m
ight
appe
ar in
it, w
heth
er ex
plic
itly o
r im
plic
itly.
Exam
ple 3
. Int
erru
ptio
n la:
"Pr
oper
ly in
mod
e 1
[whi
ch ha
s D
3, (G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
ha
s D3,
G3,
C4,
and (
D4)
as o
rien
ting t
ones
]." H
ere a
nd in
fol-
low
ing e
xam
ple c
aptio
ns, o
rien
ting to
nes c
orre
spon
ding
to sp
e-
cial
not
es in
exa
mpl
es ar
e giv
en in
bol
dfac
e; or
ient
ing t
ones
at
ypic
al of
a gi
ven a
uthe
ntic
or pl
agel
mod
e are
plac
ed in
pare
n-
thes
es.
x x x x x x
Indi
vidu
al In
terr
uptio
ns
Inte
rrup
tion la
. A
ccor
ding
to M
arch
etto
, the m
elod
ic pr
o-
gres
sion i
n Ex
ampl
e 3 m
ight
appe
ar "p
rope
rly in
mod
e I a
nd
mod
e VII
I."
Expl
anat
ion.
This
prog
ress
ion i
mpl
ies m
ode I
bec
ause
the
who
le p
assa
ge lie
s with
in th
e pro
per p
erfe
ct ra
nge o
f mod
e I
and
the s
peci
al D
3s a
nd A
3 co
rres
pond
to o
rien
ting n
otes
in
mod
e I. T
he p
rogr
essio
n also
impl
ies m
ode V
III b
ecau
se th
e no
tes l
ie w
ithin
the p
rope
r per
fect
rang
e of m
ode V
III a
nd th
e sp
ecia
l D3s
corr
espo
nd to
an or
ient
ing n
ote i
n mod
e VII
I. O
ne
mig
ht w
onde
r, gi
ven t
he fa
ct th
at m
ode V
III i
s con
sider
ed to
be
impl
ied b
y the
D3s
alon
e, w
hy m
ode I
I is n
ot al
so co
nsid
ered
to
be im
plie
d, fo
r the
who
le p
rogr
essio
n lie
s with
in th
e ran
ge of
m
ode I
I, an
d D3
and A
3 ar
e ori
entin
g not
es in
mod
e II.
How
- ev
er, a
ccor
ding
to c
rite
rion
5 ab
ove,
mod
e I is
mor
e str
ongl
y im
plie
d by t
he p
rogr
essio
n tha
n mod
e II.
This
wou
ld se
em to
ac
coun
t for M
arch
etto
's not
men
tioni
ng m
ode I
I. O
ne ca
n also
ob
serv
e tha
t Mar
chet
to lis
ts m
ode I
bef
ore m
ode
VII
I. Th
is
Indi
vidu
al In
terr
uptio
ns
Inte
rrup
tion la
. A
ccor
ding
to M
arch
etto
, the m
elod
ic pr
o-
gres
sion i
n Ex
ampl
e 3 m
ight
appe
ar "p
rope
rly in
mod
e I a
nd
mod
e VII
I."
Expl
anat
ion.
This
prog
ress
ion i
mpl
ies m
ode I
bec
ause
the
who
le p
assa
ge lie
s with
in th
e pro
per p
erfe
ct ra
nge o
f mod
e I
and
the s
peci
al D
3s a
nd A
3 co
rres
pond
to o
rien
ting n
otes
in
mod
e I. T
he p
rogr
essio
n also
impl
ies m
ode V
III b
ecau
se th
e no
tes l
ie w
ithin
the p
rope
r per
fect
rang
e of m
ode V
III a
nd th
e sp
ecia
l D3s
corr
espo
nd to
an or
ient
ing n
ote i
n mod
e VII
I. O
ne
mig
ht w
onde
r, gi
ven t
he fa
ct th
at m
ode V
III i
s con
sider
ed to
be
impl
ied b
y the
D3s
alon
e, w
hy m
ode I
I is n
ot al
so co
nsid
ered
to
be im
plie
d, fo
r the
who
le p
rogr
essio
n lie
s with
in th
e ran
ge of
m
ode I
I, an
d D3
and A
3 ar
e ori
entin
g not
es in
mod
e II.
How
- ev
er, a
ccor
ding
to c
rite
rion
5 ab
ove,
mod
e I is
mor
e str
ongl
y im
plie
d by t
he p
rogr
essio
n tha
n mod
e II.
This
wou
ld se
em to
ac
coun
t for M
arch
etto
's not
men
tioni
ng m
ode I
I. O
ne ca
n also
ob
serv
e tha
t Mar
chet
to lis
ts m
ode I
bef
ore m
ode
VII
I. Th
is
Indi
vidu
al In
terr
uptio
ns
Inte
rrup
tion la
. A
ccor
ding
to M
arch
etto
, the m
elod
ic pr
o-
gres
sion i
n Ex
ampl
e 3 m
ight
appe
ar "p
rope
rly in
mod
e I a
nd
mod
e VII
I."
Expl
anat
ion.
This
prog
ress
ion i
mpl
ies m
ode I
bec
ause
the
who
le p
assa
ge lie
s with
in th
e pro
per p
erfe
ct ra
nge o
f mod
e I
and
the s
peci
al D
3s a
nd A
3 co
rres
pond
to o
rien
ting n
otes
in
mod
e I. T
he p
rogr
essio
n also
impl
ies m
ode V
III b
ecau
se th
e no
tes l
ie w
ithin
the p
rope
r per
fect
rang
e of m
ode V
III a
nd th
e sp
ecia
l D3s
corr
espo
nd to
an or
ient
ing n
ote i
n mod
e VII
I. O
ne
mig
ht w
onde
r, gi
ven t
he fa
ct th
at m
ode V
III i
s con
sider
ed to
be
impl
ied b
y the
D3s
alon
e, w
hy m
ode I
I is n
ot al
so co
nsid
ered
to
be im
plie
d, fo
r the
who
le p
rogr
essio
n lie
s with
in th
e ran
ge of
m
ode I
I, an
d D3
and A
3 ar
e ori
entin
g not
es in
mod
e II.
How
- ev
er, a
ccor
ding
to c
rite
rion
5 ab
ove,
mod
e I is
mor
e str
ongl
y im
plie
d by t
he p
rogr
essio
n tha
n mod
e II.
This
wou
ld se
em to
ac
coun
t for M
arch
etto
's not
men
tioni
ng m
ode I
I. O
ne ca
n also
ob
serv
e tha
t Mar
chet
to lis
ts m
ode I
bef
ore m
ode
VII
I. Th
is
Indi
vidu
al In
terr
uptio
ns
Inte
rrup
tion la
. A
ccor
ding
to M
arch
etto
, the m
elod
ic pr
o-
gres
sion i
n Ex
ampl
e 3 m
ight
appe
ar "p
rope
rly in
mod
e I a
nd
mod
e VII
I."
Expl
anat
ion.
This
prog
ress
ion i
mpl
ies m
ode I
bec
ause
the
who
le p
assa
ge lie
s with
in th
e pro
per p
erfe
ct ra
nge o
f mod
e I
and
the s
peci
al D
3s a
nd A
3 co
rres
pond
to o
rien
ting n
otes
in
mod
e I. T
he p
rogr
essio
n also
impl
ies m
ode V
III b
ecau
se th
e no
tes l
ie w
ithin
the p
rope
r per
fect
rang
e of m
ode V
III a
nd th
e sp
ecia
l D3s
corr
espo
nd to
an or
ient
ing n
ote i
n mod
e VII
I. O
ne
mig
ht w
onde
r, gi
ven t
he fa
ct th
at m
ode V
III i
s con
sider
ed to
be
impl
ied b
y the
D3s
alon
e, w
hy m
ode I
I is n
ot al
so co
nsid
ered
to
be im
plie
d, fo
r the
who
le p
rogr
essio
n lie
s with
in th
e ran
ge of
m
ode I
I, an
d D3
and A
3 ar
e ori
entin
g not
es in
mod
e II.
How
- ev
er, a
ccor
ding
to c
rite
rion
5 ab
ove,
mod
e I is
mor
e str
ongl
y im
plie
d by t
he p
rogr
essio
n tha
n mod
e II.
This
wou
ld se
em to
ac
coun
t for M
arch
etto
's not
men
tioni
ng m
ode I
I. O
ne ca
n also
ob
serv
e tha
t Mar
chet
to lis
ts m
ode I
bef
ore m
ode
VII
I. Th
is
Indi
vidu
al In
terr
uptio
ns
Inte
rrup
tion la
. A
ccor
ding
to M
arch
etto
, the m
elod
ic pr
o-
gres
sion i
n Ex
ampl
e 3 m
ight
appe
ar "p
rope
rly in
mod
e I a
nd
mod
e VII
I."
Expl
anat
ion.
This
prog
ress
ion i
mpl
ies m
ode I
bec
ause
the
who
le p
assa
ge lie
s with
in th
e pro
per p
erfe
ct ra
nge o
f mod
e I
and
the s
peci
al D
3s a
nd A
3 co
rres
pond
to o
rien
ting n
otes
in
mod
e I. T
he p
rogr
essio
n also
impl
ies m
ode V
III b
ecau
se th
e no
tes l
ie w
ithin
the p
rope
r per
fect
rang
e of m
ode V
III a
nd th
e sp
ecia
l D3s
corr
espo
nd to
an or
ient
ing n
ote i
n mod
e VII
I. O
ne
mig
ht w
onde
r, gi
ven t
he fa
ct th
at m
ode V
III i
s con
sider
ed to
be
impl
ied b
y the
D3s
alon
e, w
hy m
ode I
I is n
ot al
so co
nsid
ered
to
be im
plie
d, fo
r the
who
le p
rogr
essio
n lie
s with
in th
e ran
ge of
m
ode I
I, an
d D3
and A
3 ar
e ori
entin
g not
es in
mod
e II.
How
- ev
er, a
ccor
ding
to c
rite
rion
5 ab
ove,
mod
e I is
mor
e str
ongl
y im
plie
d by t
he p
rogr
essio
n tha
n mod
e II.
This
wou
ld se
em to
ac
coun
t for M
arch
etto
's not
men
tioni
ng m
ode I
I. O
ne ca
n also
ob
serv
e tha
t Mar
chet
to lis
ts m
ode I
bef
ore m
ode
VII
I. Th
is
Indi
vidu
al In
terr
uptio
ns
Inte
rrup
tion la
. A
ccor
ding
to M
arch
etto
, the m
elod
ic pr
o-
gres
sion i
n Ex
ampl
e 3 m
ight
appe
ar "p
rope
rly in
mod
e I a
nd
mod
e VII
I."
Expl
anat
ion.
This
prog
ress
ion i
mpl
ies m
ode I
bec
ause
the
who
le p
assa
ge lie
s with
in th
e pro
per p
erfe
ct ra
nge o
f mod
e I
and
the s
peci
al D
3s a
nd A
3 co
rres
pond
to o
rien
ting n
otes
in
mod
e I. T
he p
rogr
essio
n also
impl
ies m
ode V
III b
ecau
se th
e no
tes l
ie w
ithin
the p
rope
r per
fect
rang
e of m
ode V
III a
nd th
e sp
ecia
l D3s
corr
espo
nd to
an or
ient
ing n
ote i
n mod
e VII
I. O
ne
mig
ht w
onde
r, gi
ven t
he fa
ct th
at m
ode V
III i
s con
sider
ed to
be
impl
ied b
y the
D3s
alon
e, w
hy m
ode I
I is n
ot al
so co
nsid
ered
to
be im
plie
d, fo
r the
who
le p
rogr
essio
n lie
s with
in th
e ran
ge of
m
ode I
I, an
d D3
and A
3 ar
e ori
entin
g not
es in
mod
e II.
How
- ev
er, a
ccor
ding
to c
rite
rion
5 ab
ove,
mod
e I is
mor
e str
ongl
y im
plie
d by t
he p
rogr
essio
n tha
n mod
e II.
This
wou
ld se
em to
ac
coun
t for M
arch
etto
's not
men
tioni
ng m
ode I
I. O
ne ca
n also
ob
serv
e tha
t Mar
chet
to lis
ts m
ode I
bef
ore m
ode
VII
I. Th
is
mig
ht be
con
sider
ed to
impl
y tha
t Mar
chet
to vi
ews m
ode I
as
mor
e str
ongl
y im
plie
d tha
n mod
e VII
I. Th
is w
ould
be co
nsist
- en
t with
crite
rion
3, fo
r thr
ee of
the s
peci
al no
tes c
oinc
ide w
ith
orie
ntin
g not
es in
mod
e I
(i.e.
, th
e tw
o D
3s a
nd th
e A
3),
whe
reas
only
two
spec
ial n
otes
in th
e pas
sage
(the
D3s
) coi
n-
cide
with
an or
ient
ing n
ote o
f mod
e VII
I. M
arch
etto
does
not
lis
t mod
e IV
, alth
ough
the s
peci
al no
te A
3 co
rres
pond
s to a
n or
ient
ing n
ote i
n m
ode I
V. H
owev
er, a
ccor
ding
to c
rite
rion
3 ag
ain,
mod
e IV
is no
t as s
tron
gly im
plie
d as m
ode V
III.
In su
m,
cons
isten
t with
the
mix
ture
of c
ateg
oric
al an
d re
lativ
istic
ap-
proa
ches
that
Mar
chet
to se
ems t
o ha
ve ad
opte
d in
the c
hapt
er
as a
who
le, i
t wou
ld a
ppea
r tha
t he
has m
ade m
ode
VII
I his
cuto
ff po
int i
n de
alin
g with
a c
ontin
uum
of im
plic
atio
n tha
t m
ight
also
hav
e inc
lude
d mod
es II
and I
V. M
oreo
ver,
he d
oes
this
in a
man
ner
that
is c
onsis
tent
with
the
crite
ria
liste
d ab
ove.
24
Inte
rrup
tion lb
. M
arch
etto
rela
tes t
hat i
f the
firs
t inte
rrup
- tio
n is u
sed i
n a m
ode o
ther
than
I or V
III,
it is
said
to b
e "co
m-
mix
ed, a
s in
the [
pres
ent] e
xam
ple"
(Exa
mpl
e 4 h
ere)
.
24In
the v
aria
nts o
f the
exam
ple u
sed t
o illu
stra
te th
is in
terr
uptio
n, th
ree o
f th
e sou
rces
devi
ate s
ubst
antia
lly fr
om th
e bul
k of t
he m
anus
crip
t trad
ition
. In
MS.
734
, Flo
renc
e, B
iblio
teca
Ric
card
iana
, and
MS.
606
(IV
. 9) P
isa, B
ib-
liote
ca U
nive
rsita
ria,
ther
e is
a di
ffere
nt co
ntin
uatio
n afte
r the
initi
al ri
sing
form
of th
e int
erru
ptio
n. M
ost o
f the
vari
ants
of th
e exa
mpl
es in
this
sect
ion o
f th
e tre
atise
belo
ng to
one
of t
wo
type
s: (1
) as a
bove
, the
initi
al ri
sing f
orm
is
pres
erve
d and
diffe
rent
note
s are
adde
d afte
rwar
ds; or
(2) b
oth r
ising
and f
all-
ing f
orm
s are
pres
ente
d and
a su
pple
men
tary
cont
inua
tion i
s add
ed. I
n nei
ther
ca
se is
ther
e a su
bsta
ntia
l, mea
ning
ful ch
ange
intr
oduc
ed by
the v
aria
nt. In
the
note
s tha
t acc
ompa
ny th
e ind
ivid
ual in
terr
uptio
ns de
alt w
ith be
low
, com
men
ts
are
mad
e on
ly o
n po
tent
ially
sign
ifica
nt di
ffere
nces
bet
wee
n so
urce
s. Th
is re
flect
s the
spec
ial s
tatu
s Mar
chet
to ac
cord
s to
initi
al ri
sing f
orm
s thr
ough
out
the e
leve
nth t
reat
ise. I
n M
S. D
. 39,
Cat
ania
, Bib
liote
che R
iuni
te "C
ivic
a e A
. U
rsin
o-R
ecup
ero,
" Fon
do U
rsin
o-R
ecup
ero,
thre
e exa
mpl
es of
the f
irst
inte
r-
rupt
ion a
re pr
esen
ted;
the f
irst
two b
egin
on B
2 an
d C3,
and t
he th
ird o
n D
3 as
in th
e res
t of t
he so
urce
s. Th
is w
ould
appe
ar to
repr
esen
t a m
ere e
xten
sion o
f th
e ide
a em
bodi
ed in
the f
irst
inte
rrup
tion b
eyon
d the
firs
t spec
ies o
f fift
h (D
3-
A3)
to th
e thi
rd an
d fou
rth s
peci
es (B
l,2-F
3 an
d C3-
G3,
res
pect
ivel
y).
mig
ht be
con
sider
ed to
impl
y tha
t Mar
chet
to vi
ews m
ode I
as
mor
e str
ongl
y im
plie
d tha
n mod
e VII
I. Th
is w
ould
be co
nsist
- en
t with
crite
rion
3, fo
r thr
ee of
the s
peci
al no
tes c
oinc
ide w
ith
orie
ntin
g not
es in
mod
e I
(i.e.
, th
e tw
o D
3s a
nd th
e A
3),
whe
reas
only
two
spec
ial n
otes
in th
e pas
sage
(the
D3s
) coi
n-
cide
with
an or
ient
ing n
ote o
f mod
e VII
I. M
arch
etto
does
not
lis
t mod
e IV
, alth
ough
the s
peci
al no
te A
3 co
rres
pond
s to a
n or
ient
ing n
ote i
n m
ode I
V. H
owev
er, a
ccor
ding
to c
rite
rion
3 ag
ain,
mod
e IV
is no
t as s
tron
gly im
plie
d as m
ode V
III.
In su
m,
cons
isten
t with
the
mix
ture
of c
ateg
oric
al an
d re
lativ
istic
ap-
proa
ches
that
Mar
chet
to se
ems t
o ha
ve ad
opte
d in
the c
hapt
er
as a
who
le, i
t wou
ld a
ppea
r tha
t he
has m
ade m
ode
VII
I his
cuto
ff po
int i
n de
alin
g with
a c
ontin
uum
of im
plic
atio
n tha
t m
ight
also
hav
e inc
lude
d mod
es II
and I
V. M
oreo
ver,
he d
oes
this
in a
man
ner
that
is c
onsis
tent
with
the
crite
ria
liste
d ab
ove.
24
Inte
rrup
tion lb
. M
arch
etto
rela
tes t
hat i
f the
firs
t inte
rrup
- tio
n is u
sed i
n a m
ode o
ther
than
I or V
III,
it is
said
to b
e "co
m-
mix
ed, a
s in
the [
pres
ent] e
xam
ple"
(Exa
mpl
e 4 h
ere)
.
24In
the v
aria
nts o
f the
exam
ple u
sed t
o illu
stra
te th
is in
terr
uptio
n, th
ree o
f th
e sou
rces
devi
ate s
ubst
antia
lly fr
om th
e bul
k of t
he m
anus
crip
t trad
ition
. In
MS.
734
, Flo
renc
e, B
iblio
teca
Ric
card
iana
, and
MS.
606
(IV
. 9) P
isa, B
ib-
liote
ca U
nive
rsita
ria,
ther
e is
a di
ffere
nt co
ntin
uatio
n afte
r the
initi
al ri
sing
form
of th
e int
erru
ptio
n. M
ost o
f the
vari
ants
of th
e exa
mpl
es in
this
sect
ion o
f th
e tre
atise
belo
ng to
one
of t
wo
type
s: (1
) as a
bove
, the
initi
al ri
sing f
orm
is
pres
erve
d and
diffe
rent
note
s are
adde
d afte
rwar
ds; or
(2) b
oth r
ising
and f
all-
ing f
orm
s are
pres
ente
d and
a su
pple
men
tary
cont
inua
tion i
s add
ed. I
n nei
ther
ca
se is
ther
e a su
bsta
ntia
l, mea
ning
ful ch
ange
intr
oduc
ed by
the v
aria
nt. In
the
note
s tha
t acc
ompa
ny th
e ind
ivid
ual in
terr
uptio
ns de
alt w
ith be
low
, com
men
ts
are
mad
e on
ly o
n po
tent
ially
sign
ifica
nt di
ffere
nces
bet
wee
n so
urce
s. Th
is re
flect
s the
spec
ial s
tatu
s Mar
chet
to ac
cord
s to
initi
al ri
sing f
orm
s thr
ough
out
the e
leve
nth t
reat
ise. I
n M
S. D
. 39,
Cat
ania
, Bib
liote
che R
iuni
te "C
ivic
a e A
. U
rsin
o-R
ecup
ero,
" Fon
do U
rsin
o-R
ecup
ero,
thre
e exa
mpl
es of
the f
irst
inte
r-
rupt
ion a
re pr
esen
ted;
the f
irst
two b
egin
on B
2 an
d C3,
and t
he th
ird o
n D
3 as
in th
e res
t of t
he so
urce
s. Th
is w
ould
appe
ar to
repr
esen
t a m
ere e
xten
sion o
f th
e ide
a em
bodi
ed in
the f
irst
inte
rrup
tion b
eyon
d the
firs
t spec
ies o
f fift
h (D
3-
A3)
to th
e thi
rd an
d fou
rth s
peci
es (B
l,2-F
3 an
d C3-
G3,
res
pect
ivel
y).
mig
ht be
con
sider
ed to
impl
y tha
t Mar
chet
to vi
ews m
ode I
as
mor
e str
ongl
y im
plie
d tha
n mod
e VII
I. Th
is w
ould
be co
nsist
- en
t with
crite
rion
3, fo
r thr
ee of
the s
peci
al no
tes c
oinc
ide w
ith
orie
ntin
g not
es in
mod
e I
(i.e.
, th
e tw
o D
3s a
nd th
e A
3),
whe
reas
only
two
spec
ial n
otes
in th
e pas
sage
(the
D3s
) coi
n-
cide
with
an or
ient
ing n
ote o
f mod
e VII
I. M
arch
etto
does
not
lis
t mod
e IV
, alth
ough
the s
peci
al no
te A
3 co
rres
pond
s to a
n or
ient
ing n
ote i
n m
ode I
V. H
owev
er, a
ccor
ding
to c
rite
rion
3 ag
ain,
mod
e IV
is no
t as s
tron
gly im
plie
d as m
ode V
III.
In su
m,
cons
isten
t with
the
mix
ture
of c
ateg
oric
al an
d re
lativ
istic
ap-
proa
ches
that
Mar
chet
to se
ems t
o ha
ve ad
opte
d in
the c
hapt
er
as a
who
le, i
t wou
ld a
ppea
r tha
t he
has m
ade m
ode
VII
I his
cuto
ff po
int i
n de
alin
g with
a c
ontin
uum
of im
plic
atio
n tha
t m
ight
also
hav
e inc
lude
d mod
es II
and I
V. M
oreo
ver,
he d
oes
this
in a
man
ner
that
is c
onsis
tent
with
the
crite
ria
liste
d ab
ove.
24
Inte
rrup
tion lb
. M
arch
etto
rela
tes t
hat i
f the
firs
t inte
rrup
- tio
n is u
sed i
n a m
ode o
ther
than
I or V
III,
it is
said
to b
e "co
m-
mix
ed, a
s in
the [
pres
ent] e
xam
ple"
(Exa
mpl
e 4 h
ere)
.
24In
the v
aria
nts o
f the
exam
ple u
sed t
o illu
stra
te th
is in
terr
uptio
n, th
ree o
f th
e sou
rces
devi
ate s
ubst
antia
lly fr
om th
e bul
k of t
he m
anus
crip
t trad
ition
. In
MS.
734
, Flo
renc
e, B
iblio
teca
Ric
card
iana
, and
MS.
606
(IV
. 9) P
isa, B
ib-
liote
ca U
nive
rsita
ria,
ther
e is
a di
ffere
nt co
ntin
uatio
n afte
r the
initi
al ri
sing
form
of th
e int
erru
ptio
n. M
ost o
f the
vari
ants
of th
e exa
mpl
es in
this
sect
ion o
f th
e tre
atise
belo
ng to
one
of t
wo
type
s: (1
) as a
bove
, the
initi
al ri
sing f
orm
is
pres
erve
d and
diffe
rent
note
s are
adde
d afte
rwar
ds; or
(2) b
oth r
ising
and f
all-
ing f
orm
s are
pres
ente
d and
a su
pple
men
tary
cont
inua
tion i
s add
ed. I
n nei
ther
ca
se is
ther
e a su
bsta
ntia
l, mea
ning
ful ch
ange
intr
oduc
ed by
the v
aria
nt. In
the
note
s tha
t acc
ompa
ny th
e ind
ivid
ual in
terr
uptio
ns de
alt w
ith be
low
, com
men
ts
are
mad
e on
ly o
n po
tent
ially
sign
ifica
nt di
ffere
nces
bet
wee
n so
urce
s. Th
is re
flect
s the
spec
ial s
tatu
s Mar
chet
to ac
cord
s to
initi
al ri
sing f
orm
s thr
ough
out
the e
leve
nth t
reat
ise. I
n M
S. D
. 39,
Cat
ania
, Bib
liote
che R
iuni
te "C
ivic
a e A
. U
rsin
o-R
ecup
ero,
" Fon
do U
rsin
o-R
ecup
ero,
thre
e exa
mpl
es of
the f
irst
inte
r-
rupt
ion a
re pr
esen
ted;
the f
irst
two b
egin
on B
2 an
d C3,
and t
he th
ird o
n D
3 as
in th
e res
t of t
he so
urce
s. Th
is w
ould
appe
ar to
repr
esen
t a m
ere e
xten
sion o
f th
e ide
a em
bodi
ed in
the f
irst
inte
rrup
tion b
eyon
d the
firs
t spec
ies o
f fift
h (D
3-
A3)
to th
e thi
rd an
d fou
rth s
peci
es (B
l,2-F
3 an
d C3-
G3,
res
pect
ivel
y).
mig
ht be
con
sider
ed to
impl
y tha
t Mar
chet
to vi
ews m
ode I
as
mor
e str
ongl
y im
plie
d tha
n mod
e VII
I. Th
is w
ould
be co
nsist
- en
t with
crite
rion
3, fo
r thr
ee of
the s
peci
al no
tes c
oinc
ide w
ith
orie
ntin
g not
es in
mod
e I
(i.e.
, th
e tw
o D
3s a
nd th
e A
3),
whe
reas
only
two
spec
ial n
otes
in th
e pas
sage
(the
D3s
) coi
n-
cide
with
an or
ient
ing n
ote o
f mod
e VII
I. M
arch
etto
does
not
lis
t mod
e IV
, alth
ough
the s
peci
al no
te A
3 co
rres
pond
s to a
n or
ient
ing n
ote i
n m
ode I
V. H
owev
er, a
ccor
ding
to c
rite
rion
3 ag
ain,
mod
e IV
is no
t as s
tron
gly im
plie
d as m
ode V
III.
In su
m,
cons
isten
t with
the
mix
ture
of c
ateg
oric
al an
d re
lativ
istic
ap-
proa
ches
that
Mar
chet
to se
ems t
o ha
ve ad
opte
d in
the c
hapt
er
as a
who
le, i
t wou
ld a
ppea
r tha
t he
has m
ade m
ode
VII
I his
cuto
ff po
int i
n de
alin
g with
a c
ontin
uum
of im
plic
atio
n tha
t m
ight
also
hav
e inc
lude
d mod
es II
and I
V. M
oreo
ver,
he d
oes
this
in a
man
ner
that
is c
onsis
tent
with
the
crite
ria
liste
d ab
ove.
24
Inte
rrup
tion lb
. M
arch
etto
rela
tes t
hat i
f the
firs
t inte
rrup
- tio
n is u
sed i
n a m
ode o
ther
than
I or V
III,
it is
said
to b
e "co
m-
mix
ed, a
s in
the [
pres
ent] e
xam
ple"
(Exa
mpl
e 4 h
ere)
.
24In
the v
aria
nts o
f the
exam
ple u
sed t
o illu
stra
te th
is in
terr
uptio
n, th
ree o
f th
e sou
rces
devi
ate s
ubst
antia
lly fr
om th
e bul
k of t
he m
anus
crip
t trad
ition
. In
MS.
734
, Flo
renc
e, B
iblio
teca
Ric
card
iana
, and
MS.
606
(IV
. 9) P
isa, B
ib-
liote
ca U
nive
rsita
ria,
ther
e is
a di
ffere
nt co
ntin
uatio
n afte
r the
initi
al ri
sing
form
of th
e int
erru
ptio
n. M
ost o
f the
vari
ants
of th
e exa
mpl
es in
this
sect
ion o
f th
e tre
atise
belo
ng to
one
of t
wo
type
s: (1
) as a
bove
, the
initi
al ri
sing f
orm
is
pres
erve
d and
diffe
rent
note
s are
adde
d afte
rwar
ds; or
(2) b
oth r
ising
and f
all-
ing f
orm
s are
pres
ente
d and
a su
pple
men
tary
cont
inua
tion i
s add
ed. I
n nei
ther
ca
se is
ther
e a su
bsta
ntia
l, mea
ning
ful ch
ange
intr
oduc
ed by
the v
aria
nt. In
the
note
s tha
t acc
ompa
ny th
e ind
ivid
ual in
terr
uptio
ns de
alt w
ith be
low
, com
men
ts
are
mad
e on
ly o
n po
tent
ially
sign
ifica
nt di
ffere
nces
bet
wee
n so
urce
s. Th
is re
flect
s the
spec
ial s
tatu
s Mar
chet
to ac
cord
s to
initi
al ri
sing f
orm
s thr
ough
out
the e
leve
nth t
reat
ise. I
n M
S. D
. 39,
Cat
ania
, Bib
liote
che R
iuni
te "C
ivic
a e A
. U
rsin
o-R
ecup
ero,
" Fon
do U
rsin
o-R
ecup
ero,
thre
e exa
mpl
es of
the f
irst
inte
r-
rupt
ion a
re pr
esen
ted;
the f
irst
two b
egin
on B
2 an
d C3,
and t
he th
ird o
n D
3 as
in th
e res
t of t
he so
urce
s. Th
is w
ould
appe
ar to
repr
esen
t a m
ere e
xten
sion o
f th
e ide
a em
bodi
ed in
the f
irst
inte
rrup
tion b
eyon
d the
firs
t spec
ies o
f fift
h (D
3-
A3)
to th
e thi
rd an
d fou
rth s
peci
es (B
l,2-F
3 an
d C3-
G3,
res
pect
ivel
y).
mig
ht be
con
sider
ed to
impl
y tha
t Mar
chet
to vi
ews m
ode I
as
mor
e str
ongl
y im
plie
d tha
n mod
e VII
I. Th
is w
ould
be co
nsist
- en
t with
crite
rion
3, fo
r thr
ee of
the s
peci
al no
tes c
oinc
ide w
ith
orie
ntin
g not
es in
mod
e I
(i.e.
, th
e tw
o D
3s a
nd th
e A
3),
whe
reas
only
two
spec
ial n
otes
in th
e pas
sage
(the
D3s
) coi
n-
cide
with
an or
ient
ing n
ote o
f mod
e VII
I. M
arch
etto
does
not
lis
t mod
e IV
, alth
ough
the s
peci
al no
te A
3 co
rres
pond
s to a
n or
ient
ing n
ote i
n m
ode I
V. H
owev
er, a
ccor
ding
to c
rite
rion
3 ag
ain,
mod
e IV
is no
t as s
tron
gly im
plie
d as m
ode V
III.
In su
m,
cons
isten
t with
the
mix
ture
of c
ateg
oric
al an
d re
lativ
istic
ap-
proa
ches
that
Mar
chet
to se
ems t
o ha
ve ad
opte
d in
the c
hapt
er
as a
who
le, i
t wou
ld a
ppea
r tha
t he
has m
ade m
ode
VII
I his
cuto
ff po
int i
n de
alin
g with
a c
ontin
uum
of im
plic
atio
n tha
t m
ight
also
hav
e inc
lude
d mod
es II
and I
V. M
oreo
ver,
he d
oes
this
in a
man
ner
that
is c
onsis
tent
with
the
crite
ria
liste
d ab
ove.
24
Inte
rrup
tion lb
. M
arch
etto
rela
tes t
hat i
f the
firs
t inte
rrup
- tio
n is u
sed i
n a m
ode o
ther
than
I or V
III,
it is
said
to b
e "co
m-
mix
ed, a
s in
the [
pres
ent] e
xam
ple"
(Exa
mpl
e 4 h
ere)
.
24In
the v
aria
nts o
f the
exam
ple u
sed t
o illu
stra
te th
is in
terr
uptio
n, th
ree o
f th
e sou
rces
devi
ate s
ubst
antia
lly fr
om th
e bul
k of t
he m
anus
crip
t trad
ition
. In
MS.
734
, Flo
renc
e, B
iblio
teca
Ric
card
iana
, and
MS.
606
(IV
. 9) P
isa, B
ib-
liote
ca U
nive
rsita
ria,
ther
e is
a di
ffere
nt co
ntin
uatio
n afte
r the
initi
al ri
sing
form
of th
e int
erru
ptio
n. M
ost o
f the
vari
ants
of th
e exa
mpl
es in
this
sect
ion o
f th
e tre
atise
belo
ng to
one
of t
wo
type
s: (1
) as a
bove
, the
initi
al ri
sing f
orm
is
pres
erve
d and
diffe
rent
note
s are
adde
d afte
rwar
ds; or
(2) b
oth r
ising
and f
all-
ing f
orm
s are
pres
ente
d and
a su
pple
men
tary
cont
inua
tion i
s add
ed. I
n nei
ther
ca
se is
ther
e a su
bsta
ntia
l, mea
ning
ful ch
ange
intr
oduc
ed by
the v
aria
nt. In
the
note
s tha
t acc
ompa
ny th
e ind
ivid
ual in
terr
uptio
ns de
alt w
ith be
low
, com
men
ts
are
mad
e on
ly o
n po
tent
ially
sign
ifica
nt di
ffere
nces
bet
wee
n so
urce
s. Th
is re
flect
s the
spec
ial s
tatu
s Mar
chet
to ac
cord
s to
initi
al ri
sing f
orm
s thr
ough
out
the e
leve
nth t
reat
ise. I
n M
S. D
. 39,
Cat
ania
, Bib
liote
che R
iuni
te "C
ivic
a e A
. U
rsin
o-R
ecup
ero,
" Fon
do U
rsin
o-R
ecup
ero,
thre
e exa
mpl
es of
the f
irst
inte
r-
rupt
ion a
re pr
esen
ted;
the f
irst
two b
egin
on B
2 an
d C3,
and t
he th
ird o
n D
3 as
in th
e res
t of t
he so
urce
s. Th
is w
ould
appe
ar to
repr
esen
t a m
ere e
xten
sion o
f th
e ide
a em
bodi
ed in
the f
irst
inte
rrup
tion b
eyon
d the
firs
t spec
ies o
f fift
h (D
3-
A3)
to th
e thi
rd an
d fou
rth s
peci
es (B
l,2-F
3 an
d C3-
G3,
res
pect
ivel
y).
mig
ht be
con
sider
ed to
impl
y tha
t Mar
chet
to vi
ews m
ode I
as
mor
e str
ongl
y im
plie
d tha
n mod
e VII
I. Th
is w
ould
be co
nsist
- en
t with
crite
rion
3, fo
r thr
ee of
the s
peci
al no
tes c
oinc
ide w
ith
orie
ntin
g not
es in
mod
e I
(i.e.
, th
e tw
o D
3s a
nd th
e A
3),
whe
reas
only
two
spec
ial n
otes
in th
e pas
sage
(the
D3s
) coi
n-
cide
with
an or
ient
ing n
ote o
f mod
e VII
I. M
arch
etto
does
not
lis
t mod
e IV
, alth
ough
the s
peci
al no
te A
3 co
rres
pond
s to a
n or
ient
ing n
ote i
n m
ode I
V. H
owev
er, a
ccor
ding
to c
rite
rion
3 ag
ain,
mod
e IV
is no
t as s
tron
gly im
plie
d as m
ode V
III.
In su
m,
cons
isten
t with
the
mix
ture
of c
ateg
oric
al an
d re
lativ
istic
ap-
proa
ches
that
Mar
chet
to se
ems t
o ha
ve ad
opte
d in
the c
hapt
er
as a
who
le, i
t wou
ld a
ppea
r tha
t he
has m
ade m
ode
VII
I his
cuto
ff po
int i
n de
alin
g with
a c
ontin
uum
of im
plic
atio
n tha
t m
ight
also
hav
e inc
lude
d mod
es II
and I
V. M
oreo
ver,
he d
oes
this
in a
man
ner
that
is c
onsis
tent
with
the
crite
ria
liste
d ab
ove.
24
Inte
rrup
tion lb
. M
arch
etto
rela
tes t
hat i
f the
firs
t inte
rrup
- tio
n is u
sed i
n a m
ode o
ther
than
I or V
III,
it is
said
to b
e "co
m-
mix
ed, a
s in
the [
pres
ent] e
xam
ple"
(Exa
mpl
e 4 h
ere)
.
24In
the v
aria
nts o
f the
exam
ple u
sed t
o illu
stra
te th
is in
terr
uptio
n, th
ree o
f th
e sou
rces
devi
ate s
ubst
antia
lly fr
om th
e bul
k of t
he m
anus
crip
t trad
ition
. In
MS.
734
, Flo
renc
e, B
iblio
teca
Ric
card
iana
, and
MS.
606
(IV
. 9) P
isa, B
ib-
liote
ca U
nive
rsita
ria,
ther
e is
a di
ffere
nt co
ntin
uatio
n afte
r the
initi
al ri
sing
form
of th
e int
erru
ptio
n. M
ost o
f the
vari
ants
of th
e exa
mpl
es in
this
sect
ion o
f th
e tre
atise
belo
ng to
one
of t
wo
type
s: (1
) as a
bove
, the
initi
al ri
sing f
orm
is
pres
erve
d and
diffe
rent
note
s are
adde
d afte
rwar
ds; or
(2) b
oth r
ising
and f
all-
ing f
orm
s are
pres
ente
d and
a su
pple
men
tary
cont
inua
tion i
s add
ed. I
n nei
ther
ca
se is
ther
e a su
bsta
ntia
l, mea
ning
ful ch
ange
intr
oduc
ed by
the v
aria
nt. In
the
note
s tha
t acc
ompa
ny th
e ind
ivid
ual in
terr
uptio
ns de
alt w
ith be
low
, com
men
ts
are
mad
e on
ly o
n po
tent
ially
sign
ifica
nt di
ffere
nces
bet
wee
n so
urce
s. Th
is re
flect
s the
spec
ial s
tatu
s Mar
chet
to ac
cord
s to
initi
al ri
sing f
orm
s thr
ough
out
the e
leve
nth t
reat
ise. I
n M
S. D
. 39,
Cat
ania
, Bib
liote
che R
iuni
te "C
ivic
a e A
. U
rsin
o-R
ecup
ero,
" Fon
do U
rsin
o-R
ecup
ero,
thre
e exa
mpl
es of
the f
irst
inte
r-
rupt
ion a
re pr
esen
ted;
the f
irst
two b
egin
on B
2 an
d C3,
and t
he th
ird o
n D
3 as
in th
e res
t of t
he so
urce
s. Th
is w
ould
appe
ar to
repr
esen
t a m
ere e
xten
sion o
f th
e ide
a em
bodi
ed in
the f
irst
inte
rrup
tion b
eyon
d the
firs
t spec
ies o
f fift
h (D
3-
A3)
to th
e thi
rd an
d fou
rth s
peci
es (B
l,2-F
3 an
d C3-
G3,
res
pect
ivel
y).
x x x x x x
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
127
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
127
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
127
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
127
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
127
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
127
Expl
anat
ion.
This
is th
e onl
y ins
tanc
e whe
re M
arch
etto
and
the m
ajor
ity of
thos
e who
copi
ed h
is tr
eatis
e pro
vide
d tw
o dis-
tin
ct m
usic
al ex
ampl
es in
dea
ling w
ith a
sin
gle i
nter
rupt
ion.
Fr
om th
e con
text
it se
ems t
hat h
ere,
at t
he ou
tset
of h
is di
scus
- sio
n of i
nter
rupt
ions
, Mar
chet
to is
prov
idin
g an e
labo
rate
illus
- tr
atio
n of c
omm
ixtu
re th
at ti
es in
with
his
othe
r disc
ussio
ns of
co
mm
ixtu
re. F
or, a
ccor
ding
to h
is ap
proa
ch, th
e who
le m
elod
y is
in m
ode I
V b
y vir
tue o
f the
spec
ial A
3s a
nd E
3s an
d the
con-
cl
usio
n on
E3. E
mbe
dded
in th
is m
elod
y, h
owev
er, is
a fir
st in
- te
rrup
tion o
f the
firs
t spe
cies
as im
plie
d by t
he sp
ecia
l D3
and
A3
at th
e beg
inni
ng of
the i
llust
ratio
n. M
arch
etto
mak
es it
clea
r ju
st ab
ove t
hat a
n int
erru
ptio
n nee
d not
incl
ude b
oth r
ising
and
falli
ng fo
rms,
but m
ay in
clud
e onl
y one
or th
e oth
er. H
e say
s in
the p
rece
ding
sent
ence
that
"the
first
inte
rrup
tion c
onsis
ts of
all
the t
ones
of th
e spe
cies
of fi
fth w
heth
er [t
hese
are p
rese
nted
] in
asce
nt or
des
cent
" (p
rim
a int
erru
ptio
diap
ente
fit e
x om
nibu
s su
is so
nis,
sive p
er ar
sim siv
e per
thes
im). I
n the
case
of th
is ex
- am
ple,
a ri
sing f
orm
of th
e fir
st sp
ecie
s is p
rese
nted
at th
e out
set
in su
ch a
way
as to
impl
y mod
e I (o
r VII
I). B
y vir
tue o
f the
fact
th
at th
is im
plic
atio
n of m
ode I
(or V
III)
app
ears
as p
art o
f a
mel
ody t
hat o
ther
wise
, and
as a
who
le, i
mpl
ies m
ode I
V, m
ode
I (or
VII
I) c
an b
e sa
id to
be
com
mix
ed w
ith m
ode I
V. I
n th
e w
ords
that
Mar
chet
to us
es to
intr
oduc
e thi
s exc
eptio
nal e
xam
- pl
e, "
if [th
e fir
st in
terr
uptio
n of t
he fi
rst sp
ecie
s] be
pla
ced i
n [a
m
elod
y tha
t im
plie
s] a
mod
e oth
er [t
han I
or V
III]
, it is
said
to
be co
mm
ixed
" (si
in al
iopo
natu
r, co
mm
ixta
dice
tur)
.25
Exam
ple 4
. Int
erru
ptio
n lb: "
If th
e fir
st in
terr
uptio
n is us
ed in
a m
ode o
ther
than
I or
VII
I, it
is sa
id to
be c
omm
ixed
, as i
n th
is ex
ampl
e."
nn ,,
I I
1 1
I
Expl
anat
ion.
This
is th
e onl
y ins
tanc
e whe
re M
arch
etto
and
the m
ajor
ity of
thos
e who
copi
ed h
is tr
eatis
e pro
vide
d tw
o dis-
tin
ct m
usic
al ex
ampl
es in
dea
ling w
ith a
sin
gle i
nter
rupt
ion.
Fr
om th
e con
text
it se
ems t
hat h
ere,
at t
he ou
tset
of h
is di
scus
- sio
n of i
nter
rupt
ions
, Mar
chet
to is
prov
idin
g an e
labo
rate
illus
- tr
atio
n of c
omm
ixtu
re th
at ti
es in
with
his
othe
r disc
ussio
ns of
co
mm
ixtu
re. F
or, a
ccor
ding
to h
is ap
proa
ch, th
e who
le m
elod
y is
in m
ode I
V b
y vir
tue o
f the
spec
ial A
3s a
nd E
3s an
d the
con-
cl
usio
n on
E3. E
mbe
dded
in th
is m
elod
y, h
owev
er, is
a fir
st in
- te
rrup
tion o
f the
firs
t spe
cies
as im
plie
d by t
he sp
ecia
l D3
and
A3
at th
e beg
inni
ng of
the i
llust
ratio
n. M
arch
etto
mak
es it
clea
r ju
st ab
ove t
hat a
n int
erru
ptio
n nee
d not
incl
ude b
oth r
ising
and
falli
ng fo
rms,
but m
ay in
clud
e onl
y one
or th
e oth
er. H
e say
s in
the p
rece
ding
sent
ence
that
"the
first
inte
rrup
tion c
onsis
ts of
all
the t
ones
of th
e spe
cies
of fi
fth w
heth
er [t
hese
are p
rese
nted
] in
asce
nt or
des
cent
" (p
rim
a int
erru
ptio
diap
ente
fit e
x om
nibu
s su
is so
nis,
sive p
er ar
sim siv
e per
thes
im). I
n the
case
of th
is ex
- am
ple,
a ri
sing f
orm
of th
e fir
st sp
ecie
s is p
rese
nted
at th
e out
set
in su
ch a
way
as to
impl
y mod
e I (o
r VII
I). B
y vir
tue o
f the
fact
th
at th
is im
plic
atio
n of m
ode I
(or V
III)
app
ears
as p
art o
f a
mel
ody t
hat o
ther
wise
, and
as a
who
le, i
mpl
ies m
ode I
V, m
ode
I (or
VII
I) c
an b
e sa
id to
be
com
mix
ed w
ith m
ode I
V. I
n th
e w
ords
that
Mar
chet
to us
es to
intr
oduc
e thi
s exc
eptio
nal e
xam
- pl
e, "
if [th
e fir
st in
terr
uptio
n of t
he fi
rst sp
ecie
s] be
pla
ced i
n [a
m
elod
y tha
t im
plie
s] a
mod
e oth
er [t
han I
or V
III]
, it is
said
to
be co
mm
ixed
" (si
in al
iopo
natu
r, co
mm
ixta
dice
tur)
.25
Exam
ple 4
. Int
erru
ptio
n lb: "
If th
e fir
st in
terr
uptio
n is us
ed in
a m
ode o
ther
than
I or
VII
I, it
is sa
id to
be c
omm
ixed
, as i
n th
is ex
ampl
e."
nn ,,
I I
1 1
I
Expl
anat
ion.
This
is th
e onl
y ins
tanc
e whe
re M
arch
etto
and
the m
ajor
ity of
thos
e who
copi
ed h
is tr
eatis
e pro
vide
d tw
o dis-
tin
ct m
usic
al ex
ampl
es in
dea
ling w
ith a
sin
gle i
nter
rupt
ion.
Fr
om th
e con
text
it se
ems t
hat h
ere,
at t
he ou
tset
of h
is di
scus
- sio
n of i
nter
rupt
ions
, Mar
chet
to is
prov
idin
g an e
labo
rate
illus
- tr
atio
n of c
omm
ixtu
re th
at ti
es in
with
his
othe
r disc
ussio
ns of
co
mm
ixtu
re. F
or, a
ccor
ding
to h
is ap
proa
ch, th
e who
le m
elod
y is
in m
ode I
V b
y vir
tue o
f the
spec
ial A
3s a
nd E
3s an
d the
con-
cl
usio
n on
E3. E
mbe
dded
in th
is m
elod
y, h
owev
er, is
a fir
st in
- te
rrup
tion o
f the
firs
t spe
cies
as im
plie
d by t
he sp
ecia
l D3
and
A3
at th
e beg
inni
ng of
the i
llust
ratio
n. M
arch
etto
mak
es it
clea
r ju
st ab
ove t
hat a
n int
erru
ptio
n nee
d not
incl
ude b
oth r
ising
and
falli
ng fo
rms,
but m
ay in
clud
e onl
y one
or th
e oth
er. H
e say
s in
the p
rece
ding
sent
ence
that
"the
first
inte
rrup
tion c
onsis
ts of
all
the t
ones
of th
e spe
cies
of fi
fth w
heth
er [t
hese
are p
rese
nted
] in
asce
nt or
des
cent
" (p
rim
a int
erru
ptio
diap
ente
fit e
x om
nibu
s su
is so
nis,
sive p
er ar
sim siv
e per
thes
im). I
n the
case
of th
is ex
- am
ple,
a ri
sing f
orm
of th
e fir
st sp
ecie
s is p
rese
nted
at th
e out
set
in su
ch a
way
as to
impl
y mod
e I (o
r VII
I). B
y vir
tue o
f the
fact
th
at th
is im
plic
atio
n of m
ode I
(or V
III)
app
ears
as p
art o
f a
mel
ody t
hat o
ther
wise
, and
as a
who
le, i
mpl
ies m
ode I
V, m
ode
I (or
VII
I) c
an b
e sa
id to
be
com
mix
ed w
ith m
ode I
V. I
n th
e w
ords
that
Mar
chet
to us
es to
intr
oduc
e thi
s exc
eptio
nal e
xam
- pl
e, "
if [th
e fir
st in
terr
uptio
n of t
he fi
rst sp
ecie
s] be
pla
ced i
n [a
m
elod
y tha
t im
plie
s] a
mod
e oth
er [t
han I
or V
III]
, it is
said
to
be co
mm
ixed
" (si
in al
iopo
natu
r, co
mm
ixta
dice
tur)
.25
Exam
ple 4
. Int
erru
ptio
n lb: "
If th
e fir
st in
terr
uptio
n is us
ed in
a m
ode o
ther
than
I or
VII
I, it
is sa
id to
be c
omm
ixed
, as i
n th
is ex
ampl
e."
nn ,,
I I
1 1
I
Expl
anat
ion.
This
is th
e onl
y ins
tanc
e whe
re M
arch
etto
and
the m
ajor
ity of
thos
e who
copi
ed h
is tr
eatis
e pro
vide
d tw
o dis-
tin
ct m
usic
al ex
ampl
es in
dea
ling w
ith a
sin
gle i
nter
rupt
ion.
Fr
om th
e con
text
it se
ems t
hat h
ere,
at t
he ou
tset
of h
is di
scus
- sio
n of i
nter
rupt
ions
, Mar
chet
to is
prov
idin
g an e
labo
rate
illus
- tr
atio
n of c
omm
ixtu
re th
at ti
es in
with
his
othe
r disc
ussio
ns of
co
mm
ixtu
re. F
or, a
ccor
ding
to h
is ap
proa
ch, th
e who
le m
elod
y is
in m
ode I
V b
y vir
tue o
f the
spec
ial A
3s a
nd E
3s an
d the
con-
cl
usio
n on
E3. E
mbe
dded
in th
is m
elod
y, h
owev
er, is
a fir
st in
- te
rrup
tion o
f the
firs
t spe
cies
as im
plie
d by t
he sp
ecia
l D3
and
A3
at th
e beg
inni
ng of
the i
llust
ratio
n. M
arch
etto
mak
es it
clea
r ju
st ab
ove t
hat a
n int
erru
ptio
n nee
d not
incl
ude b
oth r
ising
and
falli
ng fo
rms,
but m
ay in
clud
e onl
y one
or th
e oth
er. H
e say
s in
the p
rece
ding
sent
ence
that
"the
first
inte
rrup
tion c
onsis
ts of
all
the t
ones
of th
e spe
cies
of fi
fth w
heth
er [t
hese
are p
rese
nted
] in
asce
nt or
des
cent
" (p
rim
a int
erru
ptio
diap
ente
fit e
x om
nibu
s su
is so
nis,
sive p
er ar
sim siv
e per
thes
im). I
n the
case
of th
is ex
- am
ple,
a ri
sing f
orm
of th
e fir
st sp
ecie
s is p
rese
nted
at th
e out
set
in su
ch a
way
as to
impl
y mod
e I (o
r VII
I). B
y vir
tue o
f the
fact
th
at th
is im
plic
atio
n of m
ode I
(or V
III)
app
ears
as p
art o
f a
mel
ody t
hat o
ther
wise
, and
as a
who
le, i
mpl
ies m
ode I
V, m
ode
I (or
VII
I) c
an b
e sa
id to
be
com
mix
ed w
ith m
ode I
V. I
n th
e w
ords
that
Mar
chet
to us
es to
intr
oduc
e thi
s exc
eptio
nal e
xam
- pl
e, "
if [th
e fir
st in
terr
uptio
n of t
he fi
rst sp
ecie
s] be
pla
ced i
n [a
m
elod
y tha
t im
plie
s] a
mod
e oth
er [t
han I
or V
III]
, it is
said
to
be co
mm
ixed
" (si
in al
iopo
natu
r, co
mm
ixta
dice
tur)
.25
Exam
ple 4
. Int
erru
ptio
n lb: "
If th
e fir
st in
terr
uptio
n is us
ed in
a m
ode o
ther
than
I or
VII
I, it
is sa
id to
be c
omm
ixed
, as i
n th
is ex
ampl
e."
nn ,,
I I
1 1
I
Expl
anat
ion.
This
is th
e onl
y ins
tanc
e whe
re M
arch
etto
and
the m
ajor
ity of
thos
e who
copi
ed h
is tr
eatis
e pro
vide
d tw
o dis-
tin
ct m
usic
al ex
ampl
es in
dea
ling w
ith a
sin
gle i
nter
rupt
ion.
Fr
om th
e con
text
it se
ems t
hat h
ere,
at t
he ou
tset
of h
is di
scus
- sio
n of i
nter
rupt
ions
, Mar
chet
to is
prov
idin
g an e
labo
rate
illus
- tr
atio
n of c
omm
ixtu
re th
at ti
es in
with
his
othe
r disc
ussio
ns of
co
mm
ixtu
re. F
or, a
ccor
ding
to h
is ap
proa
ch, th
e who
le m
elod
y is
in m
ode I
V b
y vir
tue o
f the
spec
ial A
3s a
nd E
3s an
d the
con-
cl
usio
n on
E3. E
mbe
dded
in th
is m
elod
y, h
owev
er, is
a fir
st in
- te
rrup
tion o
f the
firs
t spe
cies
as im
plie
d by t
he sp
ecia
l D3
and
A3
at th
e beg
inni
ng of
the i
llust
ratio
n. M
arch
etto
mak
es it
clea
r ju
st ab
ove t
hat a
n int
erru
ptio
n nee
d not
incl
ude b
oth r
ising
and
falli
ng fo
rms,
but m
ay in
clud
e onl
y one
or th
e oth
er. H
e say
s in
the p
rece
ding
sent
ence
that
"the
first
inte
rrup
tion c
onsis
ts of
all
the t
ones
of th
e spe
cies
of fi
fth w
heth
er [t
hese
are p
rese
nted
] in
asce
nt or
des
cent
" (p
rim
a int
erru
ptio
diap
ente
fit e
x om
nibu
s su
is so
nis,
sive p
er ar
sim siv
e per
thes
im). I
n the
case
of th
is ex
- am
ple,
a ri
sing f
orm
of th
e fir
st sp
ecie
s is p
rese
nted
at th
e out
set
in su
ch a
way
as to
impl
y mod
e I (o
r VII
I). B
y vir
tue o
f the
fact
th
at th
is im
plic
atio
n of m
ode I
(or V
III)
app
ears
as p
art o
f a
mel
ody t
hat o
ther
wise
, and
as a
who
le, i
mpl
ies m
ode I
V, m
ode
I (or
VII
I) c
an b
e sa
id to
be
com
mix
ed w
ith m
ode I
V. I
n th
e w
ords
that
Mar
chet
to us
es to
intr
oduc
e thi
s exc
eptio
nal e
xam
- pl
e, "
if [th
e fir
st in
terr
uptio
n of t
he fi
rst sp
ecie
s] be
pla
ced i
n [a
m
elod
y tha
t im
plie
s] a
mod
e oth
er [t
han I
or V
III]
, it is
said
to
be co
mm
ixed
" (si
in al
iopo
natu
r, co
mm
ixta
dice
tur)
.25
Exam
ple 4
. Int
erru
ptio
n lb: "
If th
e fir
st in
terr
uptio
n is us
ed in
a m
ode o
ther
than
I or
VII
I, it
is sa
id to
be c
omm
ixed
, as i
n th
is ex
ampl
e."
nn ,,
I I
1 1
I
Expl
anat
ion.
This
is th
e onl
y ins
tanc
e whe
re M
arch
etto
and
the m
ajor
ity of
thos
e who
copi
ed h
is tr
eatis
e pro
vide
d tw
o dis-
tin
ct m
usic
al ex
ampl
es in
dea
ling w
ith a
sin
gle i
nter
rupt
ion.
Fr
om th
e con
text
it se
ems t
hat h
ere,
at t
he ou
tset
of h
is di
scus
- sio
n of i
nter
rupt
ions
, Mar
chet
to is
prov
idin
g an e
labo
rate
illus
- tr
atio
n of c
omm
ixtu
re th
at ti
es in
with
his
othe
r disc
ussio
ns of
co
mm
ixtu
re. F
or, a
ccor
ding
to h
is ap
proa
ch, th
e who
le m
elod
y is
in m
ode I
V b
y vir
tue o
f the
spec
ial A
3s a
nd E
3s an
d the
con-
cl
usio
n on
E3. E
mbe
dded
in th
is m
elod
y, h
owev
er, is
a fir
st in
- te
rrup
tion o
f the
firs
t spe
cies
as im
plie
d by t
he sp
ecia
l D3
and
A3
at th
e beg
inni
ng of
the i
llust
ratio
n. M
arch
etto
mak
es it
clea
r ju
st ab
ove t
hat a
n int
erru
ptio
n nee
d not
incl
ude b
oth r
ising
and
falli
ng fo
rms,
but m
ay in
clud
e onl
y one
or th
e oth
er. H
e say
s in
the p
rece
ding
sent
ence
that
"the
first
inte
rrup
tion c
onsis
ts of
all
the t
ones
of th
e spe
cies
of fi
fth w
heth
er [t
hese
are p
rese
nted
] in
asce
nt or
des
cent
" (p
rim
a int
erru
ptio
diap
ente
fit e
x om
nibu
s su
is so
nis,
sive p
er ar
sim siv
e per
thes
im). I
n the
case
of th
is ex
- am
ple,
a ri
sing f
orm
of th
e fir
st sp
ecie
s is p
rese
nted
at th
e out
set
in su
ch a
way
as to
impl
y mod
e I (o
r VII
I). B
y vir
tue o
f the
fact
th
at th
is im
plic
atio
n of m
ode I
(or V
III)
app
ears
as p
art o
f a
mel
ody t
hat o
ther
wise
, and
as a
who
le, i
mpl
ies m
ode I
V, m
ode
I (or
VII
I) c
an b
e sa
id to
be
com
mix
ed w
ith m
ode I
V. I
n th
e w
ords
that
Mar
chet
to us
es to
intr
oduc
e thi
s exc
eptio
nal e
xam
- pl
e, "
if [th
e fir
st in
terr
uptio
n of t
he fi
rst sp
ecie
s] be
pla
ced i
n [a
m
elod
y tha
t im
plie
s] a
mod
e oth
er [t
han I
or V
III]
, it is
said
to
be co
mm
ixed
" (si
in al
iopo
natu
r, co
mm
ixta
dice
tur)
.25
Exam
ple 4
. Int
erru
ptio
n lb: "
If th
e fir
st in
terr
uptio
n is us
ed in
a m
ode o
ther
than
I or
VII
I, it
is sa
id to
be c
omm
ixed
, as i
n th
is ex
ampl
e."
nn ,,
I I
1 1
I
x x
x x
x x
x x
x x
x x
x x
x x
x x
25In
the F
lore
ntin
e MS c
ited
in n
ote 2
4, a
bove
, the
exam
ple p
rovi
ded c
or-
resp
onds
to th
at w
hich
is us
ed in
mos
t of t
he so
urce
s for
inte
rrup
tion la
. 25
In th
e Flo
rent
ine M
S cite
d in
not
e 24,
abo
ve, t
he ex
ampl
e pro
vide
d cor
- re
spon
ds to
that
whi
ch is
used
in m
ost o
f the
sour
ces f
or in
terr
uptio
n la.
25In
the F
lore
ntin
e MS c
ited
in n
ote 2
4, a
bove
, the
exam
ple p
rovi
ded c
or-
resp
onds
to th
at w
hich
is us
ed in
mos
t of t
he so
urce
s for
inte
rrup
tion la
. 25
In th
e Flo
rent
ine M
S cite
d in
not
e 24,
abo
ve, t
he ex
ampl
e pro
vide
d cor
- re
spon
ds to
that
whi
ch is
used
in m
ost o
f the
sour
ces f
or in
terr
uptio
n la.
25In
the F
lore
ntin
e MS c
ited
in n
ote 2
4, a
bove
, the
exam
ple p
rovi
ded c
or-
resp
onds
to th
at w
hich
is us
ed in
mos
t of t
he so
urce
s for
inte
rrup
tion la
. 25
In th
e Flo
rent
ine M
S cite
d in
not
e 24,
abo
ve, t
he ex
ampl
e pro
vide
d cor
- re
spon
ds to
that
whi
ch is
used
in m
ost o
f the
sour
ces f
or in
terr
uptio
n la.
Inte
rrup
tion 2.
Mar
chet
to sp
ecifi
es th
at th
e sec
ond i
nter
rup-
tio
n (E
x. 5
) is m
ade u
p of
a to
ne a
nd a
perf
ect fo
urth
. For
this
inte
rrup
tion,
the
exam
ple
prov
ided
in t
he c
entr
al so
urce
s pr
esen
ts th
is pr
ogre
ssio
n in r
ising
form
at th
e out
set a
nd fo
llow
s it
with
two e
xtra
note
s. Th
e oth
er m
anus
crip
ts pr
esen
t the s
ame
thre
e not
es (D
3, E
3, a
nd A
3) a
t the
ir op
enin
g in r
ising
form
and
cont
inue
diffe
rent
ly. M
arch
etto
, thus
, wou
ld ap
pear
to be
refe
r-
ring
to th
e fir
st th
ree n
otes
as an
exam
ple o
f the
seco
nd in
terr
up-
tion a
nd la
ter c
opyi
sts o
r ada
pter
s of t
he tr
eatis
e app
ear to
hav
e un
ders
tood
his e
xam
ple i
n th
e sam
e way
.26 M
arch
etto
says
that
th
e se
cond
inte
rrup
tion a
lway
s im
plie
s the
four
th m
ode,
and
w
hen f
ound
in ot
her,
non-
four
th-m
ode se
tting
s, it i
s com
mix
ed.
Expl
anat
ion.
The f
irst
thre
e not
es li
e with
in th
e pro
per p
er-
fect
rang
e of t
he fo
urth
mod
e. T
he sp
ecia
l not
es, E
3 an
d A3,
se
rve t
o or
ient
the
four
th m
ode.
Alth
ough
they
also
serv
e to
orie
nt th
e thi
rd m
ode,
the p
refe
rred
read
ing a
ccor
ding
to cr
ite-
rion
6 (a
bove
) is p
laga
l rat
her t
han
auth
entic
beca
use o
f the
pe
rfec
t four
th in
terv
al be
twee
n E3
and A
3. O
ne m
ight
won
der
Exam
ple 5
. Int
erru
ptio
n 2: "
Alw
ays m
ode I
V [w
hich
has B
2,
E3, A
3 and
(B3)
as o
rien
ting t
ones
]"
' x
x y
y y
y
26Th
is sta
tem
ent s
houl
d no
t be
cons
true
d as i
mpl
ying
that
pre
para
tion o
f an
y of t
he ex
tant
sour
ces f
or th
e Luc
idar
ium
was
actu
ally
supe
rvise
d by M
ar-
chet
to. E
ven
the M
ilane
se m
anus
crip
t, whi
ch se
ems t
o be
the m
ost p
roba
ble
sour
ce to
hav
e bee
n co
mpi
led u
nder
Mar
chet
to's d
irec
tion,
prov
ides
no co
n-
clus
ive e
vide
nce t
hat i
t was
not
mer
ely a
copy
of a
n ear
lier,
now
lost
orig
inal
. Se
e H
erlin
ger,
The
Luc
idar
ium
, 22-
24.
Nev
erth
eles
s, be
caus
e the
Mila
nese
m
anus
crip
t seem
s clo
sest
to th
e ori
gina
l, I em
ploy
phra
ses s
uch a
s "M
arch
etto
sa
ys" w
hen r
efer
ring
to p
assa
ges f
rom
this
sour
ce.
Inte
rrup
tion 2.
Mar
chet
to sp
ecifi
es th
at th
e sec
ond i
nter
rup-
tio
n (E
x. 5
) is m
ade u
p of
a to
ne a
nd a
perf
ect fo
urth
. For
this
inte
rrup
tion,
the
exam
ple
prov
ided
in t
he c
entr
al so
urce
s pr
esen
ts th
is pr
ogre
ssio
n in r
ising
form
at th
e out
set a
nd fo
llow
s it
with
two e
xtra
note
s. Th
e oth
er m
anus
crip
ts pr
esen
t the s
ame
thre
e not
es (D
3, E
3, a
nd A
3) a
t the
ir op
enin
g in r
ising
form
and
cont
inue
diffe
rent
ly. M
arch
etto
, thus
, wou
ld ap
pear
to be
refe
r-
ring
to th
e fir
st th
ree n
otes
as an
exam
ple o
f the
seco
nd in
terr
up-
tion a
nd la
ter c
opyi
sts o
r ada
pter
s of t
he tr
eatis
e app
ear to
hav
e un
ders
tood
his e
xam
ple i
n th
e sam
e way
.26 M
arch
etto
says
that
th
e se
cond
inte
rrup
tion a
lway
s im
plie
s the
four
th m
ode,
and
w
hen f
ound
in ot
her,
non-
four
th-m
ode se
tting
s, it i
s com
mix
ed.
Expl
anat
ion.
The f
irst
thre
e not
es li
e with
in th
e pro
per p
er-
fect
rang
e of t
he fo
urth
mod
e. T
he sp
ecia
l not
es, E
3 an
d A3,
se
rve t
o or
ient
the
four
th m
ode.
Alth
ough
they
also
serv
e to
orie
nt th
e thi
rd m
ode,
the p
refe
rred
read
ing a
ccor
ding
to cr
ite-
rion
6 (a
bove
) is p
laga
l rat
her t
han
auth
entic
beca
use o
f the
pe
rfec
t four
th in
terv
al be
twee
n E3
and A
3. O
ne m
ight
won
der
Exam
ple 5
. Int
erru
ptio
n 2: "
Alw
ays m
ode I
V [w
hich
has B
2,
E3, A
3 and
(B3)
as o
rien
ting t
ones
]"
' x
x y
y y
y
26Th
is sta
tem
ent s
houl
d no
t be
cons
true
d as i
mpl
ying
that
pre
para
tion o
f an
y of t
he ex
tant
sour
ces f
or th
e Luc
idar
ium
was
actu
ally
supe
rvise
d by M
ar-
chet
to. E
ven
the M
ilane
se m
anus
crip
t, whi
ch se
ems t
o be
the m
ost p
roba
ble
sour
ce to
hav
e bee
n co
mpi
led u
nder
Mar
chet
to's d
irec
tion,
prov
ides
no co
n-
clus
ive e
vide
nce t
hat i
t was
not
mer
ely a
copy
of a
n ear
lier,
now
lost
orig
inal
. Se
e H
erlin
ger,
The
Luc
idar
ium
, 22-
24.
Nev
erth
eles
s, be
caus
e the
Mila
nese
m
anus
crip
t seem
s clo
sest
to th
e ori
gina
l, I em
ploy
phra
ses s
uch a
s "M
arch
etto
sa
ys" w
hen r
efer
ring
to p
assa
ges f
rom
this
sour
ce.
Inte
rrup
tion 2.
Mar
chet
to sp
ecifi
es th
at th
e sec
ond i
nter
rup-
tio
n (E
x. 5
) is m
ade u
p of
a to
ne a
nd a
perf
ect fo
urth
. For
this
inte
rrup
tion,
the
exam
ple
prov
ided
in t
he c
entr
al so
urce
s pr
esen
ts th
is pr
ogre
ssio
n in r
ising
form
at th
e out
set a
nd fo
llow
s it
with
two e
xtra
note
s. Th
e oth
er m
anus
crip
ts pr
esen
t the s
ame
thre
e not
es (D
3, E
3, a
nd A
3) a
t the
ir op
enin
g in r
ising
form
and
cont
inue
diffe
rent
ly. M
arch
etto
, thus
, wou
ld ap
pear
to be
refe
r-
ring
to th
e fir
st th
ree n
otes
as an
exam
ple o
f the
seco
nd in
terr
up-
tion a
nd la
ter c
opyi
sts o
r ada
pter
s of t
he tr
eatis
e app
ear to
hav
e un
ders
tood
his e
xam
ple i
n th
e sam
e way
.26 M
arch
etto
says
that
th
e se
cond
inte
rrup
tion a
lway
s im
plie
s the
four
th m
ode,
and
w
hen f
ound
in ot
her,
non-
four
th-m
ode se
tting
s, it i
s com
mix
ed.
Expl
anat
ion.
The f
irst
thre
e not
es li
e with
in th
e pro
per p
er-
fect
rang
e of t
he fo
urth
mod
e. T
he sp
ecia
l not
es, E
3 an
d A3,
se
rve t
o or
ient
the
four
th m
ode.
Alth
ough
they
also
serv
e to
orie
nt th
e thi
rd m
ode,
the p
refe
rred
read
ing a
ccor
ding
to cr
ite-
rion
6 (a
bove
) is p
laga
l rat
her t
han
auth
entic
beca
use o
f the
pe
rfec
t four
th in
terv
al be
twee
n E3
and A
3. O
ne m
ight
won
der
Exam
ple 5
. Int
erru
ptio
n 2: "
Alw
ays m
ode I
V [w
hich
has B
2,
E3, A
3 and
(B3)
as o
rien
ting t
ones
]"
' x
x y
y y
y
26Th
is sta
tem
ent s
houl
d no
t be
cons
true
d as i
mpl
ying
that
pre
para
tion o
f an
y of t
he ex
tant
sour
ces f
or th
e Luc
idar
ium
was
actu
ally
supe
rvise
d by M
ar-
chet
to. E
ven
the M
ilane
se m
anus
crip
t, whi
ch se
ems t
o be
the m
ost p
roba
ble
sour
ce to
hav
e bee
n co
mpi
led u
nder
Mar
chet
to's d
irec
tion,
prov
ides
no co
n-
clus
ive e
vide
nce t
hat i
t was
not
mer
ely a
copy
of a
n ear
lier,
now
lost
orig
inal
. Se
e H
erlin
ger,
The
Luc
idar
ium
, 22-
24.
Nev
erth
eles
s, be
caus
e the
Mila
nese
m
anus
crip
t seem
s clo
sest
to th
e ori
gina
l, I em
ploy
phra
ses s
uch a
s "M
arch
etto
sa
ys" w
hen r
efer
ring
to p
assa
ges f
rom
this
sour
ce.
Inte
rrup
tion 2.
Mar
chet
to sp
ecifi
es th
at th
e sec
ond i
nter
rup-
tio
n (E
x. 5
) is m
ade u
p of
a to
ne a
nd a
perf
ect fo
urth
. For
this
inte
rrup
tion,
the
exam
ple
prov
ided
in t
he c
entr
al so
urce
s pr
esen
ts th
is pr
ogre
ssio
n in r
ising
form
at th
e out
set a
nd fo
llow
s it
with
two e
xtra
note
s. Th
e oth
er m
anus
crip
ts pr
esen
t the s
ame
thre
e not
es (D
3, E
3, a
nd A
3) a
t the
ir op
enin
g in r
ising
form
and
cont
inue
diffe
rent
ly. M
arch
etto
, thus
, wou
ld ap
pear
to be
refe
r-
ring
to th
e fir
st th
ree n
otes
as an
exam
ple o
f the
seco
nd in
terr
up-
tion a
nd la
ter c
opyi
sts o
r ada
pter
s of t
he tr
eatis
e app
ear to
hav
e un
ders
tood
his e
xam
ple i
n th
e sam
e way
.26 M
arch
etto
says
that
th
e se
cond
inte
rrup
tion a
lway
s im
plie
s the
four
th m
ode,
and
w
hen f
ound
in ot
her,
non-
four
th-m
ode se
tting
s, it i
s com
mix
ed.
Expl
anat
ion.
The f
irst
thre
e not
es li
e with
in th
e pro
per p
er-
fect
rang
e of t
he fo
urth
mod
e. T
he sp
ecia
l not
es, E
3 an
d A3,
se
rve t
o or
ient
the
four
th m
ode.
Alth
ough
they
also
serv
e to
orie
nt th
e thi
rd m
ode,
the p
refe
rred
read
ing a
ccor
ding
to cr
ite-
rion
6 (a
bove
) is p
laga
l rat
her t
han
auth
entic
beca
use o
f the
pe
rfec
t four
th in
terv
al be
twee
n E3
and A
3. O
ne m
ight
won
der
Exam
ple 5
. Int
erru
ptio
n 2: "
Alw
ays m
ode I
V [w
hich
has B
2,
E3, A
3 and
(B3)
as o
rien
ting t
ones
]"
' x
x y
y y
y
26Th
is sta
tem
ent s
houl
d no
t be
cons
true
d as i
mpl
ying
that
pre
para
tion o
f an
y of t
he ex
tant
sour
ces f
or th
e Luc
idar
ium
was
actu
ally
supe
rvise
d by M
ar-
chet
to. E
ven
the M
ilane
se m
anus
crip
t, whi
ch se
ems t
o be
the m
ost p
roba
ble
sour
ce to
hav
e bee
n co
mpi
led u
nder
Mar
chet
to's d
irec
tion,
prov
ides
no co
n-
clus
ive e
vide
nce t
hat i
t was
not
mer
ely a
copy
of a
n ear
lier,
now
lost
orig
inal
. Se
e H
erlin
ger,
The
Luc
idar
ium
, 22-
24.
Nev
erth
eles
s, be
caus
e the
Mila
nese
m
anus
crip
t seem
s clo
sest
to th
e ori
gina
l, I em
ploy
phra
ses s
uch a
s "M
arch
etto
sa
ys" w
hen r
efer
ring
to p
assa
ges f
rom
this
sour
ce.
Inte
rrup
tion 2.
Mar
chet
to sp
ecifi
es th
at th
e sec
ond i
nter
rup-
tio
n (E
x. 5
) is m
ade u
p of
a to
ne a
nd a
perf
ect fo
urth
. For
this
inte
rrup
tion,
the
exam
ple
prov
ided
in t
he c
entr
al so
urce
s pr
esen
ts th
is pr
ogre
ssio
n in r
ising
form
at th
e out
set a
nd fo
llow
s it
with
two e
xtra
note
s. Th
e oth
er m
anus
crip
ts pr
esen
t the s
ame
thre
e not
es (D
3, E
3, a
nd A
3) a
t the
ir op
enin
g in r
ising
form
and
cont
inue
diffe
rent
ly. M
arch
etto
, thus
, wou
ld ap
pear
to be
refe
r-
ring
to th
e fir
st th
ree n
otes
as an
exam
ple o
f the
seco
nd in
terr
up-
tion a
nd la
ter c
opyi
sts o
r ada
pter
s of t
he tr
eatis
e app
ear to
hav
e un
ders
tood
his e
xam
ple i
n th
e sam
e way
.26 M
arch
etto
says
that
th
e se
cond
inte
rrup
tion a
lway
s im
plie
s the
four
th m
ode,
and
w
hen f
ound
in ot
her,
non-
four
th-m
ode se
tting
s, it i
s com
mix
ed.
Expl
anat
ion.
The f
irst
thre
e not
es li
e with
in th
e pro
per p
er-
fect
rang
e of t
he fo
urth
mod
e. T
he sp
ecia
l not
es, E
3 an
d A3,
se
rve t
o or
ient
the
four
th m
ode.
Alth
ough
they
also
serv
e to
orie
nt th
e thi
rd m
ode,
the p
refe
rred
read
ing a
ccor
ding
to cr
ite-
rion
6 (a
bove
) is p
laga
l rat
her t
han
auth
entic
beca
use o
f the
pe
rfec
t four
th in
terv
al be
twee
n E3
and A
3. O
ne m
ight
won
der
Exam
ple 5
. Int
erru
ptio
n 2: "
Alw
ays m
ode I
V [w
hich
has B
2,
E3, A
3 and
(B3)
as o
rien
ting t
ones
]"
' x
x y
y y
y
26Th
is sta
tem
ent s
houl
d no
t be
cons
true
d as i
mpl
ying
that
pre
para
tion o
f an
y of t
he ex
tant
sour
ces f
or th
e Luc
idar
ium
was
actu
ally
supe
rvise
d by M
ar-
chet
to. E
ven
the M
ilane
se m
anus
crip
t, whi
ch se
ems t
o be
the m
ost p
roba
ble
sour
ce to
hav
e bee
n co
mpi
led u
nder
Mar
chet
to's d
irec
tion,
prov
ides
no co
n-
clus
ive e
vide
nce t
hat i
t was
not
mer
ely a
copy
of a
n ear
lier,
now
lost
orig
inal
. Se
e H
erlin
ger,
The
Luc
idar
ium
, 22-
24.
Nev
erth
eles
s, be
caus
e the
Mila
nese
m
anus
crip
t seem
s clo
sest
to th
e ori
gina
l, I em
ploy
phra
ses s
uch a
s "M
arch
etto
sa
ys" w
hen r
efer
ring
to p
assa
ges f
rom
this
sour
ce.
Inte
rrup
tion 2.
Mar
chet
to sp
ecifi
es th
at th
e sec
ond i
nter
rup-
tio
n (E
x. 5
) is m
ade u
p of
a to
ne a
nd a
perf
ect fo
urth
. For
this
inte
rrup
tion,
the
exam
ple
prov
ided
in t
he c
entr
al so
urce
s pr
esen
ts th
is pr
ogre
ssio
n in r
ising
form
at th
e out
set a
nd fo
llow
s it
with
two e
xtra
note
s. Th
e oth
er m
anus
crip
ts pr
esen
t the s
ame
thre
e not
es (D
3, E
3, a
nd A
3) a
t the
ir op
enin
g in r
ising
form
and
cont
inue
diffe
rent
ly. M
arch
etto
, thus
, wou
ld ap
pear
to be
refe
r-
ring
to th
e fir
st th
ree n
otes
as an
exam
ple o
f the
seco
nd in
terr
up-
tion a
nd la
ter c
opyi
sts o
r ada
pter
s of t
he tr
eatis
e app
ear to
hav
e un
ders
tood
his e
xam
ple i
n th
e sam
e way
.26 M
arch
etto
says
that
th
e se
cond
inte
rrup
tion a
lway
s im
plie
s the
four
th m
ode,
and
w
hen f
ound
in ot
her,
non-
four
th-m
ode se
tting
s, it i
s com
mix
ed.
Expl
anat
ion.
The f
irst
thre
e not
es li
e with
in th
e pro
per p
er-
fect
rang
e of t
he fo
urth
mod
e. T
he sp
ecia
l not
es, E
3 an
d A3,
se
rve t
o or
ient
the
four
th m
ode.
Alth
ough
they
also
serv
e to
orie
nt th
e thi
rd m
ode,
the p
refe
rred
read
ing a
ccor
ding
to cr
ite-
rion
6 (a
bove
) is p
laga
l rat
her t
han
auth
entic
beca
use o
f the
pe
rfec
t four
th in
terv
al be
twee
n E3
and A
3. O
ne m
ight
won
der
Exam
ple 5
. Int
erru
ptio
n 2: "
Alw
ays m
ode I
V [w
hich
has B
2,
E3, A
3 and
(B3)
as o
rien
ting t
ones
]"
' x
x y
y y
y
26Th
is sta
tem
ent s
houl
d no
t be
cons
true
d as i
mpl
ying
that
pre
para
tion o
f an
y of t
he ex
tant
sour
ces f
or th
e Luc
idar
ium
was
actu
ally
supe
rvise
d by M
ar-
chet
to. E
ven
the M
ilane
se m
anus
crip
t, whi
ch se
ems t
o be
the m
ost p
roba
ble
sour
ce to
hav
e bee
n co
mpi
led u
nder
Mar
chet
to's d
irec
tion,
prov
ides
no co
n-
clus
ive e
vide
nce t
hat i
t was
not
mer
ely a
copy
of a
n ear
lier,
now
lost
orig
inal
. Se
e H
erlin
ger,
The
Luc
idar
ium
, 22-
24.
Nev
erth
eles
s, be
caus
e the
Mila
nese
m
anus
crip
t seem
s clo
sest
to th
e ori
gina
l, I em
ploy
phra
ses s
uch a
s "M
arch
etto
sa
ys" w
hen r
efer
ring
to p
assa
ges f
rom
this
sour
ce.
x x
x y
y y
x x
x y
y y
x x
x y
y y
x x
x y
y y
x x
x y
y y
x x
x y
y y
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
128
Mus
ic Th
eory
Spec
trum
12
8 M
usic
Theo
ry Sp
ectr
um
128
Mus
ic Th
eory
Spec
trum
12
8 M
usic
Theo
ry Sp
ectr
um
128
Mus
ic Th
eory
Spec
trum
12
8 M
usic
Theo
ry Sp
ectr
um
why
Mar
chet
to do
es n
ot c
onsid
er m
ode
I to
be im
plie
d. A
c-
cord
ing to
crite
rion
4, h
owev
er, b
ecau
se th
e E3 i
s clo
ser i
n tim
e to
the A
3 tha
n is t
he D
3, m
ode I
V is
mor
e str
ongl
y impl
ied t
han
mod
e I. E
ven
less
def
inite
ly im
plie
d is m
ode
VII
I, of
whi
ch
only
one o
rien
ting n
ote (
D3)
app
ears
in a
spec
ial p
ositi
on; t
his
rend
ers it
mor
e wea
kly i
mpl
ied t
han e
ither
mod
e IV
or m
ode I
. O
ne c
an a
lso o
bser
ve in
pas
sing t
hat,
in a
ll bu
t one
of
the
sour
ces, t
he re
mai
ning
note
s im
ply a
four
th-m
ode c
oncl
usio
n.
Inte
rrup
tion 3.
Mar
chet
to w
rite
s as f
ollo
ws a
bout
the t
hird
in
terr
uptio
n (Ex.
6):
"[it a
lway
s app
ears
] pro
perl
y in m
ode I
V,
[and
] ofte
n in m
ode I
I; in
othe
rs, [i
t is] c
omm
ixed
."
Expl
anat
ion.
The t
hird
inte
rrup
tion f
alls
with
in th
e ra
nges
of
the f
ourt
h and
seco
nd m
odes
. E3
and A
3, w
hich
are o
rien
t- in
g not
es in
mod
e IV
, and
D3
and G
3, w
hich
orie
nt m
ode I
I, ar
e spe
cial
. Of t
hese
spec
ial n
otes
, A3
repr
esen
ts a
conf
lict in
th
e im
plic
atio
n of m
ode I
I (sin
ce it
impl
ies i
ts a
uthe
ntic
coun
- te
rpar
t, mod
e I)
. Hen
ce, m
ode
IV is
mor
e st
rong
ly im
plie
d th
an m
ode I
I. O
ne m
ight
won
der w
hy m
ode V
III i
s not
men
- tio
ned
by M
arch
etto
. How
ever
, acc
ordi
ng to
cri
teri
a 7 a
nd 9,
m
ode I
I is m
ore s
tron
gly i
mpl
ied t
han m
ode V
III.
One
mig
ht
also
won
der a
t Mar
chet
to's f
ailu
re to
disc
uss m
ode
I at
this
poin
t; ho
wev
er, D
3 an
d G
3, w
hich
are c
hara
cter
istic
of m
ode
Exam
ple 6
. Int
erru
ptio
n 3: "
Prop
erly
in m
ode I
V [w
hich
has
B2, E
3, A
3 an
d (B
3) a
s ori
entin
g ton
es] a
nd of
ten
in m
ode I
I [w
hich
has A
2, D
3, G
3 and
(A3)
as or
ient
ing t
ones
]"
why
Mar
chet
to do
es n
ot c
onsid
er m
ode
I to
be im
plie
d. A
c-
cord
ing to
crite
rion
4, h
owev
er, b
ecau
se th
e E3 i
s clo
ser i
n tim
e to
the A
3 tha
n is t
he D
3, m
ode I
V is
mor
e str
ongl
y impl
ied t
han
mod
e I. E
ven
less
def
inite
ly im
plie
d is m
ode
VII
I, of
whi
ch
only
one o
rien
ting n
ote (
D3)
app
ears
in a
spec
ial p
ositi
on; t
his
rend
ers it
mor
e wea
kly i
mpl
ied t
han e
ither
mod
e IV
or m
ode I
. O
ne c
an a
lso o
bser
ve in
pas
sing t
hat,
in a
ll bu
t one
of
the
sour
ces, t
he re
mai
ning
note
s im
ply a
four
th-m
ode c
oncl
usio
n.
Inte
rrup
tion 3.
Mar
chet
to w
rite
s as f
ollo
ws a
bout
the t
hird
in
terr
uptio
n (Ex.
6):
"[it a
lway
s app
ears
] pro
perl
y in m
ode I
V,
[and
] ofte
n in m
ode I
I; in
othe
rs, [i
t is] c
omm
ixed
."
Expl
anat
ion.
The t
hird
inte
rrup
tion f
alls
with
in th
e ra
nges
of
the f
ourt
h and
seco
nd m
odes
. E3
and A
3, w
hich
are o
rien
t- in
g not
es in
mod
e IV
, and
D3
and G
3, w
hich
orie
nt m
ode I
I, ar
e spe
cial
. Of t
hese
spec
ial n
otes
, A3
repr
esen
ts a
conf
lict in
th
e im
plic
atio
n of m
ode I
I (sin
ce it
impl
ies i
ts a
uthe
ntic
coun
- te
rpar
t, mod
e I)
. Hen
ce, m
ode
IV is
mor
e st
rong
ly im
plie
d th
an m
ode I
I. O
ne m
ight
won
der w
hy m
ode V
III i
s not
men
- tio
ned
by M
arch
etto
. How
ever
, acc
ordi
ng to
cri
teri
a 7 a
nd 9,
m
ode I
I is m
ore s
tron
gly i
mpl
ied t
han m
ode V
III.
One
mig
ht
also
won
der a
t Mar
chet
to's f
ailu
re to
disc
uss m
ode
I at
this
poin
t; ho
wev
er, D
3 an
d G
3, w
hich
are c
hara
cter
istic
of m
ode
Exam
ple 6
. Int
erru
ptio
n 3: "
Prop
erly
in m
ode I
V [w
hich
has
B2, E
3, A
3 an
d (B
3) a
s ori
entin
g ton
es] a
nd of
ten
in m
ode I
I [w
hich
has A
2, D
3, G
3 and
(A3)
as or
ient
ing t
ones
]"
why
Mar
chet
to do
es n
ot c
onsid
er m
ode
I to
be im
plie
d. A
c-
cord
ing to
crite
rion
4, h
owev
er, b
ecau
se th
e E3 i
s clo
ser i
n tim
e to
the A
3 tha
n is t
he D
3, m
ode I
V is
mor
e str
ongl
y impl
ied t
han
mod
e I. E
ven
less
def
inite
ly im
plie
d is m
ode
VII
I, of
whi
ch
only
one o
rien
ting n
ote (
D3)
app
ears
in a
spec
ial p
ositi
on; t
his
rend
ers it
mor
e wea
kly i
mpl
ied t
han e
ither
mod
e IV
or m
ode I
. O
ne c
an a
lso o
bser
ve in
pas
sing t
hat,
in a
ll bu
t one
of
the
sour
ces, t
he re
mai
ning
note
s im
ply a
four
th-m
ode c
oncl
usio
n.
Inte
rrup
tion 3.
Mar
chet
to w
rite
s as f
ollo
ws a
bout
the t
hird
in
terr
uptio
n (Ex.
6):
"[it a
lway
s app
ears
] pro
perl
y in m
ode I
V,
[and
] ofte
n in m
ode I
I; in
othe
rs, [i
t is] c
omm
ixed
."
Expl
anat
ion.
The t
hird
inte
rrup
tion f
alls
with
in th
e ra
nges
of
the f
ourt
h and
seco
nd m
odes
. E3
and A
3, w
hich
are o
rien
t- in
g not
es in
mod
e IV
, and
D3
and G
3, w
hich
orie
nt m
ode I
I, ar
e spe
cial
. Of t
hese
spec
ial n
otes
, A3
repr
esen
ts a
conf
lict in
th
e im
plic
atio
n of m
ode I
I (sin
ce it
impl
ies i
ts a
uthe
ntic
coun
- te
rpar
t, mod
e I)
. Hen
ce, m
ode
IV is
mor
e st
rong
ly im
plie
d th
an m
ode I
I. O
ne m
ight
won
der w
hy m
ode V
III i
s not
men
- tio
ned
by M
arch
etto
. How
ever
, acc
ordi
ng to
cri
teri
a 7 a
nd 9,
m
ode I
I is m
ore s
tron
gly i
mpl
ied t
han m
ode V
III.
One
mig
ht
also
won
der a
t Mar
chet
to's f
ailu
re to
disc
uss m
ode
I at
this
poin
t; ho
wev
er, D
3 an
d G
3, w
hich
are c
hara
cter
istic
of m
ode
Exam
ple 6
. Int
erru
ptio
n 3: "
Prop
erly
in m
ode I
V [w
hich
has
B2, E
3, A
3 an
d (B
3) a
s ori
entin
g ton
es] a
nd of
ten
in m
ode I
I [w
hich
has A
2, D
3, G
3 and
(A3)
as or
ient
ing t
ones
]"
why
Mar
chet
to do
es n
ot c
onsid
er m
ode
I to
be im
plie
d. A
c-
cord
ing to
crite
rion
4, h
owev
er, b
ecau
se th
e E3 i
s clo
ser i
n tim
e to
the A
3 tha
n is t
he D
3, m
ode I
V is
mor
e str
ongl
y impl
ied t
han
mod
e I. E
ven
less
def
inite
ly im
plie
d is m
ode
VII
I, of
whi
ch
only
one o
rien
ting n
ote (
D3)
app
ears
in a
spec
ial p
ositi
on; t
his
rend
ers it
mor
e wea
kly i
mpl
ied t
han e
ither
mod
e IV
or m
ode I
. O
ne c
an a
lso o
bser
ve in
pas
sing t
hat,
in a
ll bu
t one
of
the
sour
ces, t
he re
mai
ning
note
s im
ply a
four
th-m
ode c
oncl
usio
n.
Inte
rrup
tion 3.
Mar
chet
to w
rite
s as f
ollo
ws a
bout
the t
hird
in
terr
uptio
n (Ex.
6):
"[it a
lway
s app
ears
] pro
perl
y in m
ode I
V,
[and
] ofte
n in m
ode I
I; in
othe
rs, [i
t is] c
omm
ixed
."
Expl
anat
ion.
The t
hird
inte
rrup
tion f
alls
with
in th
e ra
nges
of
the f
ourt
h and
seco
nd m
odes
. E3
and A
3, w
hich
are o
rien
t- in
g not
es in
mod
e IV
, and
D3
and G
3, w
hich
orie
nt m
ode I
I, ar
e spe
cial
. Of t
hese
spec
ial n
otes
, A3
repr
esen
ts a
conf
lict in
th
e im
plic
atio
n of m
ode I
I (sin
ce it
impl
ies i
ts a
uthe
ntic
coun
- te
rpar
t, mod
e I)
. Hen
ce, m
ode
IV is
mor
e st
rong
ly im
plie
d th
an m
ode I
I. O
ne m
ight
won
der w
hy m
ode V
III i
s not
men
- tio
ned
by M
arch
etto
. How
ever
, acc
ordi
ng to
cri
teri
a 7 a
nd 9,
m
ode I
I is m
ore s
tron
gly i
mpl
ied t
han m
ode V
III.
One
mig
ht
also
won
der a
t Mar
chet
to's f
ailu
re to
disc
uss m
ode
I at
this
poin
t; ho
wev
er, D
3 an
d G
3, w
hich
are c
hara
cter
istic
of m
ode
Exam
ple 6
. Int
erru
ptio
n 3: "
Prop
erly
in m
ode I
V [w
hich
has
B2, E
3, A
3 an
d (B
3) a
s ori
entin
g ton
es] a
nd of
ten
in m
ode I
I [w
hich
has A
2, D
3, G
3 and
(A3)
as or
ient
ing t
ones
]"
why
Mar
chet
to do
es n
ot c
onsid
er m
ode
I to
be im
plie
d. A
c-
cord
ing to
crite
rion
4, h
owev
er, b
ecau
se th
e E3 i
s clo
ser i
n tim
e to
the A
3 tha
n is t
he D
3, m
ode I
V is
mor
e str
ongl
y impl
ied t
han
mod
e I. E
ven
less
def
inite
ly im
plie
d is m
ode
VII
I, of
whi
ch
only
one o
rien
ting n
ote (
D3)
app
ears
in a
spec
ial p
ositi
on; t
his
rend
ers it
mor
e wea
kly i
mpl
ied t
han e
ither
mod
e IV
or m
ode I
. O
ne c
an a
lso o
bser
ve in
pas
sing t
hat,
in a
ll bu
t one
of
the
sour
ces, t
he re
mai
ning
note
s im
ply a
four
th-m
ode c
oncl
usio
n.
Inte
rrup
tion 3.
Mar
chet
to w
rite
s as f
ollo
ws a
bout
the t
hird
in
terr
uptio
n (Ex.
6):
"[it a
lway
s app
ears
] pro
perl
y in m
ode I
V,
[and
] ofte
n in m
ode I
I; in
othe
rs, [i
t is] c
omm
ixed
."
Expl
anat
ion.
The t
hird
inte
rrup
tion f
alls
with
in th
e ra
nges
of
the f
ourt
h and
seco
nd m
odes
. E3
and A
3, w
hich
are o
rien
t- in
g not
es in
mod
e IV
, and
D3
and G
3, w
hich
orie
nt m
ode I
I, ar
e spe
cial
. Of t
hese
spec
ial n
otes
, A3
repr
esen
ts a
conf
lict in
th
e im
plic
atio
n of m
ode I
I (sin
ce it
impl
ies i
ts a
uthe
ntic
coun
- te
rpar
t, mod
e I)
. Hen
ce, m
ode
IV is
mor
e st
rong
ly im
plie
d th
an m
ode I
I. O
ne m
ight
won
der w
hy m
ode V
III i
s not
men
- tio
ned
by M
arch
etto
. How
ever
, acc
ordi
ng to
cri
teri
a 7 a
nd 9,
m
ode I
I is m
ore s
tron
gly i
mpl
ied t
han m
ode V
III.
One
mig
ht
also
won
der a
t Mar
chet
to's f
ailu
re to
disc
uss m
ode
I at
this
poin
t; ho
wev
er, D
3 an
d G
3, w
hich
are c
hara
cter
istic
of m
ode
Exam
ple 6
. Int
erru
ptio
n 3: "
Prop
erly
in m
ode I
V [w
hich
has
B2, E
3, A
3 an
d (B
3) a
s ori
entin
g ton
es] a
nd of
ten
in m
ode I
I [w
hich
has A
2, D
3, G
3 and
(A3)
as or
ient
ing t
ones
]"
why
Mar
chet
to do
es n
ot c
onsid
er m
ode
I to
be im
plie
d. A
c-
cord
ing to
crite
rion
4, h
owev
er, b
ecau
se th
e E3 i
s clo
ser i
n tim
e to
the A
3 tha
n is t
he D
3, m
ode I
V is
mor
e str
ongl
y impl
ied t
han
mod
e I. E
ven
less
def
inite
ly im
plie
d is m
ode
VII
I, of
whi
ch
only
one o
rien
ting n
ote (
D3)
app
ears
in a
spec
ial p
ositi
on; t
his
rend
ers it
mor
e wea
kly i
mpl
ied t
han e
ither
mod
e IV
or m
ode I
. O
ne c
an a
lso o
bser
ve in
pas
sing t
hat,
in a
ll bu
t one
of
the
sour
ces, t
he re
mai
ning
note
s im
ply a
four
th-m
ode c
oncl
usio
n.
Inte
rrup
tion 3.
Mar
chet
to w
rite
s as f
ollo
ws a
bout
the t
hird
in
terr
uptio
n (Ex.
6):
"[it a
lway
s app
ears
] pro
perl
y in m
ode I
V,
[and
] ofte
n in m
ode I
I; in
othe
rs, [i
t is] c
omm
ixed
."
Expl
anat
ion.
The t
hird
inte
rrup
tion f
alls
with
in th
e ra
nges
of
the f
ourt
h and
seco
nd m
odes
. E3
and A
3, w
hich
are o
rien
t- in
g not
es in
mod
e IV
, and
D3
and G
3, w
hich
orie
nt m
ode I
I, ar
e spe
cial
. Of t
hese
spec
ial n
otes
, A3
repr
esen
ts a
conf
lict in
th
e im
plic
atio
n of m
ode I
I (sin
ce it
impl
ies i
ts a
uthe
ntic
coun
- te
rpar
t, mod
e I)
. Hen
ce, m
ode
IV is
mor
e st
rong
ly im
plie
d th
an m
ode I
I. O
ne m
ight
won
der w
hy m
ode V
III i
s not
men
- tio
ned
by M
arch
etto
. How
ever
, acc
ordi
ng to
cri
teri
a 7 a
nd 9,
m
ode I
I is m
ore s
tron
gly i
mpl
ied t
han m
ode V
III.
One
mig
ht
also
won
der a
t Mar
chet
to's f
ailu
re to
disc
uss m
ode
I at
this
poin
t; ho
wev
er, D
3 an
d G
3, w
hich
are c
hara
cter
istic
of m
ode
Exam
ple 6
. Int
erru
ptio
n 3: "
Prop
erly
in m
ode I
V [w
hich
has
B2, E
3, A
3 an
d (B
3) a
s ori
entin
g ton
es] a
nd of
ten
in m
ode I
I [w
hich
has A
2, D
3, G
3 and
(A3)
as or
ient
ing t
ones
]"
II, a
re te
mpo
rally
clos
er th
an ar
e D3
and A
3, w
hich
are c
hara
c-
teri
stic
of m
ode
I (cr
iteri
on 4
).27
Inte
rrup
tion 4
. Mar
chet
to sa
ys th
at th
e fou
rth i
nter
rupt
ion
(Ex.
7) a
ppea
rs "
prop
erly
in th
e se
cond
mod
e, r
arel
y in
the
first
."
Expl
anat
ion.
The r
ange
of th
e fou
rth i
nter
rupt
ion li
es w
ithin
th
e pro
per p
erfe
ct am
bitu
ses o
f mod
es I
and I
I. N
otes
D3
and
G3,
whi
ch ar
e cha
ract
erist
ic of
mod
e II,
and n
otes
D3
and A
3,
char
acte
rist
ic of
mod
e I, a
ppea
r in sp
ecia
l pos
ition
s. M
ode I
I is
mor
e str
ongl
y im
plie
d th
an m
ode
I by
virt
ue of
its o
rien
ting
note
s ap
pear
ing c
lose
r to
geth
er in
tim
e (c
rite
rion
4). M
ode
VII
I with
its or
ient
ing n
otes
D3
and G
3 app
ears
not t
o be m
en-
tione
d be
caus
e acc
ordi
ng to
cri
teri
a 7 a
nd 9
it is
less
stro
ngly
im
plie
d tha
n m
ode
II. M
ode
IV, w
ith it
s ori
entin
g not
e A
3,
seem
s not
to b
e di
scus
sed b
ecau
se o
nly
one
of it
s or
ient
ing
27Th
e Cat
ania
n MS
cite
d in
note
24 re
late
s tha
t "th
is in
terr
uptio
n [is
used
] pr
oper
ly in
mod
e II a
nd ra
rely
in m
ode I
." T
he fa
ilure
to m
entio
n m
ode I
V
seem
s baf
fling
; how
ever
, it sh
ould
be n
oted
that
this
man
uscr
ipt em
ploy
s suc
h bi
zarr
e rea
ding
s thro
ugho
ut th
e pas
sage
whe
re it
trea
ts in
terr
uptio
ns 3,
4, a
nd
5. F
or ex
ampl
e, in
a d
iscus
sion o
f the
4th i
nter
rupt
ion,
it pr
esen
ts an
exam
ple
corr
espo
ndin
g to th
e 5th
and a
n as
sess
men
t of p
ropr
iety
that
seem
s to
corr
es-
pond
to th
at fo
r the
3rd;
in th
e acc
ount
of th
e 5th
inte
rrup
tion,
it pr
esen
ts as
its
exam
ple t
he il
lust
ratio
n use
d in
othe
r sou
rces
for t
he 4t
h alo
ng w
ith th
e ass
ess-
m
ent e
mpl
oyed
in ot
her s
ourc
es fo
r the
5th.
One
can n
ote f
urth
er th
at th
e ex-
pl
anat
ion i
t pro
vide
s for
the 3
rd in
terr
uptio
n is th
at w
hich
is us
ed el
sew
here
for
the 4
th. T
hese
obse
rvat
ions
can b
e red
uced
to ta
bula
r form
as fo
llow
s:
II, a
re te
mpo
rally
clos
er th
an ar
e D3
and A
3, w
hich
are c
hara
c-
teri
stic
of m
ode
I (cr
iteri
on 4
).27
Inte
rrup
tion 4
. Mar
chet
to sa
ys th
at th
e fou
rth i
nter
rupt
ion
(Ex.
7) a
ppea
rs "
prop
erly
in th
e se
cond
mod
e, r
arel
y in
the
first
."
Expl
anat
ion.
The r
ange
of th
e fou
rth i
nter
rupt
ion li
es w
ithin
th
e pro
per p
erfe
ct am
bitu
ses o
f mod
es I
and I
I. N
otes
D3
and
G3,
whi
ch ar
e cha
ract
erist
ic of
mod
e II,
and n
otes
D3
and A
3,
char
acte
rist
ic of
mod
e I, a
ppea
r in sp
ecia
l pos
ition
s. M
ode I
I is
mor
e str
ongl
y im
plie
d th
an m
ode
I by
virt
ue of
its o
rien
ting
note
s ap
pear
ing c
lose
r to
geth
er in
tim
e (c
rite
rion
4). M
ode
VII
I with
its or
ient
ing n
otes
D3
and G
3 app
ears
not t
o be m
en-
tione
d be
caus
e acc
ordi
ng to
cri
teri
a 7 a
nd 9
it is
less
stro
ngly
im
plie
d tha
n m
ode
II. M
ode
IV, w
ith it
s ori
entin
g not
e A
3,
seem
s not
to b
e di
scus
sed b
ecau
se o
nly
one
of it
s or
ient
ing
27Th
e Cat
ania
n MS
cite
d in
note
24 re
late
s tha
t "th
is in
terr
uptio
n [is
used
] pr
oper
ly in
mod
e II a
nd ra
rely
in m
ode I
." T
he fa
ilure
to m
entio
n m
ode I
V
seem
s baf
fling
; how
ever
, it sh
ould
be n
oted
that
this
man
uscr
ipt em
ploy
s suc
h bi
zarr
e rea
ding
s thro
ugho
ut th
e pas
sage
whe
re it
trea
ts in
terr
uptio
ns 3,
4, a
nd
5. F
or ex
ampl
e, in
a d
iscus
sion o
f the
4th i
nter
rupt
ion,
it pr
esen
ts an
exam
ple
corr
espo
ndin
g to th
e 5th
and a
n as
sess
men
t of p
ropr
iety
that
seem
s to
corr
es-
pond
to th
at fo
r the
3rd;
in th
e acc
ount
of th
e 5th
inte
rrup
tion,
it pr
esen
ts as
its
exam
ple t
he il
lust
ratio
n use
d in
othe
r sou
rces
for t
he 4t
h alo
ng w
ith th
e ass
ess-
m
ent e
mpl
oyed
in ot
her s
ourc
es fo
r the
5th.
One
can n
ote f
urth
er th
at th
e ex-
pl
anat
ion i
t pro
vide
s for
the 3
rd in
terr
uptio
n is th
at w
hich
is us
ed el
sew
here
for
the 4
th. T
hese
obse
rvat
ions
can b
e red
uced
to ta
bula
r form
as fo
llow
s:
II, a
re te
mpo
rally
clos
er th
an ar
e D3
and A
3, w
hich
are c
hara
c-
teri
stic
of m
ode
I (cr
iteri
on 4
).27
Inte
rrup
tion 4
. Mar
chet
to sa
ys th
at th
e fou
rth i
nter
rupt
ion
(Ex.
7) a
ppea
rs "
prop
erly
in th
e se
cond
mod
e, r
arel
y in
the
first
."
Expl
anat
ion.
The r
ange
of th
e fou
rth i
nter
rupt
ion li
es w
ithin
th
e pro
per p
erfe
ct am
bitu
ses o
f mod
es I
and I
I. N
otes
D3
and
G3,
whi
ch ar
e cha
ract
erist
ic of
mod
e II,
and n
otes
D3
and A
3,
char
acte
rist
ic of
mod
e I, a
ppea
r in sp
ecia
l pos
ition
s. M
ode I
I is
mor
e str
ongl
y im
plie
d th
an m
ode
I by
virt
ue of
its o
rien
ting
note
s ap
pear
ing c
lose
r to
geth
er in
tim
e (c
rite
rion
4). M
ode
VII
I with
its or
ient
ing n
otes
D3
and G
3 app
ears
not t
o be m
en-
tione
d be
caus
e acc
ordi
ng to
cri
teri
a 7 a
nd 9
it is
less
stro
ngly
im
plie
d tha
n m
ode
II. M
ode
IV, w
ith it
s ori
entin
g not
e A
3,
seem
s not
to b
e di
scus
sed b
ecau
se o
nly
one
of it
s or
ient
ing
27Th
e Cat
ania
n MS
cite
d in
note
24 re
late
s tha
t "th
is in
terr
uptio
n [is
used
] pr
oper
ly in
mod
e II a
nd ra
rely
in m
ode I
." T
he fa
ilure
to m
entio
n m
ode I
V
seem
s baf
fling
; how
ever
, it sh
ould
be n
oted
that
this
man
uscr
ipt em
ploy
s suc
h bi
zarr
e rea
ding
s thro
ugho
ut th
e pas
sage
whe
re it
trea
ts in
terr
uptio
ns 3,
4, a
nd
5. F
or ex
ampl
e, in
a d
iscus
sion o
f the
4th i
nter
rupt
ion,
it pr
esen
ts an
exam
ple
corr
espo
ndin
g to th
e 5th
and a
n as
sess
men
t of p
ropr
iety
that
seem
s to
corr
es-
pond
to th
at fo
r the
3rd;
in th
e acc
ount
of th
e 5th
inte
rrup
tion,
it pr
esen
ts as
its
exam
ple t
he il
lust
ratio
n use
d in
othe
r sou
rces
for t
he 4t
h alo
ng w
ith th
e ass
ess-
m
ent e
mpl
oyed
in ot
her s
ourc
es fo
r the
5th.
One
can n
ote f
urth
er th
at th
e ex-
pl
anat
ion i
t pro
vide
s for
the 3
rd in
terr
uptio
n is th
at w
hich
is us
ed el
sew
here
for
the 4
th. T
hese
obse
rvat
ions
can b
e red
uced
to ta
bula
r form
as fo
llow
s:
II, a
re te
mpo
rally
clos
er th
an ar
e D3
and A
3, w
hich
are c
hara
c-
teri
stic
of m
ode
I (cr
iteri
on 4
).27
Inte
rrup
tion 4
. Mar
chet
to sa
ys th
at th
e fou
rth i
nter
rupt
ion
(Ex.
7) a
ppea
rs "
prop
erly
in th
e se
cond
mod
e, r
arel
y in
the
first
."
Expl
anat
ion.
The r
ange
of th
e fou
rth i
nter
rupt
ion li
es w
ithin
th
e pro
per p
erfe
ct am
bitu
ses o
f mod
es I
and I
I. N
otes
D3
and
G3,
whi
ch ar
e cha
ract
erist
ic of
mod
e II,
and n
otes
D3
and A
3,
char
acte
rist
ic of
mod
e I, a
ppea
r in sp
ecia
l pos
ition
s. M
ode I
I is
mor
e str
ongl
y im
plie
d th
an m
ode
I by
virt
ue of
its o
rien
ting
note
s ap
pear
ing c
lose
r to
geth
er in
tim
e (c
rite
rion
4). M
ode
VII
I with
its or
ient
ing n
otes
D3
and G
3 app
ears
not t
o be m
en-
tione
d be
caus
e acc
ordi
ng to
cri
teri
a 7 a
nd 9
it is
less
stro
ngly
im
plie
d tha
n m
ode
II. M
ode
IV, w
ith it
s ori
entin
g not
e A
3,
seem
s not
to b
e di
scus
sed b
ecau
se o
nly
one
of it
s or
ient
ing
27Th
e Cat
ania
n MS
cite
d in
note
24 re
late
s tha
t "th
is in
terr
uptio
n [is
used
] pr
oper
ly in
mod
e II a
nd ra
rely
in m
ode I
." T
he fa
ilure
to m
entio
n m
ode I
V
seem
s baf
fling
; how
ever
, it sh
ould
be n
oted
that
this
man
uscr
ipt em
ploy
s suc
h bi
zarr
e rea
ding
s thro
ugho
ut th
e pas
sage
whe
re it
trea
ts in
terr
uptio
ns 3,
4, a
nd
5. F
or ex
ampl
e, in
a d
iscus
sion o
f the
4th i
nter
rupt
ion,
it pr
esen
ts an
exam
ple
corr
espo
ndin
g to th
e 5th
and a
n as
sess
men
t of p
ropr
iety
that
seem
s to
corr
es-
pond
to th
at fo
r the
3rd;
in th
e acc
ount
of th
e 5th
inte
rrup
tion,
it pr
esen
ts as
its
exam
ple t
he il
lust
ratio
n use
d in
othe
r sou
rces
for t
he 4t
h alo
ng w
ith th
e ass
ess-
m
ent e
mpl
oyed
in ot
her s
ourc
es fo
r the
5th.
One
can n
ote f
urth
er th
at th
e ex-
pl
anat
ion i
t pro
vide
s for
the 3
rd in
terr
uptio
n is th
at w
hich
is us
ed el
sew
here
for
the 4
th. T
hese
obse
rvat
ions
can b
e red
uced
to ta
bula
r form
as fo
llow
s:
II, a
re te
mpo
rally
clos
er th
an ar
e D3
and A
3, w
hich
are c
hara
c-
teri
stic
of m
ode
I (cr
iteri
on 4
).27
Inte
rrup
tion 4
. Mar
chet
to sa
ys th
at th
e fou
rth i
nter
rupt
ion
(Ex.
7) a
ppea
rs "
prop
erly
in th
e se
cond
mod
e, r
arel
y in
the
first
."
Expl
anat
ion.
The r
ange
of th
e fou
rth i
nter
rupt
ion li
es w
ithin
th
e pro
per p
erfe
ct am
bitu
ses o
f mod
es I
and I
I. N
otes
D3
and
G3,
whi
ch ar
e cha
ract
erist
ic of
mod
e II,
and n
otes
D3
and A
3,
char
acte
rist
ic of
mod
e I, a
ppea
r in sp
ecia
l pos
ition
s. M
ode I
I is
mor
e str
ongl
y im
plie
d th
an m
ode
I by
virt
ue of
its o
rien
ting
note
s ap
pear
ing c
lose
r to
geth
er in
tim
e (c
rite
rion
4). M
ode
VII
I with
its or
ient
ing n
otes
D3
and G
3 app
ears
not t
o be m
en-
tione
d be
caus
e acc
ordi
ng to
cri
teri
a 7 a
nd 9
it is
less
stro
ngly
im
plie
d tha
n m
ode
II. M
ode
IV, w
ith it
s ori
entin
g not
e A
3,
seem
s not
to b
e di
scus
sed b
ecau
se o
nly
one
of it
s or
ient
ing
27Th
e Cat
ania
n MS
cite
d in
note
24 re
late
s tha
t "th
is in
terr
uptio
n [is
used
] pr
oper
ly in
mod
e II a
nd ra
rely
in m
ode I
." T
he fa
ilure
to m
entio
n m
ode I
V
seem
s baf
fling
; how
ever
, it sh
ould
be n
oted
that
this
man
uscr
ipt em
ploy
s suc
h bi
zarr
e rea
ding
s thro
ugho
ut th
e pas
sage
whe
re it
trea
ts in
terr
uptio
ns 3,
4, a
nd
5. F
or ex
ampl
e, in
a d
iscus
sion o
f the
4th i
nter
rupt
ion,
it pr
esen
ts an
exam
ple
corr
espo
ndin
g to th
e 5th
and a
n as
sess
men
t of p
ropr
iety
that
seem
s to
corr
es-
pond
to th
at fo
r the
3rd;
in th
e acc
ount
of th
e 5th
inte
rrup
tion,
it pr
esen
ts as
its
exam
ple t
he il
lust
ratio
n use
d in
othe
r sou
rces
for t
he 4t
h alo
ng w
ith th
e ass
ess-
m
ent e
mpl
oyed
in ot
her s
ourc
es fo
r the
5th.
One
can n
ote f
urth
er th
at th
e ex-
pl
anat
ion i
t pro
vide
s for
the 3
rd in
terr
uptio
n is th
at w
hich
is us
ed el
sew
here
for
the 4
th. T
hese
obse
rvat
ions
can b
e red
uced
to ta
bula
r form
as fo
llow
s:
II, a
re te
mpo
rally
clos
er th
an ar
e D3
and A
3, w
hich
are c
hara
c-
teri
stic
of m
ode
I (cr
iteri
on 4
).27
Inte
rrup
tion 4
. Mar
chet
to sa
ys th
at th
e fou
rth i
nter
rupt
ion
(Ex.
7) a
ppea
rs "
prop
erly
in th
e se
cond
mod
e, r
arel
y in
the
first
."
Expl
anat
ion.
The r
ange
of th
e fou
rth i
nter
rupt
ion li
es w
ithin
th
e pro
per p
erfe
ct am
bitu
ses o
f mod
es I
and I
I. N
otes
D3
and
G3,
whi
ch ar
e cha
ract
erist
ic of
mod
e II,
and n
otes
D3
and A
3,
char
acte
rist
ic of
mod
e I, a
ppea
r in sp
ecia
l pos
ition
s. M
ode I
I is
mor
e str
ongl
y im
plie
d th
an m
ode
I by
virt
ue of
its o
rien
ting
note
s ap
pear
ing c
lose
r to
geth
er in
tim
e (c
rite
rion
4). M
ode
VII
I with
its or
ient
ing n
otes
D3
and G
3 app
ears
not t
o be m
en-
tione
d be
caus
e acc
ordi
ng to
cri
teri
a 7 a
nd 9
it is
less
stro
ngly
im
plie
d tha
n m
ode
II. M
ode
IV, w
ith it
s ori
entin
g not
e A
3,
seem
s not
to b
e di
scus
sed b
ecau
se o
nly
one
of it
s or
ient
ing
27Th
e Cat
ania
n MS
cite
d in
note
24 re
late
s tha
t "th
is in
terr
uptio
n [is
used
] pr
oper
ly in
mod
e II a
nd ra
rely
in m
ode I
." T
he fa
ilure
to m
entio
n m
ode I
V
seem
s baf
fling
; how
ever
, it sh
ould
be n
oted
that
this
man
uscr
ipt em
ploy
s suc
h bi
zarr
e rea
ding
s thro
ugho
ut th
e pas
sage
whe
re it
trea
ts in
terr
uptio
ns 3,
4, a
nd
5. F
or ex
ampl
e, in
a d
iscus
sion o
f the
4th i
nter
rupt
ion,
it pr
esen
ts an
exam
ple
corr
espo
ndin
g to th
e 5th
and a
n as
sess
men
t of p
ropr
iety
that
seem
s to
corr
es-
pond
to th
at fo
r the
3rd;
in th
e acc
ount
of th
e 5th
inte
rrup
tion,
it pr
esen
ts as
its
exam
ple t
he il
lust
ratio
n use
d in
othe
r sou
rces
for t
he 4t
h alo
ng w
ith th
e ass
ess-
m
ent e
mpl
oyed
in ot
her s
ourc
es fo
r the
5th.
One
can n
ote f
urth
er th
at th
e ex-
pl
anat
ion i
t pro
vide
s for
the 3
rd in
terr
uptio
n is th
at w
hich
is us
ed el
sew
here
for
the 4
th. T
hese
obse
rvat
ions
can b
e red
uced
to ta
bula
r form
as fo
llow
s:
no. o
f int
erru
ptio
n ac
cord
ing t
o C
atan
ian
MS:
3 4 5 no
. of i
nter
rupt
ion
acco
rdin
g to
Cat
ania
n M
S:
3 4 5 no. o
f int
erru
ptio
n ac
cord
ing t
o C
atan
ian
MS:
3 4 5 no
. of i
nter
rupt
ion
acco
rdin
g to
Cat
ania
n M
S:
3 4 5 no. o
f int
erru
ptio
n ac
cord
ing t
o C
atan
ian
MS:
3 4 5 no
. of i
nter
rupt
ion
acco
rdin
g to
Cat
ania
n M
S:
3 4 5
no. o
f int
erru
ptio
n in
no. o
f int
erru
ptio
n in
whi
ch ex
ampl
e is f
ound
w
hich
asse
ssm
ent is
in
othe
r sou
rces
: fo
und i
n ot
her s
ourc
es:
no. o
f int
erru
ptio
n in
no. o
f int
erru
ptio
n in
whi
ch ex
ampl
e is f
ound
w
hich
asse
ssm
ent is
in
othe
r sou
rces
: fo
und i
n ot
her s
ourc
es:
no. o
f int
erru
ptio
n in
no. o
f int
erru
ptio
n in
whi
ch ex
ampl
e is f
ound
w
hich
asse
ssm
ent is
in
othe
r sou
rces
: fo
und i
n ot
her s
ourc
es:
no. o
f int
erru
ptio
n in
no. o
f int
erru
ptio
n in
whi
ch ex
ampl
e is f
ound
w
hich
asse
ssm
ent is
in
othe
r sou
rces
: fo
und i
n ot
her s
ourc
es:
no. o
f int
erru
ptio
n in
no. o
f int
erru
ptio
n in
whi
ch ex
ampl
e is f
ound
w
hich
asse
ssm
ent is
in
othe
r sou
rces
: fo
und i
n ot
her s
ourc
es:
no. o
f int
erru
ptio
n in
no. o
f int
erru
ptio
n in
whi
ch ex
ampl
e is f
ound
w
hich
asse
ssm
ent is
in
othe
r sou
rces
: fo
und i
n ot
her s
ourc
es:
3 5 4 3 5 4 3 5 4 3 5 4 3 5 4 3 5 4
4 3 5 4 3 5 4 3 5 4 3 5 4 3 5 4 3 5
Beca
use o
f the
gene
ral c
onfu
sion t
hat a
ppea
rs to
hav
e occ
urre
d in
the c
ompi
la-
tion o
f thi
s pas
sage
in M
S Cat
ania
, thes
e var
iant
s can
be d
ismiss
ed fo
r the
pur-
po
ses o
f thi
s stu
dy.
Beca
use o
f the
gene
ral c
onfu
sion t
hat a
ppea
rs to
hav
e occ
urre
d in
the c
ompi
la-
tion o
f thi
s pas
sage
in M
S Cat
ania
, thes
e var
iant
s can
be d
ismiss
ed fo
r the
pur-
po
ses o
f thi
s stu
dy.
Beca
use o
f the
gene
ral c
onfu
sion t
hat a
ppea
rs to
hav
e occ
urre
d in
the c
ompi
la-
tion o
f thi
s pas
sage
in M
S Cat
ania
, thes
e var
iant
s can
be d
ismiss
ed fo
r the
pur-
po
ses o
f thi
s stu
dy.
Beca
use o
f the
gene
ral c
onfu
sion t
hat a
ppea
rs to
hav
e occ
urre
d in
the c
ompi
la-
tion o
f thi
s pas
sage
in M
S Cat
ania
, thes
e var
iant
s can
be d
ismiss
ed fo
r the
pur-
po
ses o
f thi
s stu
dy.
Beca
use o
f the
gene
ral c
onfu
sion t
hat a
ppea
rs to
hav
e occ
urre
d in
the c
ompi
la-
tion o
f thi
s pas
sage
in M
S Cat
ania
, thes
e var
iant
s can
be d
ismiss
ed fo
r the
pur-
po
ses o
f thi
s stu
dy.
Beca
use o
f the
gene
ral c
onfu
sion t
hat a
ppea
rs to
hav
e occ
urre
d in
the c
ompi
la-
tion o
f thi
s pas
sage
in M
S Cat
ania
, thes
e var
iant
s can
be d
ismiss
ed fo
r the
pur-
po
ses o
f thi
s stu
dy.
y y
x x
y y
y y
y y
x x
y y
y y
y y
x x
y y
y y
y y
x x
y y
y y
y y
x x
y y
y y
y y
x x
y y
y y
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
129
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
129
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
129
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
129
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
129
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
129
note
s is p
rese
nted
in a
spec
ial m
anne
r and
this
note
is n
ot th
e fin
alis;
acco
rdin
gly,
it is
mor
e wea
kly i
mpl
ied t
han m
odes
I, II
, or
eve
n V
III
(cri
teri
a 3
and
7).2
8
Exam
ple 7
. Int
erru
ptio
n 4: "
Prop
erly
in m
ode I
I [w
hich
has A
2,
D3,
G3 a
nd (A
3) as
orie
ntin
g ton
es] a
nd m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
]"
A
note
s is p
rese
nted
in a
spec
ial m
anne
r and
this
note
is n
ot th
e fin
alis;
acco
rdin
gly,
it is
mor
e wea
kly i
mpl
ied t
han m
odes
I, II
, or
eve
n V
III
(cri
teri
a 3
and
7).2
8
Exam
ple 7
. Int
erru
ptio
n 4: "
Prop
erly
in m
ode I
I [w
hich
has A
2,
D3,
G3 a
nd (A
3) as
orie
ntin
g ton
es] a
nd m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
]"
A
note
s is p
rese
nted
in a
spec
ial m
anne
r and
this
note
is n
ot th
e fin
alis;
acco
rdin
gly,
it is
mor
e wea
kly i
mpl
ied t
han m
odes
I, II
, or
eve
n V
III
(cri
teri
a 3
and
7).2
8
Exam
ple 7
. Int
erru
ptio
n 4: "
Prop
erly
in m
ode I
I [w
hich
has A
2,
D3,
G3 a
nd (A
3) as
orie
ntin
g ton
es] a
nd m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
]"
A
note
s is p
rese
nted
in a
spec
ial m
anne
r and
this
note
is n
ot th
e fin
alis;
acco
rdin
gly,
it is
mor
e wea
kly i
mpl
ied t
han m
odes
I, II
, or
eve
n V
III
(cri
teri
a 3
and
7).2
8
Exam
ple 7
. Int
erru
ptio
n 4: "
Prop
erly
in m
ode I
I [w
hich
has A
2,
D3,
G3 a
nd (A
3) as
orie
ntin
g ton
es] a
nd m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
]"
A
note
s is p
rese
nted
in a
spec
ial m
anne
r and
this
note
is n
ot th
e fin
alis;
acco
rdin
gly,
it is
mor
e wea
kly i
mpl
ied t
han m
odes
I, II
, or
eve
n V
III
(cri
teri
a 3
and
7).2
8
Exam
ple 7
. Int
erru
ptio
n 4: "
Prop
erly
in m
ode I
I [w
hich
has A
2,
D3,
G3 a
nd (A
3) as
orie
ntin
g ton
es] a
nd m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
]"
A
note
s is p
rese
nted
in a
spec
ial m
anne
r and
this
note
is n
ot th
e fin
alis;
acco
rdin
gly,
it is
mor
e wea
kly i
mpl
ied t
han m
odes
I, II
, or
eve
n V
III
(cri
teri
a 3
and
7).2
8
Exam
ple 7
. Int
erru
ptio
n 4: "
Prop
erly
in m
ode I
I [w
hich
has A
2,
D3,
G3 a
nd (A
3) as
orie
ntin
g ton
es] a
nd m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
]"
A 'x
'x
'x
'x
'x
'x
x x
x x
x x
x x
x x
x x
y y
y y
y y
y y
y y
y y
y y
y y
y y
Exam
ple 8
. Int
erru
ptio
n 5a:
"Pro
perl
y in m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
has
D3,
G3,
(C4)
and D
4 as
orie
ntin
g ton
es)"
8 x
x x
y y
y Y
Y
Inte
rrup
tion 5
a. O
f the
fifth
inte
rrup
tion (
Ex. 8
) Mar
chet
to
wri
tes t
hat i
t is
used
in m
odes
I an
d V
III.
It li
es w
ithin
the
prop
er pe
rfec
t ran
ges o
f mod
es I
and V
III.
D3
is an
orie
ntin
g no
te in
bot
h, a
nd A
3 or
ient
s mod
e I. P
erha
ps M
arch
etto
men
- tio
ns m
ode I
bef
ore m
ode V
III b
ecau
se th
e for
mer
is im
plie
d m
ore s
tron
gly b
y vir
tue o
f tw
o of i
ts or
ient
ing n
otes
, rat
her th
an
just
one,
bei
ng pl
aced
in th
ree,
rath
er th
an on
ly tw
o, sp
ecia
l po-
sit
ions
(cri
teri
on 3)
. Mod
e II i
s not
men
tione
d by v
irtu
e of G
3's
abse
nce a
s a sp
ecia
l not
e in
cont
rast
with
the a
ppea
ranc
e of A
3
28A
t this
poin
t, M
S. 20
6, R
ome,
Bib
liote
ca V
atic
ana,
Cap
poni
ani, p
rese
nts
the v
erba
l ass
essm
ent e
mpl
oyed
in ot
her s
ourc
es fo
r int
erru
ptio
n 6. T
his v
ari-
ant i
s a
corr
uptio
n, an
d, h
ence
, can
be
dism
issed
in th
is st
udy.
Cf.
note
27
abov
e.
Exam
ple 8
. Int
erru
ptio
n 5a:
"Pro
perl
y in m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
has
D3,
G3,
(C4)
and D
4 as
orie
ntin
g ton
es)"
8 x
x x
y y
y Y
Y
Inte
rrup
tion 5
a. O
f the
fifth
inte
rrup
tion (
Ex. 8
) Mar
chet
to
wri
tes t
hat i
t is
used
in m
odes
I an
d V
III.
It li
es w
ithin
the
prop
er pe
rfec
t ran
ges o
f mod
es I
and V
III.
D3
is an
orie
ntin
g no
te in
bot
h, a
nd A
3 or
ient
s mod
e I. P
erha
ps M
arch
etto
men
- tio
ns m
ode I
bef
ore m
ode V
III b
ecau
se th
e for
mer
is im
plie
d m
ore s
tron
gly b
y vir
tue o
f tw
o of i
ts or
ient
ing n
otes
, rat
her th
an
just
one,
bei
ng pl
aced
in th
ree,
rath
er th
an on
ly tw
o, sp
ecia
l po-
sit
ions
(cri
teri
on 3)
. Mod
e II i
s not
men
tione
d by v
irtu
e of G
3's
abse
nce a
s a sp
ecia
l not
e in
cont
rast
with
the a
ppea
ranc
e of A
3
28A
t this
poin
t, M
S. 20
6, R
ome,
Bib
liote
ca V
atic
ana,
Cap
poni
ani, p
rese
nts
the v
erba
l ass
essm
ent e
mpl
oyed
in ot
her s
ourc
es fo
r int
erru
ptio
n 6. T
his v
ari-
ant i
s a
corr
uptio
n, an
d, h
ence
, can
be
dism
issed
in th
is st
udy.
Cf.
note
27
abov
e.
Exam
ple 8
. Int
erru
ptio
n 5a:
"Pro
perl
y in m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
has
D3,
G3,
(C4)
and D
4 as
orie
ntin
g ton
es)"
8 x
x x
y y
y Y
Y
Inte
rrup
tion 5
a. O
f the
fifth
inte
rrup
tion (
Ex. 8
) Mar
chet
to
wri
tes t
hat i
t is
used
in m
odes
I an
d V
III.
It li
es w
ithin
the
prop
er pe
rfec
t ran
ges o
f mod
es I
and V
III.
D3
is an
orie
ntin
g no
te in
bot
h, a
nd A
3 or
ient
s mod
e I. P
erha
ps M
arch
etto
men
- tio
ns m
ode I
bef
ore m
ode V
III b
ecau
se th
e for
mer
is im
plie
d m
ore s
tron
gly b
y vir
tue o
f tw
o of i
ts or
ient
ing n
otes
, rat
her th
an
just
one,
bei
ng pl
aced
in th
ree,
rath
er th
an on
ly tw
o, sp
ecia
l po-
sit
ions
(cri
teri
on 3)
. Mod
e II i
s not
men
tione
d by v
irtu
e of G
3's
abse
nce a
s a sp
ecia
l not
e in
cont
rast
with
the a
ppea
ranc
e of A
3
28A
t this
poin
t, M
S. 20
6, R
ome,
Bib
liote
ca V
atic
ana,
Cap
poni
ani, p
rese
nts
the v
erba
l ass
essm
ent e
mpl
oyed
in ot
her s
ourc
es fo
r int
erru
ptio
n 6. T
his v
ari-
ant i
s a
corr
uptio
n, an
d, h
ence
, can
be
dism
issed
in th
is st
udy.
Cf.
note
27
abov
e.
Exam
ple 8
. Int
erru
ptio
n 5a:
"Pro
perl
y in m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
has
D3,
G3,
(C4)
and D
4 as
orie
ntin
g ton
es)"
8 x
x x
y y
y Y
Y
Inte
rrup
tion 5
a. O
f the
fifth
inte
rrup
tion (
Ex. 8
) Mar
chet
to
wri
tes t
hat i
t is
used
in m
odes
I an
d V
III.
It li
es w
ithin
the
prop
er pe
rfec
t ran
ges o
f mod
es I
and V
III.
D3
is an
orie
ntin
g no
te in
bot
h, a
nd A
3 or
ient
s mod
e I. P
erha
ps M
arch
etto
men
- tio
ns m
ode I
bef
ore m
ode V
III b
ecau
se th
e for
mer
is im
plie
d m
ore s
tron
gly b
y vir
tue o
f tw
o of i
ts or
ient
ing n
otes
, rat
her th
an
just
one,
bei
ng pl
aced
in th
ree,
rath
er th
an on
ly tw
o, sp
ecia
l po-
sit
ions
(cri
teri
on 3)
. Mod
e II i
s not
men
tione
d by v
irtu
e of G
3's
abse
nce a
s a sp
ecia
l not
e in
cont
rast
with
the a
ppea
ranc
e of A
3
28A
t this
poin
t, M
S. 20
6, R
ome,
Bib
liote
ca V
atic
ana,
Cap
poni
ani, p
rese
nts
the v
erba
l ass
essm
ent e
mpl
oyed
in ot
her s
ourc
es fo
r int
erru
ptio
n 6. T
his v
ari-
ant i
s a
corr
uptio
n, an
d, h
ence
, can
be
dism
issed
in th
is st
udy.
Cf.
note
27
abov
e.
Exam
ple 8
. Int
erru
ptio
n 5a:
"Pro
perl
y in m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
has
D3,
G3,
(C4)
and D
4 as
orie
ntin
g ton
es)"
8 x
x x
y y
y Y
Y
Inte
rrup
tion 5
a. O
f the
fifth
inte
rrup
tion (
Ex. 8
) Mar
chet
to
wri
tes t
hat i
t is
used
in m
odes
I an
d V
III.
It li
es w
ithin
the
prop
er pe
rfec
t ran
ges o
f mod
es I
and V
III.
D3
is an
orie
ntin
g no
te in
bot
h, a
nd A
3 or
ient
s mod
e I. P
erha
ps M
arch
etto
men
- tio
ns m
ode I
bef
ore m
ode V
III b
ecau
se th
e for
mer
is im
plie
d m
ore s
tron
gly b
y vir
tue o
f tw
o of i
ts or
ient
ing n
otes
, rat
her th
an
just
one,
bei
ng pl
aced
in th
ree,
rath
er th
an on
ly tw
o, sp
ecia
l po-
sit
ions
(cri
teri
on 3)
. Mod
e II i
s not
men
tione
d by v
irtu
e of G
3's
abse
nce a
s a sp
ecia
l not
e in
cont
rast
with
the a
ppea
ranc
e of A
3
28A
t this
poin
t, M
S. 20
6, R
ome,
Bib
liote
ca V
atic
ana,
Cap
poni
ani, p
rese
nts
the v
erba
l ass
essm
ent e
mpl
oyed
in ot
her s
ourc
es fo
r int
erru
ptio
n 6. T
his v
ari-
ant i
s a
corr
uptio
n, an
d, h
ence
, can
be
dism
issed
in th
is st
udy.
Cf.
note
27
abov
e.
Exam
ple 8
. Int
erru
ptio
n 5a:
"Pro
perl
y in m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
has
D3,
G3,
(C4)
and D
4 as
orie
ntin
g ton
es)"
8 x
x x
y y
y Y
Y
Inte
rrup
tion 5
a. O
f the
fifth
inte
rrup
tion (
Ex. 8
) Mar
chet
to
wri
tes t
hat i
t is
used
in m
odes
I an
d V
III.
It li
es w
ithin
the
prop
er pe
rfec
t ran
ges o
f mod
es I
and V
III.
D3
is an
orie
ntin
g no
te in
bot
h, a
nd A
3 or
ient
s mod
e I. P
erha
ps M
arch
etto
men
- tio
ns m
ode I
bef
ore m
ode V
III b
ecau
se th
e for
mer
is im
plie
d m
ore s
tron
gly b
y vir
tue o
f tw
o of i
ts or
ient
ing n
otes
, rat
her th
an
just
one,
bei
ng pl
aced
in th
ree,
rath
er th
an on
ly tw
o, sp
ecia
l po-
sit
ions
(cri
teri
on 3)
. Mod
e II i
s not
men
tione
d by v
irtu
e of G
3's
abse
nce a
s a sp
ecia
l not
e in
cont
rast
with
the a
ppea
ranc
e of A
3
28A
t this
poin
t, M
S. 20
6, R
ome,
Bib
liote
ca V
atic
ana,
Cap
poni
ani, p
rese
nts
the v
erba
l ass
essm
ent e
mpl
oyed
in ot
her s
ourc
es fo
r int
erru
ptio
n 6. T
his v
ari-
ant i
s a
corr
uptio
n, an
d, h
ence
, can
be
dism
issed
in th
is st
udy.
Cf.
note
27
abov
e.
(cri
teri
on 5)
. Sim
ilarl
y, m
ode I
V se
ems n
ot to
be m
entio
ned b
e-
caus
e of t
he a
bsen
ce of
its f
inal
is, E
3, a
nd in
spite
of th
e pre
s-
ence
of A
3; ot
herw
ise th
is ca
se w
ould
seem
to b
e par
alle
l to th
at
of m
ode V
III.
Mod
e VI s
eem
s not
to b
e men
tione
d bec
ause
the
only
one
of i
ts o
rien
ting n
otes
to a
ppea
r, na
mel
y, F
3, is
the
"lea
st sp
ecia
l" of
the s
peci
al no
tes b
y vir
tue o
f its
med
ial p
osi-
tion (
crite
rion
8).
Inte
rrup
tion 5
b. M
arch
etto
prov
ides
a se
cond
exam
ple o
f th
e fift
h int
erru
ptio
n (Ex
. 9) w
ith th
e acc
ompa
nyin
g wor
ds: "
if it
is pl
aced
on A
gra
vis [
i.e.,
in th
e im
prop
er lo
catio
n bas
ed on
A
2, a
s in
the a
bove
exam
ple]
, [it]
prop
erly
[impl
ies]
mod
e II."
Ex
plan
atio
n. M
ode I
I is t
he on
ly m
ode w
ith a p
rope
r per
fect
ra
nge t
hat c
an ac
com
mod
ate t
his i
nter
rupt
ion (c
f. cr
iteri
on 1)
. Be
yond
this,
Mar
chet
to's r
easo
ning
appe
ars to
be
para
llel to
th
at w
hich
he em
ploy
s with
rega
rd to
the i
mpl
icat
ion o
f mod
e V
III b
y int
erru
ptio
n 5a.
29
(cri
teri
on 5)
. Sim
ilarl
y, m
ode I
V se
ems n
ot to
be m
entio
ned b
e-
caus
e of t
he a
bsen
ce of
its f
inal
is, E
3, a
nd in
spite
of th
e pre
s-
ence
of A
3; ot
herw
ise th
is ca
se w
ould
seem
to b
e par
alle
l to th
at
of m
ode V
III.
Mod
e VI s
eem
s not
to b
e men
tione
d bec
ause
the
only
one
of i
ts o
rien
ting n
otes
to a
ppea
r, na
mel
y, F
3, is
the
"lea
st sp
ecia
l" of
the s
peci
al no
tes b
y vir
tue o
f its
med
ial p
osi-
tion (
crite
rion
8).
Inte
rrup
tion 5
b. M
arch
etto
prov
ides
a se
cond
exam
ple o
f th
e fift
h int
erru
ptio
n (Ex
. 9) w
ith th
e acc
ompa
nyin
g wor
ds: "
if it
is pl
aced
on A
gra
vis [
i.e.,
in th
e im
prop
er lo
catio
n bas
ed on
A
2, a
s in
the a
bove
exam
ple]
, [it]
prop
erly
[impl
ies]
mod
e II."
Ex
plan
atio
n. M
ode I
I is t
he on
ly m
ode w
ith a p
rope
r per
fect
ra
nge t
hat c
an ac
com
mod
ate t
his i
nter
rupt
ion (c
f. cr
iteri
on 1)
. Be
yond
this,
Mar
chet
to's r
easo
ning
appe
ars to
be
para
llel to
th
at w
hich
he em
ploy
s with
rega
rd to
the i
mpl
icat
ion o
f mod
e V
III b
y int
erru
ptio
n 5a.
29
(cri
teri
on 5)
. Sim
ilarl
y, m
ode I
V se
ems n
ot to
be m
entio
ned b
e-
caus
e of t
he a
bsen
ce of
its f
inal
is, E
3, a
nd in
spite
of th
e pre
s-
ence
of A
3; ot
herw
ise th
is ca
se w
ould
seem
to b
e par
alle
l to th
at
of m
ode V
III.
Mod
e VI s
eem
s not
to b
e men
tione
d bec
ause
the
only
one
of i
ts o
rien
ting n
otes
to a
ppea
r, na
mel
y, F
3, is
the
"lea
st sp
ecia
l" of
the s
peci
al no
tes b
y vir
tue o
f its
med
ial p
osi-
tion (
crite
rion
8).
Inte
rrup
tion 5
b. M
arch
etto
prov
ides
a se
cond
exam
ple o
f th
e fift
h int
erru
ptio
n (Ex
. 9) w
ith th
e acc
ompa
nyin
g wor
ds: "
if it
is pl
aced
on A
gra
vis [
i.e.,
in th
e im
prop
er lo
catio
n bas
ed on
A
2, a
s in
the a
bove
exam
ple]
, [it]
prop
erly
[impl
ies]
mod
e II."
Ex
plan
atio
n. M
ode I
I is t
he on
ly m
ode w
ith a p
rope
r per
fect
ra
nge t
hat c
an ac
com
mod
ate t
his i
nter
rupt
ion (c
f. cr
iteri
on 1)
. Be
yond
this,
Mar
chet
to's r
easo
ning
appe
ars to
be
para
llel to
th
at w
hich
he em
ploy
s with
rega
rd to
the i
mpl
icat
ion o
f mod
e V
III b
y int
erru
ptio
n 5a.
29
(cri
teri
on 5)
. Sim
ilarl
y, m
ode I
V se
ems n
ot to
be m
entio
ned b
e-
caus
e of t
he a
bsen
ce of
its f
inal
is, E
3, a
nd in
spite
of th
e pre
s-
ence
of A
3; ot
herw
ise th
is ca
se w
ould
seem
to b
e par
alle
l to th
at
of m
ode V
III.
Mod
e VI s
eem
s not
to b
e men
tione
d bec
ause
the
only
one
of i
ts o
rien
ting n
otes
to a
ppea
r, na
mel
y, F
3, is
the
"lea
st sp
ecia
l" of
the s
peci
al no
tes b
y vir
tue o
f its
med
ial p
osi-
tion (
crite
rion
8).
Inte
rrup
tion 5
b. M
arch
etto
prov
ides
a se
cond
exam
ple o
f th
e fift
h int
erru
ptio
n (Ex
. 9) w
ith th
e acc
ompa
nyin
g wor
ds: "
if it
is pl
aced
on A
gra
vis [
i.e.,
in th
e im
prop
er lo
catio
n bas
ed on
A
2, a
s in
the a
bove
exam
ple]
, [it]
prop
erly
[impl
ies]
mod
e II."
Ex
plan
atio
n. M
ode I
I is t
he on
ly m
ode w
ith a p
rope
r per
fect
ra
nge t
hat c
an ac
com
mod
ate t
his i
nter
rupt
ion (c
f. cr
iteri
on 1)
. Be
yond
this,
Mar
chet
to's r
easo
ning
appe
ars to
be
para
llel to
th
at w
hich
he em
ploy
s with
rega
rd to
the i
mpl
icat
ion o
f mod
e V
III b
y int
erru
ptio
n 5a.
29
(cri
teri
on 5)
. Sim
ilarl
y, m
ode I
V se
ems n
ot to
be m
entio
ned b
e-
caus
e of t
he a
bsen
ce of
its f
inal
is, E
3, a
nd in
spite
of th
e pre
s-
ence
of A
3; ot
herw
ise th
is ca
se w
ould
seem
to b
e par
alle
l to th
at
of m
ode V
III.
Mod
e VI s
eem
s not
to b
e men
tione
d bec
ause
the
only
one
of i
ts o
rien
ting n
otes
to a
ppea
r, na
mel
y, F
3, is
the
"lea
st sp
ecia
l" of
the s
peci
al no
tes b
y vir
tue o
f its
med
ial p
osi-
tion (
crite
rion
8).
Inte
rrup
tion 5
b. M
arch
etto
prov
ides
a se
cond
exam
ple o
f th
e fift
h int
erru
ptio
n (Ex
. 9) w
ith th
e acc
ompa
nyin
g wor
ds: "
if it
is pl
aced
on A
gra
vis [
i.e.,
in th
e im
prop
er lo
catio
n bas
ed on
A
2, a
s in
the a
bove
exam
ple]
, [it]
prop
erly
[impl
ies]
mod
e II."
Ex
plan
atio
n. M
ode I
I is t
he on
ly m
ode w
ith a p
rope
r per
fect
ra
nge t
hat c
an ac
com
mod
ate t
his i
nter
rupt
ion (c
f. cr
iteri
on 1)
. Be
yond
this,
Mar
chet
to's r
easo
ning
appe
ars to
be
para
llel to
th
at w
hich
he em
ploy
s with
rega
rd to
the i
mpl
icat
ion o
f mod
e V
III b
y int
erru
ptio
n 5a.
29
(cri
teri
on 5)
. Sim
ilarl
y, m
ode I
V se
ems n
ot to
be m
entio
ned b
e-
caus
e of t
he a
bsen
ce of
its f
inal
is, E
3, a
nd in
spite
of th
e pre
s-
ence
of A
3; ot
herw
ise th
is ca
se w
ould
seem
to b
e par
alle
l to th
at
of m
ode V
III.
Mod
e VI s
eem
s not
to b
e men
tione
d bec
ause
the
only
one
of i
ts o
rien
ting n
otes
to a
ppea
r, na
mel
y, F
3, is
the
"lea
st sp
ecia
l" of
the s
peci
al no
tes b
y vir
tue o
f its
med
ial p
osi-
tion (
crite
rion
8).
Inte
rrup
tion 5
b. M
arch
etto
prov
ides
a se
cond
exam
ple o
f th
e fift
h int
erru
ptio
n (Ex
. 9) w
ith th
e acc
ompa
nyin
g wor
ds: "
if it
is pl
aced
on A
gra
vis [
i.e.,
in th
e im
prop
er lo
catio
n bas
ed on
A
2, a
s in
the a
bove
exam
ple]
, [it]
prop
erly
[impl
ies]
mod
e II."
Ex
plan
atio
n. M
ode I
I is t
he on
ly m
ode w
ith a p
rope
r per
fect
ra
nge t
hat c
an ac
com
mod
ate t
his i
nter
rupt
ion (c
f. cr
iteri
on 1)
. Be
yond
this,
Mar
chet
to's r
easo
ning
appe
ars to
be
para
llel to
th
at w
hich
he em
ploy
s with
rega
rd to
the i
mpl
icat
ion o
f mod
e V
III b
y int
erru
ptio
n 5a.
29
Exam
ple 9
. Int
erru
ptio
n 5b:
"If
the f
ifth i
nter
rupt
ion is
pla
ced
on A
2, it
is p
rope
r in
mod
e II [
whi
ch ha
s A2,
D3,
G3 a
nd (A
3)
as or
ient
ing t
ones
]."
x x
x
y y
y y
y
29Th
e Mila
nese
and
Flo
rent
ine M
SS, c
ited
abov
e, a
s wel
l as M
SS E
in-
siede
ln, S
tifts
bibl
ioth
ek, 68
9, S
evill
e, B
iblio
teca
Cap
itula
r Col
ombi
na, 5.
2.25
, an
d Was
hing
ton,
Libr
ary o
f Con
gres
s, M
usic
Div
ision
, ML
171.
J6 pr
ovid
e as
thei
r illu
stra
tions
of th
e 5th
inte
rrup
tion e
xam
ples
that
are a
nalo
gous
to th
ose
used
in ot
her s
ourc
es fo
r the
7th.
As c
orru
ptio
ns, th
ese v
aria
nts ca
n be i
gnor
ed.
Inte
rest
ingl
y, H
erlin
ger,
Luc
idar
ium
, pp.
22-
24,
post
ulat
es an
earl
y dat
e for
th
e Mila
nese
MS;
this
wou
ld su
gges
t tha
t the
com
pile
rs of
oth
er, la
ter s
ourc
es
corr
ecte
d the
ambi
guity
whi
ch ap
pear
s in it
.
Exam
ple 9
. Int
erru
ptio
n 5b:
"If
the f
ifth i
nter
rupt
ion is
pla
ced
on A
2, it
is p
rope
r in
mod
e II [
whi
ch ha
s A2,
D3,
G3 a
nd (A
3)
as or
ient
ing t
ones
]."
x x
x
y y
y y
y
29Th
e Mila
nese
and
Flo
rent
ine M
SS, c
ited
abov
e, a
s wel
l as M
SS E
in-
siede
ln, S
tifts
bibl
ioth
ek, 68
9, S
evill
e, B
iblio
teca
Cap
itula
r Col
ombi
na, 5.
2.25
, an
d Was
hing
ton,
Libr
ary o
f Con
gres
s, M
usic
Div
ision
, ML
171.
J6 pr
ovid
e as
thei
r illu
stra
tions
of th
e 5th
inte
rrup
tion e
xam
ples
that
are a
nalo
gous
to th
ose
used
in ot
her s
ourc
es fo
r the
7th.
As c
orru
ptio
ns, th
ese v
aria
nts ca
n be i
gnor
ed.
Inte
rest
ingl
y, H
erlin
ger,
Luc
idar
ium
, pp.
22-
24,
post
ulat
es an
earl
y dat
e for
th
e Mila
nese
MS;
this
wou
ld su
gges
t tha
t the
com
pile
rs of
oth
er, la
ter s
ourc
es
corr
ecte
d the
ambi
guity
whi
ch ap
pear
s in it
.
Exam
ple 9
. Int
erru
ptio
n 5b:
"If
the f
ifth i
nter
rupt
ion is
pla
ced
on A
2, it
is p
rope
r in
mod
e II [
whi
ch ha
s A2,
D3,
G3 a
nd (A
3)
as or
ient
ing t
ones
]."
x x
x
y y
y y
y
29Th
e Mila
nese
and
Flo
rent
ine M
SS, c
ited
abov
e, a
s wel
l as M
SS E
in-
siede
ln, S
tifts
bibl
ioth
ek, 68
9, S
evill
e, B
iblio
teca
Cap
itula
r Col
ombi
na, 5.
2.25
, an
d Was
hing
ton,
Libr
ary o
f Con
gres
s, M
usic
Div
ision
, ML
171.
J6 pr
ovid
e as
thei
r illu
stra
tions
of th
e 5th
inte
rrup
tion e
xam
ples
that
are a
nalo
gous
to th
ose
used
in ot
her s
ourc
es fo
r the
7th.
As c
orru
ptio
ns, th
ese v
aria
nts ca
n be i
gnor
ed.
Inte
rest
ingl
y, H
erlin
ger,
Luc
idar
ium
, pp.
22-
24,
post
ulat
es an
earl
y dat
e for
th
e Mila
nese
MS;
this
wou
ld su
gges
t tha
t the
com
pile
rs of
oth
er, la
ter s
ourc
es
corr
ecte
d the
ambi
guity
whi
ch ap
pear
s in it
.
Exam
ple 9
. Int
erru
ptio
n 5b:
"If
the f
ifth i
nter
rupt
ion is
pla
ced
on A
2, it
is p
rope
r in
mod
e II [
whi
ch ha
s A2,
D3,
G3 a
nd (A
3)
as or
ient
ing t
ones
]."
x x
x
y y
y y
y
29Th
e Mila
nese
and
Flo
rent
ine M
SS, c
ited
abov
e, a
s wel
l as M
SS E
in-
siede
ln, S
tifts
bibl
ioth
ek, 68
9, S
evill
e, B
iblio
teca
Cap
itula
r Col
ombi
na, 5.
2.25
, an
d Was
hing
ton,
Libr
ary o
f Con
gres
s, M
usic
Div
ision
, ML
171.
J6 pr
ovid
e as
thei
r illu
stra
tions
of th
e 5th
inte
rrup
tion e
xam
ples
that
are a
nalo
gous
to th
ose
used
in ot
her s
ourc
es fo
r the
7th.
As c
orru
ptio
ns, th
ese v
aria
nts ca
n be i
gnor
ed.
Inte
rest
ingl
y, H
erlin
ger,
Luc
idar
ium
, pp.
22-
24,
post
ulat
es an
earl
y dat
e for
th
e Mila
nese
MS;
this
wou
ld su
gges
t tha
t the
com
pile
rs of
oth
er, la
ter s
ourc
es
corr
ecte
d the
ambi
guity
whi
ch ap
pear
s in it
.
Exam
ple 9
. Int
erru
ptio
n 5b:
"If
the f
ifth i
nter
rupt
ion is
pla
ced
on A
2, it
is p
rope
r in
mod
e II [
whi
ch ha
s A2,
D3,
G3 a
nd (A
3)
as or
ient
ing t
ones
]."
x x
x
y y
y y
y
29Th
e Mila
nese
and
Flo
rent
ine M
SS, c
ited
abov
e, a
s wel
l as M
SS E
in-
siede
ln, S
tifts
bibl
ioth
ek, 68
9, S
evill
e, B
iblio
teca
Cap
itula
r Col
ombi
na, 5.
2.25
, an
d Was
hing
ton,
Libr
ary o
f Con
gres
s, M
usic
Div
ision
, ML
171.
J6 pr
ovid
e as
thei
r illu
stra
tions
of th
e 5th
inte
rrup
tion e
xam
ples
that
are a
nalo
gous
to th
ose
used
in ot
her s
ourc
es fo
r the
7th.
As c
orru
ptio
ns, th
ese v
aria
nts ca
n be i
gnor
ed.
Inte
rest
ingl
y, H
erlin
ger,
Luc
idar
ium
, pp.
22-
24,
post
ulat
es an
earl
y dat
e for
th
e Mila
nese
MS;
this
wou
ld su
gges
t tha
t the
com
pile
rs of
oth
er, la
ter s
ourc
es
corr
ecte
d the
ambi
guity
whi
ch ap
pear
s in it
.
Exam
ple 9
. Int
erru
ptio
n 5b:
"If
the f
ifth i
nter
rupt
ion is
pla
ced
on A
2, it
is p
rope
r in
mod
e II [
whi
ch ha
s A2,
D3,
G3 a
nd (A
3)
as or
ient
ing t
ones
]."
x x
x
y y
y y
y
29Th
e Mila
nese
and
Flo
rent
ine M
SS, c
ited
abov
e, a
s wel
l as M
SS E
in-
siede
ln, S
tifts
bibl
ioth
ek, 68
9, S
evill
e, B
iblio
teca
Cap
itula
r Col
ombi
na, 5.
2.25
, an
d Was
hing
ton,
Libr
ary o
f Con
gres
s, M
usic
Div
ision
, ML
171.
J6 pr
ovid
e as
thei
r illu
stra
tions
of th
e 5th
inte
rrup
tion e
xam
ples
that
are a
nalo
gous
to th
ose
used
in ot
her s
ourc
es fo
r the
7th.
As c
orru
ptio
ns, th
ese v
aria
nts ca
n be i
gnor
ed.
Inte
rest
ingl
y, H
erlin
ger,
Luc
idar
ium
, pp.
22-
24,
post
ulat
es an
earl
y dat
e for
th
e Mila
nese
MS;
this
wou
ld su
gges
t tha
t the
com
pile
rs of
oth
er, la
ter s
ourc
es
corr
ecte
d the
ambi
guity
whi
ch ap
pear
s in it
.
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
130
Mus
ic Th
eory
Spec
trum
13
0 M
usic
Theo
ry Sp
ectr
um
130
Mus
ic Th
eory
Spec
trum
13
0 M
usic
Theo
ry Sp
ectr
um
130
Mus
ic Th
eory
Spec
trum
13
0 M
usic
Theo
ry Sp
ectr
um
Inte
rrup
tion 6.
Mar
chet
to de
clar
es th
at th
e six
th in
terr
uptio
n (E
x. 1
0) im
plie
s mod
e I "
rare
ly,"
mod
es II
and
VII
I "of
ten,
" an
d IV
and V
I "so
met
imes
." Th
e man
uscr
ipt tr
aditi
on is
high
ly
vari
able
here
. In
one s
ourc
e, th
e ter
m pr
opri
o rep
lace
s pri
mo
(i.e.
, mod
e I);
in an
othe
r sou
rce,
men
tion o
f mod
e IV
is o
mit-
te
d; in
yet a
noth
er so
urce
, the p
assa
ge tr
eatin
g mod
es V
III,
IV,
and V
I is f
ollo
wed
by th
e com
men
t that
"in
deed
if it
is lo
cate
d [im
prop
erly
] on A
gra
vis,
[it] p
rope
rly [
impl
ies]
mod
e II"
; and
fin
ally
, in st
ill an
othe
r pai
r of s
ourc
es th
e lat
ter p
assa
ge re
plac
es
the r
efer
ence
s to m
odes
VII
I, IV
, and
VI.
Expl
anat
ion.
The s
ixth
inte
rrup
tion f
alls
with
in th
e pro
per
perf
ect r
ange
s of a
ll the
mod
es m
entio
ned b
y Mar
chet
to an
d his
follo
wer
s. Eac
h mod
e is r
epre
sent
ed by
one o
r tw
o of i
ts or
ient
- in
g not
es pr
esen
ted i
n a s
peci
al po
sitio
n. A
s for
the o
rder
ing o
f th
ese,
mod
e I w
ould
appe
ar to
be m
ost s
tron
gly i
mpl
ied,
fol-
low
ed b
y m
odes
IV, V
III,
and
VI.
Obv
ious
ly, f
ollo
wer
s of
Mar
chet
to ha
d diff
icul
ties w
ith th
is pa
ssag
e; th
e ano
mal
ous in
- cl
usio
n of m
ode I
I mig
ht ha
ve be
en th
e sou
rce o
f the
ir di
fficu
l- tie
s. Th
e spe
cific
atio
n of m
ode I
I for
the c
ase o
f an
impr
oper
lo
catio
n on A
2 (i.
e., A
gra
vis)
acco
rds w
ith th
e log
ic in
volv
ed in
th
e par
alle
l case
of in
terr
uptio
n 5b,
and i
t mig
ht ha
ve be
en th
e so
urce
of th
e ano
mal
ous a
ppea
ranc
e of m
ode I
I in t
he lis
t of t
he
prop
erly
loca
ted i
nter
rupt
ions
.
Inte
rrup
tion 6.
Mar
chet
to de
clar
es th
at th
e six
th in
terr
uptio
n (E
x. 1
0) im
plie
s mod
e I "
rare
ly,"
mod
es II
and
VII
I "of
ten,
" an
d IV
and V
I "so
met
imes
." Th
e man
uscr
ipt tr
aditi
on is
high
ly
vari
able
here
. In
one s
ourc
e, th
e ter
m pr
opri
o rep
lace
s pri
mo
(i.e.
, mod
e I);
in an
othe
r sou
rce,
men
tion o
f mod
e IV
is o
mit-
te
d; in
yet a
noth
er so
urce
, the p
assa
ge tr
eatin
g mod
es V
III,
IV,
and V
I is f
ollo
wed
by th
e com
men
t that
"in
deed
if it
is lo
cate
d [im
prop
erly
] on A
gra
vis,
[it] p
rope
rly [
impl
ies]
mod
e II"
; and
fin
ally
, in st
ill an
othe
r pai
r of s
ourc
es th
e lat
ter p
assa
ge re
plac
es
the r
efer
ence
s to m
odes
VII
I, IV
, and
VI.
Expl
anat
ion.
The s
ixth
inte
rrup
tion f
alls
with
in th
e pro
per
perf
ect r
ange
s of a
ll the
mod
es m
entio
ned b
y Mar
chet
to an
d his
follo
wer
s. Eac
h mod
e is r
epre
sent
ed by
one o
r tw
o of i
ts or
ient
- in
g not
es pr
esen
ted i
n a s
peci
al po
sitio
n. A
s for
the o
rder
ing o
f th
ese,
mod
e I w
ould
appe
ar to
be m
ost s
tron
gly i
mpl
ied,
fol-
low
ed b
y m
odes
IV, V
III,
and
VI.
Obv
ious
ly, f
ollo
wer
s of
Mar
chet
to ha
d diff
icul
ties w
ith th
is pa
ssag
e; th
e ano
mal
ous in
- cl
usio
n of m
ode I
I mig
ht ha
ve be
en th
e sou
rce o
f the
ir di
fficu
l- tie
s. Th
e spe
cific
atio
n of m
ode I
I for
the c
ase o
f an
impr
oper
lo
catio
n on A
2 (i.
e., A
gra
vis)
acco
rds w
ith th
e log
ic in
volv
ed in
th
e par
alle
l case
of in
terr
uptio
n 5b,
and i
t mig
ht ha
ve be
en th
e so
urce
of th
e ano
mal
ous a
ppea
ranc
e of m
ode I
I in t
he lis
t of t
he
prop
erly
loca
ted i
nter
rupt
ions
.
Inte
rrup
tion 6.
Mar
chet
to de
clar
es th
at th
e six
th in
terr
uptio
n (E
x. 1
0) im
plie
s mod
e I "
rare
ly,"
mod
es II
and
VII
I "of
ten,
" an
d IV
and V
I "so
met
imes
." Th
e man
uscr
ipt tr
aditi
on is
high
ly
vari
able
here
. In
one s
ourc
e, th
e ter
m pr
opri
o rep
lace
s pri
mo
(i.e.
, mod
e I);
in an
othe
r sou
rce,
men
tion o
f mod
e IV
is o
mit-
te
d; in
yet a
noth
er so
urce
, the p
assa
ge tr
eatin
g mod
es V
III,
IV,
and V
I is f
ollo
wed
by th
e com
men
t that
"in
deed
if it
is lo
cate
d [im
prop
erly
] on A
gra
vis,
[it] p
rope
rly [
impl
ies]
mod
e II"
; and
fin
ally
, in st
ill an
othe
r pai
r of s
ourc
es th
e lat
ter p
assa
ge re
plac
es
the r
efer
ence
s to m
odes
VII
I, IV
, and
VI.
Expl
anat
ion.
The s
ixth
inte
rrup
tion f
alls
with
in th
e pro
per
perf
ect r
ange
s of a
ll the
mod
es m
entio
ned b
y Mar
chet
to an
d his
follo
wer
s. Eac
h mod
e is r
epre
sent
ed by
one o
r tw
o of i
ts or
ient
- in
g not
es pr
esen
ted i
n a s
peci
al po
sitio
n. A
s for
the o
rder
ing o
f th
ese,
mod
e I w
ould
appe
ar to
be m
ost s
tron
gly i
mpl
ied,
fol-
low
ed b
y m
odes
IV, V
III,
and
VI.
Obv
ious
ly, f
ollo
wer
s of
Mar
chet
to ha
d diff
icul
ties w
ith th
is pa
ssag
e; th
e ano
mal
ous in
- cl
usio
n of m
ode I
I mig
ht ha
ve be
en th
e sou
rce o
f the
ir di
fficu
l- tie
s. Th
e spe
cific
atio
n of m
ode I
I for
the c
ase o
f an
impr
oper
lo
catio
n on A
2 (i.
e., A
gra
vis)
acco
rds w
ith th
e log
ic in
volv
ed in
th
e par
alle
l case
of in
terr
uptio
n 5b,
and i
t mig
ht ha
ve be
en th
e so
urce
of th
e ano
mal
ous a
ppea
ranc
e of m
ode I
I in t
he lis
t of t
he
prop
erly
loca
ted i
nter
rupt
ions
.
Inte
rrup
tion 6.
Mar
chet
to de
clar
es th
at th
e six
th in
terr
uptio
n (E
x. 1
0) im
plie
s mod
e I "
rare
ly,"
mod
es II
and
VII
I "of
ten,
" an
d IV
and V
I "so
met
imes
." Th
e man
uscr
ipt tr
aditi
on is
high
ly
vari
able
here
. In
one s
ourc
e, th
e ter
m pr
opri
o rep
lace
s pri
mo
(i.e.
, mod
e I);
in an
othe
r sou
rce,
men
tion o
f mod
e IV
is o
mit-
te
d; in
yet a
noth
er so
urce
, the p
assa
ge tr
eatin
g mod
es V
III,
IV,
and V
I is f
ollo
wed
by th
e com
men
t that
"in
deed
if it
is lo
cate
d [im
prop
erly
] on A
gra
vis,
[it] p
rope
rly [
impl
ies]
mod
e II"
; and
fin
ally
, in st
ill an
othe
r pai
r of s
ourc
es th
e lat
ter p
assa
ge re
plac
es
the r
efer
ence
s to m
odes
VII
I, IV
, and
VI.
Expl
anat
ion.
The s
ixth
inte
rrup
tion f
alls
with
in th
e pro
per
perf
ect r
ange
s of a
ll the
mod
es m
entio
ned b
y Mar
chet
to an
d his
follo
wer
s. Eac
h mod
e is r
epre
sent
ed by
one o
r tw
o of i
ts or
ient
- in
g not
es pr
esen
ted i
n a s
peci
al po
sitio
n. A
s for
the o
rder
ing o
f th
ese,
mod
e I w
ould
appe
ar to
be m
ost s
tron
gly i
mpl
ied,
fol-
low
ed b
y m
odes
IV, V
III,
and
VI.
Obv
ious
ly, f
ollo
wer
s of
Mar
chet
to ha
d diff
icul
ties w
ith th
is pa
ssag
e; th
e ano
mal
ous in
- cl
usio
n of m
ode I
I mig
ht ha
ve be
en th
e sou
rce o
f the
ir di
fficu
l- tie
s. Th
e spe
cific
atio
n of m
ode I
I for
the c
ase o
f an
impr
oper
lo
catio
n on A
2 (i.
e., A
gra
vis)
acco
rds w
ith th
e log
ic in
volv
ed in
th
e par
alle
l case
of in
terr
uptio
n 5b,
and i
t mig
ht ha
ve be
en th
e so
urce
of th
e ano
mal
ous a
ppea
ranc
e of m
ode I
I in t
he lis
t of t
he
prop
erly
loca
ted i
nter
rupt
ions
.
Inte
rrup
tion 6.
Mar
chet
to de
clar
es th
at th
e six
th in
terr
uptio
n (E
x. 1
0) im
plie
s mod
e I "
rare
ly,"
mod
es II
and
VII
I "of
ten,
" an
d IV
and V
I "so
met
imes
." Th
e man
uscr
ipt tr
aditi
on is
high
ly
vari
able
here
. In
one s
ourc
e, th
e ter
m pr
opri
o rep
lace
s pri
mo
(i.e.
, mod
e I);
in an
othe
r sou
rce,
men
tion o
f mod
e IV
is o
mit-
te
d; in
yet a
noth
er so
urce
, the p
assa
ge tr
eatin
g mod
es V
III,
IV,
and V
I is f
ollo
wed
by th
e com
men
t that
"in
deed
if it
is lo
cate
d [im
prop
erly
] on A
gra
vis,
[it] p
rope
rly [
impl
ies]
mod
e II"
; and
fin
ally
, in st
ill an
othe
r pai
r of s
ourc
es th
e lat
ter p
assa
ge re
plac
es
the r
efer
ence
s to m
odes
VII
I, IV
, and
VI.
Expl
anat
ion.
The s
ixth
inte
rrup
tion f
alls
with
in th
e pro
per
perf
ect r
ange
s of a
ll the
mod
es m
entio
ned b
y Mar
chet
to an
d his
follo
wer
s. Eac
h mod
e is r
epre
sent
ed by
one o
r tw
o of i
ts or
ient
- in
g not
es pr
esen
ted i
n a s
peci
al po
sitio
n. A
s for
the o
rder
ing o
f th
ese,
mod
e I w
ould
appe
ar to
be m
ost s
tron
gly i
mpl
ied,
fol-
low
ed b
y m
odes
IV, V
III,
and
VI.
Obv
ious
ly, f
ollo
wer
s of
Mar
chet
to ha
d diff
icul
ties w
ith th
is pa
ssag
e; th
e ano
mal
ous in
- cl
usio
n of m
ode I
I mig
ht ha
ve be
en th
e sou
rce o
f the
ir di
fficu
l- tie
s. Th
e spe
cific
atio
n of m
ode I
I for
the c
ase o
f an
impr
oper
lo
catio
n on A
2 (i.
e., A
gra
vis)
acco
rds w
ith th
e log
ic in
volv
ed in
th
e par
alle
l case
of in
terr
uptio
n 5b,
and i
t mig
ht ha
ve be
en th
e so
urce
of th
e ano
mal
ous a
ppea
ranc
e of m
ode I
I in t
he lis
t of t
he
prop
erly
loca
ted i
nter
rupt
ions
.
Inte
rrup
tion 6.
Mar
chet
to de
clar
es th
at th
e six
th in
terr
uptio
n (E
x. 1
0) im
plie
s mod
e I "
rare
ly,"
mod
es II
and
VII
I "of
ten,
" an
d IV
and V
I "so
met
imes
." Th
e man
uscr
ipt tr
aditi
on is
high
ly
vari
able
here
. In
one s
ourc
e, th
e ter
m pr
opri
o rep
lace
s pri
mo
(i.e.
, mod
e I);
in an
othe
r sou
rce,
men
tion o
f mod
e IV
is o
mit-
te
d; in
yet a
noth
er so
urce
, the p
assa
ge tr
eatin
g mod
es V
III,
IV,
and V
I is f
ollo
wed
by th
e com
men
t that
"in
deed
if it
is lo
cate
d [im
prop
erly
] on A
gra
vis,
[it] p
rope
rly [
impl
ies]
mod
e II"
; and
fin
ally
, in st
ill an
othe
r pai
r of s
ourc
es th
e lat
ter p
assa
ge re
plac
es
the r
efer
ence
s to m
odes
VII
I, IV
, and
VI.
Expl
anat
ion.
The s
ixth
inte
rrup
tion f
alls
with
in th
e pro
per
perf
ect r
ange
s of a
ll the
mod
es m
entio
ned b
y Mar
chet
to an
d his
follo
wer
s. Eac
h mod
e is r
epre
sent
ed by
one o
r tw
o of i
ts or
ient
- in
g not
es pr
esen
ted i
n a s
peci
al po
sitio
n. A
s for
the o
rder
ing o
f th
ese,
mod
e I w
ould
appe
ar to
be m
ost s
tron
gly i
mpl
ied,
fol-
low
ed b
y m
odes
IV, V
III,
and
VI.
Obv
ious
ly, f
ollo
wer
s of
Mar
chet
to ha
d diff
icul
ties w
ith th
is pa
ssag
e; th
e ano
mal
ous in
- cl
usio
n of m
ode I
I mig
ht ha
ve be
en th
e sou
rce o
f the
ir di
fficu
l- tie
s. Th
e spe
cific
atio
n of m
ode I
I for
the c
ase o
f an
impr
oper
lo
catio
n on A
2 (i.
e., A
gra
vis)
acco
rds w
ith th
e log
ic in
volv
ed in
th
e par
alle
l case
of in
terr
uptio
n 5b,
and i
t mig
ht ha
ve be
en th
e so
urce
of th
e ano
mal
ous a
ppea
ranc
e of m
ode I
I in t
he lis
t of t
he
prop
erly
loca
ted i
nter
rupt
ions
.
Inte
rrup
tion 7
. Mar
chet
to sa
ys th
at th
e sev
enth
inte
rrup
tion
(Ex.
11)
is u
sed
"in m
odes
I an
d VII
I and
som
etim
es in
mod
e V
I; if
it is
loca
ted o
n A
gra
vis [
i.e.,
A2]
, [it i
mpl
ies]
mod
e II."
Ex
plan
atio
n. T
he s
even
th i
nter
rupt
ion
appe
ars
in t
he
prop
er pe
rfec
t ran
ges o
f mod
es I,
VII
I, an
d VI.
Mod
e I, w
hich
M
arch
etto
men
tions
first
, is m
ost s
tron
gly i
mpl
ied b
y vir
tue o
f th
e fac
t tha
t its t
wo o
rien
ting n
otes
, D3
and A
3, a
ppea
r in ve
ry
spec
ial p
ositi
ons.
Mod
e VII
I, w
hich
is re
pres
ente
d by o
nly o
ne
orie
ntin
g not
e in
a spe
cial
posit
ion,
is th
ereb
y les
s str
ongl
y im
- pl
ied
than
mod
e I. H
owev
er, b
y vi
rtue
of th
e do
uble
spec
ial-
ness
of D
3 as
oppo
sed t
o th
e med
ial p
ositi
on of
F3,
mod
e VII
I is
mor
e st
rong
ly im
plie
d th
an m
ode
VI
(whi
ch is
men
tione
d la
st).
The o
miss
ion o
f mod
e IV
corr
espo
nds to
the c
ase o
f int
er-
rupt
ion 5
a. T
he re
ason
ing b
ehin
d ass
igni
ng th
is in
terr
uptio
n to
mod
e II w
hen
it is
loca
ted
on lo
w A
(A
2) c
orre
spon
ds to
the
inst
ance
s disc
usse
d with
rega
rd to
inte
rrup
tions
5b an
d 6.
Exam
ple 1
1. In
terr
uptio
n 7: "
Prop
erly
in m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
has
D3,
G3,
C4 a
nd (D
4) a
s ori
entin
g ton
es] a
nd so
met
imes
mod
e V
I [w
hich
has C
3, F
3, B
6'3 a
nd (C
4) as
orie
ntin
g ton
es]"
Y _
_
. -
Inte
rrup
tion 7
. Mar
chet
to sa
ys th
at th
e sev
enth
inte
rrup
tion
(Ex.
11)
is u
sed
"in m
odes
I an
d VII
I and
som
etim
es in
mod
e V
I; if
it is
loca
ted o
n A
gra
vis [
i.e.,
A2]
, [it i
mpl
ies]
mod
e II."
Ex
plan
atio
n. T
he s
even
th i
nter
rupt
ion
appe
ars
in t
he
prop
er pe
rfec
t ran
ges o
f mod
es I,
VII
I, an
d VI.
Mod
e I, w
hich
M
arch
etto
men
tions
first
, is m
ost s
tron
gly i
mpl
ied b
y vir
tue o
f th
e fac
t tha
t its t
wo o
rien
ting n
otes
, D3
and A
3, a
ppea
r in ve
ry
spec
ial p
ositi
ons.
Mod
e VII
I, w
hich
is re
pres
ente
d by o
nly o
ne
orie
ntin
g not
e in
a spe
cial
posit
ion,
is th
ereb
y les
s str
ongl
y im
- pl
ied
than
mod
e I. H
owev
er, b
y vi
rtue
of th
e do
uble
spec
ial-
ness
of D
3 as
oppo
sed t
o th
e med
ial p
ositi
on of
F3,
mod
e VII
I is
mor
e st
rong
ly im
plie
d th
an m
ode
VI
(whi
ch is
men
tione
d la
st).
The o
miss
ion o
f mod
e IV
corr
espo
nds to
the c
ase o
f int
er-
rupt
ion 5
a. T
he re
ason
ing b
ehin
d ass
igni
ng th
is in
terr
uptio
n to
mod
e II w
hen
it is
loca
ted
on lo
w A
(A
2) c
orre
spon
ds to
the
inst
ance
s disc
usse
d with
rega
rd to
inte
rrup
tions
5b an
d 6.
Exam
ple 1
1. In
terr
uptio
n 7: "
Prop
erly
in m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
has
D3,
G3,
C4 a
nd (D
4) a
s ori
entin
g ton
es] a
nd so
met
imes
mod
e V
I [w
hich
has C
3, F
3, B
6'3 a
nd (C
4) as
orie
ntin
g ton
es]"
Y _
_
. -
Inte
rrup
tion 7
. Mar
chet
to sa
ys th
at th
e sev
enth
inte
rrup
tion
(Ex.
11)
is u
sed
"in m
odes
I an
d VII
I and
som
etim
es in
mod
e V
I; if
it is
loca
ted o
n A
gra
vis [
i.e.,
A2]
, [it i
mpl
ies]
mod
e II."
Ex
plan
atio
n. T
he s
even
th i
nter
rupt
ion
appe
ars
in t
he
prop
er pe
rfec
t ran
ges o
f mod
es I,
VII
I, an
d VI.
Mod
e I, w
hich
M
arch
etto
men
tions
first
, is m
ost s
tron
gly i
mpl
ied b
y vir
tue o
f th
e fac
t tha
t its t
wo o
rien
ting n
otes
, D3
and A
3, a
ppea
r in ve
ry
spec
ial p
ositi
ons.
Mod
e VII
I, w
hich
is re
pres
ente
d by o
nly o
ne
orie
ntin
g not
e in
a spe
cial
posit
ion,
is th
ereb
y les
s str
ongl
y im
- pl
ied
than
mod
e I. H
owev
er, b
y vi
rtue
of th
e do
uble
spec
ial-
ness
of D
3 as
oppo
sed t
o th
e med
ial p
ositi
on of
F3,
mod
e VII
I is
mor
e st
rong
ly im
plie
d th
an m
ode
VI
(whi
ch is
men
tione
d la
st).
The o
miss
ion o
f mod
e IV
corr
espo
nds to
the c
ase o
f int
er-
rupt
ion 5
a. T
he re
ason
ing b
ehin
d ass
igni
ng th
is in
terr
uptio
n to
mod
e II w
hen
it is
loca
ted
on lo
w A
(A
2) c
orre
spon
ds to
the
inst
ance
s disc
usse
d with
rega
rd to
inte
rrup
tions
5b an
d 6.
Exam
ple 1
1. In
terr
uptio
n 7: "
Prop
erly
in m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
has
D3,
G3,
C4 a
nd (D
4) a
s ori
entin
g ton
es] a
nd so
met
imes
mod
e V
I [w
hich
has C
3, F
3, B
6'3 a
nd (C
4) as
orie
ntin
g ton
es]"
Y _
_
. -
Inte
rrup
tion 7
. Mar
chet
to sa
ys th
at th
e sev
enth
inte
rrup
tion
(Ex.
11)
is u
sed
"in m
odes
I an
d VII
I and
som
etim
es in
mod
e V
I; if
it is
loca
ted o
n A
gra
vis [
i.e.,
A2]
, [it i
mpl
ies]
mod
e II."
Ex
plan
atio
n. T
he s
even
th i
nter
rupt
ion
appe
ars
in t
he
prop
er pe
rfec
t ran
ges o
f mod
es I,
VII
I, an
d VI.
Mod
e I, w
hich
M
arch
etto
men
tions
first
, is m
ost s
tron
gly i
mpl
ied b
y vir
tue o
f th
e fac
t tha
t its t
wo o
rien
ting n
otes
, D3
and A
3, a
ppea
r in ve
ry
spec
ial p
ositi
ons.
Mod
e VII
I, w
hich
is re
pres
ente
d by o
nly o
ne
orie
ntin
g not
e in
a spe
cial
posit
ion,
is th
ereb
y les
s str
ongl
y im
- pl
ied
than
mod
e I. H
owev
er, b
y vi
rtue
of th
e do
uble
spec
ial-
ness
of D
3 as
oppo
sed t
o th
e med
ial p
ositi
on of
F3,
mod
e VII
I is
mor
e st
rong
ly im
plie
d th
an m
ode
VI
(whi
ch is
men
tione
d la
st).
The o
miss
ion o
f mod
e IV
corr
espo
nds to
the c
ase o
f int
er-
rupt
ion 5
a. T
he re
ason
ing b
ehin
d ass
igni
ng th
is in
terr
uptio
n to
mod
e II w
hen
it is
loca
ted
on lo
w A
(A
2) c
orre
spon
ds to
the
inst
ance
s disc
usse
d with
rega
rd to
inte
rrup
tions
5b an
d 6.
Exam
ple 1
1. In
terr
uptio
n 7: "
Prop
erly
in m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
has
D3,
G3,
C4 a
nd (D
4) a
s ori
entin
g ton
es] a
nd so
met
imes
mod
e V
I [w
hich
has C
3, F
3, B
6'3 a
nd (C
4) as
orie
ntin
g ton
es]"
Y _
_
. -
Inte
rrup
tion 7
. Mar
chet
to sa
ys th
at th
e sev
enth
inte
rrup
tion
(Ex.
11)
is u
sed
"in m
odes
I an
d VII
I and
som
etim
es in
mod
e V
I; if
it is
loca
ted o
n A
gra
vis [
i.e.,
A2]
, [it i
mpl
ies]
mod
e II."
Ex
plan
atio
n. T
he s
even
th i
nter
rupt
ion
appe
ars
in t
he
prop
er pe
rfec
t ran
ges o
f mod
es I,
VII
I, an
d VI.
Mod
e I, w
hich
M
arch
etto
men
tions
first
, is m
ost s
tron
gly i
mpl
ied b
y vir
tue o
f th
e fac
t tha
t its t
wo o
rien
ting n
otes
, D3
and A
3, a
ppea
r in ve
ry
spec
ial p
ositi
ons.
Mod
e VII
I, w
hich
is re
pres
ente
d by o
nly o
ne
orie
ntin
g not
e in
a spe
cial
posit
ion,
is th
ereb
y les
s str
ongl
y im
- pl
ied
than
mod
e I. H
owev
er, b
y vi
rtue
of th
e do
uble
spec
ial-
ness
of D
3 as
oppo
sed t
o th
e med
ial p
ositi
on of
F3,
mod
e VII
I is
mor
e st
rong
ly im
plie
d th
an m
ode
VI
(whi
ch is
men
tione
d la
st).
The o
miss
ion o
f mod
e IV
corr
espo
nds to
the c
ase o
f int
er-
rupt
ion 5
a. T
he re
ason
ing b
ehin
d ass
igni
ng th
is in
terr
uptio
n to
mod
e II w
hen
it is
loca
ted
on lo
w A
(A
2) c
orre
spon
ds to
the
inst
ance
s disc
usse
d with
rega
rd to
inte
rrup
tions
5b an
d 6.
Exam
ple 1
1. In
terr
uptio
n 7: "
Prop
erly
in m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
has
D3,
G3,
C4 a
nd (D
4) a
s ori
entin
g ton
es] a
nd so
met
imes
mod
e V
I [w
hich
has C
3, F
3, B
6'3 a
nd (C
4) as
orie
ntin
g ton
es]"
Y _
_
. -
Inte
rrup
tion 7
. Mar
chet
to sa
ys th
at th
e sev
enth
inte
rrup
tion
(Ex.
11)
is u
sed
"in m
odes
I an
d VII
I and
som
etim
es in
mod
e V
I; if
it is
loca
ted o
n A
gra
vis [
i.e.,
A2]
, [it i
mpl
ies]
mod
e II."
Ex
plan
atio
n. T
he s
even
th i
nter
rupt
ion
appe
ars
in t
he
prop
er pe
rfec
t ran
ges o
f mod
es I,
VII
I, an
d VI.
Mod
e I, w
hich
M
arch
etto
men
tions
first
, is m
ost s
tron
gly i
mpl
ied b
y vir
tue o
f th
e fac
t tha
t its t
wo o
rien
ting n
otes
, D3
and A
3, a
ppea
r in ve
ry
spec
ial p
ositi
ons.
Mod
e VII
I, w
hich
is re
pres
ente
d by o
nly o
ne
orie
ntin
g not
e in
a spe
cial
posit
ion,
is th
ereb
y les
s str
ongl
y im
- pl
ied
than
mod
e I. H
owev
er, b
y vi
rtue
of th
e do
uble
spec
ial-
ness
of D
3 as
oppo
sed t
o th
e med
ial p
ositi
on of
F3,
mod
e VII
I is
mor
e st
rong
ly im
plie
d th
an m
ode
VI
(whi
ch is
men
tione
d la
st).
The o
miss
ion o
f mod
e IV
corr
espo
nds to
the c
ase o
f int
er-
rupt
ion 5
a. T
he re
ason
ing b
ehin
d ass
igni
ng th
is in
terr
uptio
n to
mod
e II w
hen
it is
loca
ted
on lo
w A
(A
2) c
orre
spon
ds to
the
inst
ance
s disc
usse
d with
rega
rd to
inte
rrup
tions
5b an
d 6.
Exam
ple 1
1. In
terr
uptio
n 7: "
Prop
erly
in m
ode I
[whi
ch ha
s D3,
(G
3), A
3 and
D4
as or
ient
ing t
ones
] and
mod
e VII
I [w
hich
has
D3,
G3,
C4 a
nd (D
4) a
s ori
entin
g ton
es] a
nd so
met
imes
mod
e V
I [w
hich
has C
3, F
3, B
6'3 a
nd (C
4) as
orie
ntin
g ton
es]"
Y _
_
. -
Exam
ple 1
0. In
terr
uptio
n 6: "
Ofte
n [!]
mod
e II [
whi
ch ha
s A2,
D
3, G
3 an
d (A
3) a
s or
ient
ing t
ones
] and
ofte
n m
ode
VII
I [w
hich
has D
3, G
3, C
4 and
(D4)
as o
rien
ting t
ones
] and
som
e-
times
mod
e IV
[whi
ch ha
s B2,
E3,
A3,
and
(B3)
as o
rien
ting
tone
s] an
d so
met
imes
mod
e V
I [w
hich
has C
3, F
3, B
l,3 a
nd
(C4)
as o
rien
ting t
ones
] and
rare
ly [!
] mod
e I [w
hich
has D
3,
(G3)
, A3 a
nd D
4 as
orie
ntin
g ton
es]"
- -i
. II
Exam
ple 1
0. In
terr
uptio
n 6: "
Ofte
n [!]
mod
e II [
whi
ch ha
s A2,
D
3, G
3 an
d (A
3) a
s or
ient
ing t
ones
] and
ofte
n m
ode
VII
I [w
hich
has D
3, G
3, C
4 and
(D4)
as o
rien
ting t
ones
] and
som
e-
times
mod
e IV
[whi
ch ha
s B2,
E3,
A3,
and
(B3)
as o
rien
ting
tone
s] an
d so
met
imes
mod
e V
I [w
hich
has C
3, F
3, B
l,3 a
nd
(C4)
as o
rien
ting t
ones
] and
rare
ly [!
] mod
e I [w
hich
has D
3,
(G3)
, A3 a
nd D
4 as
orie
ntin
g ton
es]"
- -i
. II
Exam
ple 1
0. In
terr
uptio
n 6: "
Ofte
n [!]
mod
e II [
whi
ch ha
s A2,
D
3, G
3 an
d (A
3) a
s or
ient
ing t
ones
] and
ofte
n m
ode
VII
I [w
hich
has D
3, G
3, C
4 and
(D4)
as o
rien
ting t
ones
] and
som
e-
times
mod
e IV
[whi
ch ha
s B2,
E3,
A3,
and
(B3)
as o
rien
ting
tone
s] an
d so
met
imes
mod
e V
I [w
hich
has C
3, F
3, B
l,3 a
nd
(C4)
as o
rien
ting t
ones
] and
rare
ly [!
] mod
e I [w
hich
has D
3,
(G3)
, A3 a
nd D
4 as
orie
ntin
g ton
es]"
- -i
. II
Exam
ple 1
0. In
terr
uptio
n 6: "
Ofte
n [!]
mod
e II [
whi
ch ha
s A2,
D
3, G
3 an
d (A
3) a
s or
ient
ing t
ones
] and
ofte
n m
ode
VII
I [w
hich
has D
3, G
3, C
4 and
(D4)
as o
rien
ting t
ones
] and
som
e-
times
mod
e IV
[whi
ch ha
s B2,
E3,
A3,
and
(B3)
as o
rien
ting
tone
s] an
d so
met
imes
mod
e V
I [w
hich
has C
3, F
3, B
l,3 a
nd
(C4)
as o
rien
ting t
ones
] and
rare
ly [!
] mod
e I [w
hich
has D
3,
(G3)
, A3 a
nd D
4 as
orie
ntin
g ton
es]"
- -i
. II
Exam
ple 1
0. In
terr
uptio
n 6: "
Ofte
n [!]
mod
e II [
whi
ch ha
s A2,
D
3, G
3 an
d (A
3) a
s or
ient
ing t
ones
] and
ofte
n m
ode
VII
I [w
hich
has D
3, G
3, C
4 and
(D4)
as o
rien
ting t
ones
] and
som
e-
times
mod
e IV
[whi
ch ha
s B2,
E3,
A3,
and
(B3)
as o
rien
ting
tone
s] an
d so
met
imes
mod
e V
I [w
hich
has C
3, F
3, B
l,3 a
nd
(C4)
as o
rien
ting t
ones
] and
rare
ly [!
] mod
e I [w
hich
has D
3,
(G3)
, A3 a
nd D
4 as
orie
ntin
g ton
es]"
- -i
. II
Exam
ple 1
0. In
terr
uptio
n 6: "
Ofte
n [!]
mod
e II [
whi
ch ha
s A2,
D
3, G
3 an
d (A
3) a
s or
ient
ing t
ones
] and
ofte
n m
ode
VII
I [w
hich
has D
3, G
3, C
4 and
(D4)
as o
rien
ting t
ones
] and
som
e-
times
mod
e IV
[whi
ch ha
s B2,
E3,
A3,
and
(B3)
as o
rien
ting
tone
s] an
d so
met
imes
mod
e V
I [w
hich
has C
3, F
3, B
l,3 a
nd
(C4)
as o
rien
ting t
ones
] and
rare
ly [!
] mod
e I [w
hich
has D
3,
(G3)
, A3 a
nd D
4 as
orie
ntin
g ton
es]"
- -i
. II
x x x x x x
y y
y y
y y
y y
y y
y y
y y
y y
y y
y y
y y
y y
x x
y y
x x
y y
x x
y y
x x
y y
x x
y y
x x
y y
Inte
rrup
tion 8
. Mar
chet
to sa
ys th
at th
e las
t of t
he in
terr
up-
tions
(Ex.
12)
is u
sed
"alw
ays"
in m
ode I
and
"so
met
imes
" in
mod
e IV
. It a
ppea
rs in
the p
rope
r per
fect
rang
es of
bot
h mod
es.
Mod
e I, a
ccor
ding
to cr
iteri
on 5,
is a
pref
erre
d rea
ding
to m
ode
II. O
nly
one
orie
ntin
g not
e of
mod
e IV
, nam
ely A
3, i
s pre
- se
nted
in a
spec
ial p
ositi
on; t
his r
ende
rs m
ode I
V le
ss st
rong
ly
impl
ied t
han m
ode I
. Mar
chet
to's f
ailu
re to
men
tion m
ode V
III
appe
ars to
be i
ncon
siste
nt w
ith hi
s tre
atm
ent o
f oth
er in
terr
up-
tions
. How
ever
, Mar
chet
to se
ems
preo
ccup
ied a
t thi
s poi
nt
Inte
rrup
tion 8
. Mar
chet
to sa
ys th
at th
e las
t of t
he in
terr
up-
tions
(Ex.
12)
is u
sed
"alw
ays"
in m
ode I
and
"so
met
imes
" in
mod
e IV
. It a
ppea
rs in
the p
rope
r per
fect
rang
es of
bot
h mod
es.
Mod
e I, a
ccor
ding
to cr
iteri
on 5,
is a
pref
erre
d rea
ding
to m
ode
II. O
nly
one
orie
ntin
g not
e of
mod
e IV
, nam
ely A
3, i
s pre
- se
nted
in a
spec
ial p
ositi
on; t
his r
ende
rs m
ode I
V le
ss st
rong
ly
impl
ied t
han m
ode I
. Mar
chet
to's f
ailu
re to
men
tion m
ode V
III
appe
ars to
be i
ncon
siste
nt w
ith hi
s tre
atm
ent o
f oth
er in
terr
up-
tions
. How
ever
, Mar
chet
to se
ems
preo
ccup
ied a
t thi
s poi
nt
Inte
rrup
tion 8
. Mar
chet
to sa
ys th
at th
e las
t of t
he in
terr
up-
tions
(Ex.
12)
is u
sed
"alw
ays"
in m
ode I
and
"so
met
imes
" in
mod
e IV
. It a
ppea
rs in
the p
rope
r per
fect
rang
es of
bot
h mod
es.
Mod
e I, a
ccor
ding
to cr
iteri
on 5,
is a
pref
erre
d rea
ding
to m
ode
II. O
nly
one
orie
ntin
g not
e of
mod
e IV
, nam
ely A
3, i
s pre
- se
nted
in a
spec
ial p
ositi
on; t
his r
ende
rs m
ode I
V le
ss st
rong
ly
impl
ied t
han m
ode I
. Mar
chet
to's f
ailu
re to
men
tion m
ode V
III
appe
ars to
be i
ncon
siste
nt w
ith hi
s tre
atm
ent o
f oth
er in
terr
up-
tions
. How
ever
, Mar
chet
to se
ems
preo
ccup
ied a
t thi
s poi
nt
Inte
rrup
tion 8
. Mar
chet
to sa
ys th
at th
e las
t of t
he in
terr
up-
tions
(Ex.
12)
is u
sed
"alw
ays"
in m
ode I
and
"so
met
imes
" in
mod
e IV
. It a
ppea
rs in
the p
rope
r per
fect
rang
es of
bot
h mod
es.
Mod
e I, a
ccor
ding
to cr
iteri
on 5,
is a
pref
erre
d rea
ding
to m
ode
II. O
nly
one
orie
ntin
g not
e of
mod
e IV
, nam
ely A
3, i
s pre
- se
nted
in a
spec
ial p
ositi
on; t
his r
ende
rs m
ode I
V le
ss st
rong
ly
impl
ied t
han m
ode I
. Mar
chet
to's f
ailu
re to
men
tion m
ode V
III
appe
ars to
be i
ncon
siste
nt w
ith hi
s tre
atm
ent o
f oth
er in
terr
up-
tions
. How
ever
, Mar
chet
to se
ems
preo
ccup
ied a
t thi
s poi
nt
Inte
rrup
tion 8
. Mar
chet
to sa
ys th
at th
e las
t of t
he in
terr
up-
tions
(Ex.
12)
is u
sed
"alw
ays"
in m
ode I
and
"so
met
imes
" in
mod
e IV
. It a
ppea
rs in
the p
rope
r per
fect
rang
es of
bot
h mod
es.
Mod
e I, a
ccor
ding
to cr
iteri
on 5,
is a
pref
erre
d rea
ding
to m
ode
II. O
nly
one
orie
ntin
g not
e of
mod
e IV
, nam
ely A
3, i
s pre
- se
nted
in a
spec
ial p
ositi
on; t
his r
ende
rs m
ode I
V le
ss st
rong
ly
impl
ied t
han m
ode I
. Mar
chet
to's f
ailu
re to
men
tion m
ode V
III
appe
ars to
be i
ncon
siste
nt w
ith hi
s tre
atm
ent o
f oth
er in
terr
up-
tions
. How
ever
, Mar
chet
to se
ems
preo
ccup
ied a
t thi
s poi
nt
Inte
rrup
tion 8
. Mar
chet
to sa
ys th
at th
e las
t of t
he in
terr
up-
tions
(Ex.
12)
is u
sed
"alw
ays"
in m
ode I
and
"so
met
imes
" in
mod
e IV
. It a
ppea
rs in
the p
rope
r per
fect
rang
es of
bot
h mod
es.
Mod
e I, a
ccor
ding
to cr
iteri
on 5,
is a
pref
erre
d rea
ding
to m
ode
II. O
nly
one
orie
ntin
g not
e of
mod
e IV
, nam
ely A
3, i
s pre
- se
nted
in a
spec
ial p
ositi
on; t
his r
ende
rs m
ode I
V le
ss st
rong
ly
impl
ied t
han m
ode I
. Mar
chet
to's f
ailu
re to
men
tion m
ode V
III
appe
ars to
be i
ncon
siste
nt w
ith hi
s tre
atm
ent o
f oth
er in
terr
up-
tions
. How
ever
, Mar
chet
to se
ems
preo
ccup
ied a
t thi
s poi
nt
x y
y y
x y
y y
x y
y y
x y
y y
x y
y y
x y
y y Th
is co
nten
t dow
nloa
ded
from
130
.63.
180.
147
on T
hu, 2
1 M
ay 2
015
03:2
1:26
UTC
All
use
subj
ect t
o JS
TOR
Term
s and
Con
ditio
ns
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
131
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
131
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
131
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
131
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
131
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
131
Exam
ple 1
2. In
terr
uptio
n 8: "
Alw
ays in
mod
e I [w
hich
has D
3,
(G3)
, A3 a
nd D
4 as
orie
ntin
g ton
es] a
nd so
met
imes
in m
ode I
V
[whi
ch ha
s B2,
E3,
A3 a
nd (B
3) a
s ori
entin
g ton
es]"
y y
y
with
the
enor
mou
s str
engt
h of
thi
s int
erru
ptio
n in
impl
ying
m
ode I
, for
he
goes
on
to sa
y the
follo
win
g: "o
ne sh
ould
ob-
serv
e tha
t thi
s spe
cies
of fi
fth, w
hich
cons
ists o
f a si
ngle
inte
rval
, is
of su
ch gr
eat s
tren
gth [
auct
orita
s] th
at, n
o m
atte
r wha
t hap
- pe
ns, i
f it i
s re
peat
ed [r
eper
cuss
a] in
a m
elod
y tw
o or
thre
e tim
es, n
o m
atte
r how
far t
he m
elod
y de
scen
ds, a
nd ev
en if
it
asce
nds n
o fur
ther
than
a fift
h abo
ve [u
ltra]
its fin
al [fi
nis]
, suc
h a
mel
ody i
s cal
led
auth
entic
." W
hat g
ives
the d
irec
t leap
of a
fif
th it
s gre
at p
ower
wou
ld se
em to
be
the
ultim
ate d
egre
e of
spec
ial-n
ess o
f its
com
pone
nt no
tes,
for b
oth D
3 an
d A3
are e
x-
trem
ely s
peci
al by
virt
ue of
bei
ng n
ot o
nly m
embe
rs of
a le
ap
but a
lso ex
trem
es an
d tem
pora
lly as
clos
e as p
ossib
le to
one a
n-
othe
r (cr
iteri
a 8 an
d 4).
In th
is lig
ht, o
ne ca
n ign
ore t
he sl
ight
ly
baffl
ing m
entio
n of m
ode I
V a
nd th
e cor
resp
ondi
ngly
puzz
ling
omiss
ion
of a
ref
eren
ce to
mod
e V
III,
for
wha
t Mar
chet
to
seem
s mos
t int
ent o
n at
this
poin
t is e
mph
asiz
ing t
he su
perl
a-
tive i
mpl
icat
ive s
tren
gth o
f dir
ect le
aps.
So st
rong
inde
ed is
the
asso
ciat
ion o
f the
per
fect
fifth
D3-
A3
with
an au
then
tic fo
rm
that
it ca
n, on
repe
titio
n, im
ply a
n aut
hent
ic m
ode e
ven t
houg
h th
e ran
ge m
ight
corr
espo
nd to
that
nor
mal
ly as
soci
ated
with
a pl
agal
mod
e.30
Mor
eove
r, in
conc
ludi
ng th
is se
ctio
n of h
is tr
ea-
30Po
wer
s, "M
ode,
" 393
, per
cept
ivel
y tra
ces M
arch
etto
's not
ion t
hat r
epet
i- tio
n of t
he 1
-5 s
peci
es se
rves
to ch
arac
teri
ze a m
elod
y as a
uthe
ntic
to th
e ide
a fo
und i
n th
e Dia
logu
s tha
t rep
etiti
on of
the f
ifth d
egre
e (5)
hel
ps to
dist
ingu
ish
an a
uthe
ntic
from
a p
laga
l. Th
e sa
me
Latin
root
(rep
ercu
ss-) i
s, as
Pow
ers
poin
ts ou
t, em
ploy
ed in
the t
wo t
reat
ises t
o co
nvey
the c
once
pt of
repe
titio
n.
Exam
ple 1
2. In
terr
uptio
n 8: "
Alw
ays in
mod
e I [w
hich
has D
3,
(G3)
, A3 a
nd D
4 as
orie
ntin
g ton
es] a
nd so
met
imes
in m
ode I
V
[whi
ch ha
s B2,
E3,
A3 a
nd (B
3) a
s ori
entin
g ton
es]"
y y
y
with
the
enor
mou
s str
engt
h of
thi
s int
erru
ptio
n in
impl
ying
m
ode I
, for
he
goes
on
to sa
y the
follo
win
g: "o
ne sh
ould
ob-
serv
e tha
t thi
s spe
cies
of fi
fth, w
hich
cons
ists o
f a si
ngle
inte
rval
, is
of su
ch gr
eat s
tren
gth [
auct
orita
s] th
at, n
o m
atte
r wha
t hap
- pe
ns, i
f it i
s re
peat
ed [r
eper
cuss
a] in
a m
elod
y tw
o or
thre
e tim
es, n
o m
atte
r how
far t
he m
elod
y de
scen
ds, a
nd ev
en if
it
asce
nds n
o fur
ther
than
a fift
h abo
ve [u
ltra]
its fin
al [fi
nis]
, suc
h a
mel
ody i
s cal
led
auth
entic
." W
hat g
ives
the d
irec
t leap
of a
fif
th it
s gre
at p
ower
wou
ld se
em to
be
the
ultim
ate d
egre
e of
spec
ial-n
ess o
f its
com
pone
nt no
tes,
for b
oth D
3 an
d A3
are e
x-
trem
ely s
peci
al by
virt
ue of
bei
ng n
ot o
nly m
embe
rs of
a le
ap
but a
lso ex
trem
es an
d tem
pora
lly as
clos
e as p
ossib
le to
one a
n-
othe
r (cr
iteri
a 8 an
d 4).
In th
is lig
ht, o
ne ca
n ign
ore t
he sl
ight
ly
baffl
ing m
entio
n of m
ode I
V a
nd th
e cor
resp
ondi
ngly
puzz
ling
omiss
ion
of a
ref
eren
ce to
mod
e V
III,
for
wha
t Mar
chet
to
seem
s mos
t int
ent o
n at
this
poin
t is e
mph
asiz
ing t
he su
perl
a-
tive i
mpl
icat
ive s
tren
gth o
f dir
ect le
aps.
So st
rong
inde
ed is
the
asso
ciat
ion o
f the
per
fect
fifth
D3-
A3
with
an au
then
tic fo
rm
that
it ca
n, on
repe
titio
n, im
ply a
n aut
hent
ic m
ode e
ven t
houg
h th
e ran
ge m
ight
corr
espo
nd to
that
nor
mal
ly as
soci
ated
with
a pl
agal
mod
e.30
Mor
eove
r, in
conc
ludi
ng th
is se
ctio
n of h
is tr
ea-
30Po
wer
s, "M
ode,
" 393
, per
cept
ivel
y tra
ces M
arch
etto
's not
ion t
hat r
epet
i- tio
n of t
he 1
-5 s
peci
es se
rves
to ch
arac
teri
ze a m
elod
y as a
uthe
ntic
to th
e ide
a fo
und i
n th
e Dia
logu
s tha
t rep
etiti
on of
the f
ifth d
egre
e (5)
hel
ps to
dist
ingu
ish
an a
uthe
ntic
from
a p
laga
l. Th
e sa
me
Latin
root
(rep
ercu
ss-) i
s, as
Pow
ers
poin
ts ou
t, em
ploy
ed in
the t
wo t
reat
ises t
o co
nvey
the c
once
pt of
repe
titio
n.
Exam
ple 1
2. In
terr
uptio
n 8: "
Alw
ays in
mod
e I [w
hich
has D
3,
(G3)
, A3 a
nd D
4 as
orie
ntin
g ton
es] a
nd so
met
imes
in m
ode I
V
[whi
ch ha
s B2,
E3,
A3 a
nd (B
3) a
s ori
entin
g ton
es]"
y y
y
with
the
enor
mou
s str
engt
h of
thi
s int
erru
ptio
n in
impl
ying
m
ode I
, for
he
goes
on
to sa
y the
follo
win
g: "o
ne sh
ould
ob-
serv
e tha
t thi
s spe
cies
of fi
fth, w
hich
cons
ists o
f a si
ngle
inte
rval
, is
of su
ch gr
eat s
tren
gth [
auct
orita
s] th
at, n
o m
atte
r wha
t hap
- pe
ns, i
f it i
s re
peat
ed [r
eper
cuss
a] in
a m
elod
y tw
o or
thre
e tim
es, n
o m
atte
r how
far t
he m
elod
y de
scen
ds, a
nd ev
en if
it
asce
nds n
o fur
ther
than
a fift
h abo
ve [u
ltra]
its fin
al [fi
nis]
, suc
h a
mel
ody i
s cal
led
auth
entic
." W
hat g
ives
the d
irec
t leap
of a
fif
th it
s gre
at p
ower
wou
ld se
em to
be
the
ultim
ate d
egre
e of
spec
ial-n
ess o
f its
com
pone
nt no
tes,
for b
oth D
3 an
d A3
are e
x-
trem
ely s
peci
al by
virt
ue of
bei
ng n
ot o
nly m
embe
rs of
a le
ap
but a
lso ex
trem
es an
d tem
pora
lly as
clos
e as p
ossib
le to
one a
n-
othe
r (cr
iteri
a 8 an
d 4).
In th
is lig
ht, o
ne ca
n ign
ore t
he sl
ight
ly
baffl
ing m
entio
n of m
ode I
V a
nd th
e cor
resp
ondi
ngly
puzz
ling
omiss
ion
of a
ref
eren
ce to
mod
e V
III,
for
wha
t Mar
chet
to
seem
s mos
t int
ent o
n at
this
poin
t is e
mph
asiz
ing t
he su
perl
a-
tive i
mpl
icat
ive s
tren
gth o
f dir
ect le
aps.
So st
rong
inde
ed is
the
asso
ciat
ion o
f the
per
fect
fifth
D3-
A3
with
an au
then
tic fo
rm
that
it ca
n, on
repe
titio
n, im
ply a
n aut
hent
ic m
ode e
ven t
houg
h th
e ran
ge m
ight
corr
espo
nd to
that
nor
mal
ly as
soci
ated
with
a pl
agal
mod
e.30
Mor
eove
r, in
conc
ludi
ng th
is se
ctio
n of h
is tr
ea-
30Po
wer
s, "M
ode,
" 393
, per
cept
ivel
y tra
ces M
arch
etto
's not
ion t
hat r
epet
i- tio
n of t
he 1
-5 s
peci
es se
rves
to ch
arac
teri
ze a m
elod
y as a
uthe
ntic
to th
e ide
a fo
und i
n th
e Dia
logu
s tha
t rep
etiti
on of
the f
ifth d
egre
e (5)
hel
ps to
dist
ingu
ish
an a
uthe
ntic
from
a p
laga
l. Th
e sa
me
Latin
root
(rep
ercu
ss-) i
s, as
Pow
ers
poin
ts ou
t, em
ploy
ed in
the t
wo t
reat
ises t
o co
nvey
the c
once
pt of
repe
titio
n.
Exam
ple 1
2. In
terr
uptio
n 8: "
Alw
ays in
mod
e I [w
hich
has D
3,
(G3)
, A3 a
nd D
4 as
orie
ntin
g ton
es] a
nd so
met
imes
in m
ode I
V
[whi
ch ha
s B2,
E3,
A3 a
nd (B
3) a
s ori
entin
g ton
es]"
y y
y
with
the
enor
mou
s str
engt
h of
thi
s int
erru
ptio
n in
impl
ying
m
ode I
, for
he
goes
on
to sa
y the
follo
win
g: "o
ne sh
ould
ob-
serv
e tha
t thi
s spe
cies
of fi
fth, w
hich
cons
ists o
f a si
ngle
inte
rval
, is
of su
ch gr
eat s
tren
gth [
auct
orita
s] th
at, n
o m
atte
r wha
t hap
- pe
ns, i
f it i
s re
peat
ed [r
eper
cuss
a] in
a m
elod
y tw
o or
thre
e tim
es, n
o m
atte
r how
far t
he m
elod
y de
scen
ds, a
nd ev
en if
it
asce
nds n
o fur
ther
than
a fift
h abo
ve [u
ltra]
its fin
al [fi
nis]
, suc
h a
mel
ody i
s cal
led
auth
entic
." W
hat g
ives
the d
irec
t leap
of a
fif
th it
s gre
at p
ower
wou
ld se
em to
be
the
ultim
ate d
egre
e of
spec
ial-n
ess o
f its
com
pone
nt no
tes,
for b
oth D
3 an
d A3
are e
x-
trem
ely s
peci
al by
virt
ue of
bei
ng n
ot o
nly m
embe
rs of
a le
ap
but a
lso ex
trem
es an
d tem
pora
lly as
clos
e as p
ossib
le to
one a
n-
othe
r (cr
iteri
a 8 an
d 4).
In th
is lig
ht, o
ne ca
n ign
ore t
he sl
ight
ly
baffl
ing m
entio
n of m
ode I
V a
nd th
e cor
resp
ondi
ngly
puzz
ling
omiss
ion
of a
ref
eren
ce to
mod
e V
III,
for
wha
t Mar
chet
to
seem
s mos
t int
ent o
n at
this
poin
t is e
mph
asiz
ing t
he su
perl
a-
tive i
mpl
icat
ive s
tren
gth o
f dir
ect le
aps.
So st
rong
inde
ed is
the
asso
ciat
ion o
f the
per
fect
fifth
D3-
A3
with
an au
then
tic fo
rm
that
it ca
n, on
repe
titio
n, im
ply a
n aut
hent
ic m
ode e
ven t
houg
h th
e ran
ge m
ight
corr
espo
nd to
that
nor
mal
ly as
soci
ated
with
a pl
agal
mod
e.30
Mor
eove
r, in
conc
ludi
ng th
is se
ctio
n of h
is tr
ea-
30Po
wer
s, "M
ode,
" 393
, per
cept
ivel
y tra
ces M
arch
etto
's not
ion t
hat r
epet
i- tio
n of t
he 1
-5 s
peci
es se
rves
to ch
arac
teri
ze a m
elod
y as a
uthe
ntic
to th
e ide
a fo
und i
n th
e Dia
logu
s tha
t rep
etiti
on of
the f
ifth d
egre
e (5)
hel
ps to
dist
ingu
ish
an a
uthe
ntic
from
a p
laga
l. Th
e sa
me
Latin
root
(rep
ercu
ss-) i
s, as
Pow
ers
poin
ts ou
t, em
ploy
ed in
the t
wo t
reat
ises t
o co
nvey
the c
once
pt of
repe
titio
n.
Exam
ple 1
2. In
terr
uptio
n 8: "
Alw
ays in
mod
e I [w
hich
has D
3,
(G3)
, A3 a
nd D
4 as
orie
ntin
g ton
es] a
nd so
met
imes
in m
ode I
V
[whi
ch ha
s B2,
E3,
A3 a
nd (B
3) a
s ori
entin
g ton
es]"
y y
y
with
the
enor
mou
s str
engt
h of
thi
s int
erru
ptio
n in
impl
ying
m
ode I
, for
he
goes
on
to sa
y the
follo
win
g: "o
ne sh
ould
ob-
serv
e tha
t thi
s spe
cies
of fi
fth, w
hich
cons
ists o
f a si
ngle
inte
rval
, is
of su
ch gr
eat s
tren
gth [
auct
orita
s] th
at, n
o m
atte
r wha
t hap
- pe
ns, i
f it i
s re
peat
ed [r
eper
cuss
a] in
a m
elod
y tw
o or
thre
e tim
es, n
o m
atte
r how
far t
he m
elod
y de
scen
ds, a
nd ev
en if
it
asce
nds n
o fur
ther
than
a fift
h abo
ve [u
ltra]
its fin
al [fi
nis]
, suc
h a
mel
ody i
s cal
led
auth
entic
." W
hat g
ives
the d
irec
t leap
of a
fif
th it
s gre
at p
ower
wou
ld se
em to
be
the
ultim
ate d
egre
e of
spec
ial-n
ess o
f its
com
pone
nt no
tes,
for b
oth D
3 an
d A3
are e
x-
trem
ely s
peci
al by
virt
ue of
bei
ng n
ot o
nly m
embe
rs of
a le
ap
but a
lso ex
trem
es an
d tem
pora
lly as
clos
e as p
ossib
le to
one a
n-
othe
r (cr
iteri
a 8 an
d 4).
In th
is lig
ht, o
ne ca
n ign
ore t
he sl
ight
ly
baffl
ing m
entio
n of m
ode I
V a
nd th
e cor
resp
ondi
ngly
puzz
ling
omiss
ion
of a
ref
eren
ce to
mod
e V
III,
for
wha
t Mar
chet
to
seem
s mos
t int
ent o
n at
this
poin
t is e
mph
asiz
ing t
he su
perl
a-
tive i
mpl
icat
ive s
tren
gth o
f dir
ect le
aps.
So st
rong
inde
ed is
the
asso
ciat
ion o
f the
per
fect
fifth
D3-
A3
with
an au
then
tic fo
rm
that
it ca
n, on
repe
titio
n, im
ply a
n aut
hent
ic m
ode e
ven t
houg
h th
e ran
ge m
ight
corr
espo
nd to
that
nor
mal
ly as
soci
ated
with
a pl
agal
mod
e.30
Mor
eove
r, in
conc
ludi
ng th
is se
ctio
n of h
is tr
ea-
30Po
wer
s, "M
ode,
" 393
, per
cept
ivel
y tra
ces M
arch
etto
's not
ion t
hat r
epet
i- tio
n of t
he 1
-5 s
peci
es se
rves
to ch
arac
teri
ze a m
elod
y as a
uthe
ntic
to th
e ide
a fo
und i
n th
e Dia
logu
s tha
t rep
etiti
on of
the f
ifth d
egre
e (5)
hel
ps to
dist
ingu
ish
an a
uthe
ntic
from
a p
laga
l. Th
e sa
me
Latin
root
(rep
ercu
ss-) i
s, as
Pow
ers
poin
ts ou
t, em
ploy
ed in
the t
wo t
reat
ises t
o co
nvey
the c
once
pt of
repe
titio
n.
Exam
ple 1
2. In
terr
uptio
n 8: "
Alw
ays in
mod
e I [w
hich
has D
3,
(G3)
, A3 a
nd D
4 as
orie
ntin
g ton
es] a
nd so
met
imes
in m
ode I
V
[whi
ch ha
s B2,
E3,
A3 a
nd (B
3) a
s ori
entin
g ton
es]"
y y
y
with
the
enor
mou
s str
engt
h of
thi
s int
erru
ptio
n in
impl
ying
m
ode I
, for
he
goes
on
to sa
y the
follo
win
g: "o
ne sh
ould
ob-
serv
e tha
t thi
s spe
cies
of fi
fth, w
hich
cons
ists o
f a si
ngle
inte
rval
, is
of su
ch gr
eat s
tren
gth [
auct
orita
s] th
at, n
o m
atte
r wha
t hap
- pe
ns, i
f it i
s re
peat
ed [r
eper
cuss
a] in
a m
elod
y tw
o or
thre
e tim
es, n
o m
atte
r how
far t
he m
elod
y de
scen
ds, a
nd ev
en if
it
asce
nds n
o fur
ther
than
a fift
h abo
ve [u
ltra]
its fin
al [fi
nis]
, suc
h a
mel
ody i
s cal
led
auth
entic
." W
hat g
ives
the d
irec
t leap
of a
fif
th it
s gre
at p
ower
wou
ld se
em to
be
the
ultim
ate d
egre
e of
spec
ial-n
ess o
f its
com
pone
nt no
tes,
for b
oth D
3 an
d A3
are e
x-
trem
ely s
peci
al by
virt
ue of
bei
ng n
ot o
nly m
embe
rs of
a le
ap
but a
lso ex
trem
es an
d tem
pora
lly as
clos
e as p
ossib
le to
one a
n-
othe
r (cr
iteri
a 8 an
d 4).
In th
is lig
ht, o
ne ca
n ign
ore t
he sl
ight
ly
baffl
ing m
entio
n of m
ode I
V a
nd th
e cor
resp
ondi
ngly
puzz
ling
omiss
ion
of a
ref
eren
ce to
mod
e V
III,
for
wha
t Mar
chet
to
seem
s mos
t int
ent o
n at
this
poin
t is e
mph
asiz
ing t
he su
perl
a-
tive i
mpl
icat
ive s
tren
gth o
f dir
ect le
aps.
So st
rong
inde
ed is
the
asso
ciat
ion o
f the
per
fect
fifth
D3-
A3
with
an au
then
tic fo
rm
that
it ca
n, on
repe
titio
n, im
ply a
n aut
hent
ic m
ode e
ven t
houg
h th
e ran
ge m
ight
corr
espo
nd to
that
nor
mal
ly as
soci
ated
with
a pl
agal
mod
e.30
Mor
eove
r, in
conc
ludi
ng th
is se
ctio
n of h
is tr
ea-
30Po
wer
s, "M
ode,
" 393
, per
cept
ivel
y tra
ces M
arch
etto
's not
ion t
hat r
epet
i- tio
n of t
he 1
-5 s
peci
es se
rves
to ch
arac
teri
ze a m
elod
y as a
uthe
ntic
to th
e ide
a fo
und i
n th
e Dia
logu
s tha
t rep
etiti
on of
the f
ifth d
egre
e (5)
hel
ps to
dist
ingu
ish
an a
uthe
ntic
from
a p
laga
l. Th
e sa
me
Latin
root
(rep
ercu
ss-) i
s, as
Pow
ers
poin
ts ou
t, em
ploy
ed in
the t
wo t
reat
ises t
o co
nvey
the c
once
pt of
repe
titio
n.
tise,
Mar
chet
to dr
ives
the p
oint
hom
e aga
in by
stat
ing t
hat "
we
say
the
sam
e of a
ll ot
her m
odes
; con
cern
ing i
nter
rupt
ions
of
othe
r spe
cies
, we d
o not
inte
nd [t
o say
] any
thin
g else
[her
e] ex
- ce
pt th
at th
ey ca
n be p
lace
d in
auth
entic
and p
laga
l mod
es ex
- ce
pt in
the c
ase o
f[an
inte
rrup
tion]
that
cons
ists o
f a si
ngle
inte
r-
val [
i.e.,
a dir
ect le
ap] a
s we h
ave [
alre
ady]
said
" (m
y ita
lics)
.31
Mar
chet
to's T
heor
y of I
nter
rupt
ions
, and I
ssue
s in M
oder
n M
usic
The
ory
Tow
ard t
he ou
tset
of th
is st
udy,
I sa
id th
at M
arch
etto
's ap-
pr
oach
to m
elod
ic an
alys
is see
ms q
uite
mod
ern.
As o
ne g
rap-
pl
es w
ith h
is ac
coun
t of i
nter
rupt
ions
, one
enc
ount
ers is
sues
th
at ar
e cur
rent
ly al
ive i
n m
usic
theo
ry. I
hav
e alr
eady
poin
ted
out t
hat M
arch
etto
is co
ncer
ned w
ith co
nnec
tions
betw
een l
o-
cal,
fore
grou
nd ev
ents
and
glob
al, b
ackg
roun
d var
iabl
es in
a
piec
e. T
he an
alyt
ical
tech
niqu
e im
plic
it in M
arch
etto
's acc
ount
of
inte
rrup
tions
proc
eeds
from
fore
grou
nd to
bac
kgro
und.
To
use t
erm
s of t
he m
oder
n the
orist
Eug
ene N
arm
our,
Mar
chet
- to
's an
alyt
ic pr
oced
ure i
s one
of "
asce
nt,"
that
is, a
n an
alyt
ic
prog
ress
ion "
from
botto
m to
top.
" In
this
rega
rd, M
arch
etto
re
sem
bles
such
mod
ern t
heor
ists a
s Leo
nard
Mey
er an
d Nar
- m
our,
him
self,
who
sim
ilarl
y pro
ceed
from
fore
grou
nd to
bac
k-
grou
nd, th
at is,
from
indi
vidu
al to
nes t
o lar
ger s
pans
, in co
ntra
st
with
Sche
nker
ians
, who
, acc
ordi
ng to
Nar
mou
r, pr
ocee
d fro
m
back
grou
nd to
for
egro
und i
n th
eir a
pplic
atio
n of t
he U
rsat
z m
odel
.32
Mar
chet
to's i
nter
est in
nar
row
mel
odie
s her
e can
be tr
aced
as fa
r bac
k as t
he
begi
nnin
g of t
he el
even
th ce
ntur
y, w
hen
Bern
o of R
eich
enau
disc
usse
d que
s-
tions
that
arise
from
this
situa
tion (
Ger
bert
, ed.
, Scr
ipto
res E
ccle
siast
ici 2:
60a,
an
d th
e To
nale
Sanc
ti Be
rnar
di di
scus
sed i
n G
iimpe
l, Zur
Inte
rpre
tatio
n der
Tonu
s-D
efin
ition
, 45-4
6.
31Lu
cida
rium
, 11, 4
,248
, pp.
516
-17.
32
See E
ugen
e Nar
mou
r, Be
yond
Sche
nker
ism: T
he N
eed f
orA
ltern
ativ
es in
M
usic
Ana
lysis
(Chi
cago
: Uni
vers
ity of
Chi
cago
Pres
s, 19
77) e
sp. 1
22-6
6.
tise,
Mar
chet
to dr
ives
the p
oint
hom
e aga
in by
stat
ing t
hat "
we
say
the
sam
e of a
ll ot
her m
odes
; con
cern
ing i
nter
rupt
ions
of
othe
r spe
cies
, we d
o not
inte
nd [t
o say
] any
thin
g else
[her
e] ex
- ce
pt th
at th
ey ca
n be p
lace
d in
auth
entic
and p
laga
l mod
es ex
- ce
pt in
the c
ase o
f[an
inte
rrup
tion]
that
cons
ists o
f a si
ngle
inte
r-
val [
i.e.,
a dir
ect le
ap] a
s we h
ave [
alre
ady]
said
" (m
y ita
lics)
.31
Mar
chet
to's T
heor
y of I
nter
rupt
ions
, and I
ssue
s in M
oder
n M
usic
The
ory
Tow
ard t
he ou
tset
of th
is st
udy,
I sa
id th
at M
arch
etto
's ap-
pr
oach
to m
elod
ic an
alys
is see
ms q
uite
mod
ern.
As o
ne g
rap-
pl
es w
ith h
is ac
coun
t of i
nter
rupt
ions
, one
enc
ount
ers is
sues
th
at ar
e cur
rent
ly al
ive i
n m
usic
theo
ry. I
hav
e alr
eady
poin
ted
out t
hat M
arch
etto
is co
ncer
ned w
ith co
nnec
tions
betw
een l
o-
cal,
fore
grou
nd ev
ents
and
glob
al, b
ackg
roun
d var
iabl
es in
a
piec
e. T
he an
alyt
ical
tech
niqu
e im
plic
it in M
arch
etto
's acc
ount
of
inte
rrup
tions
proc
eeds
from
fore
grou
nd to
bac
kgro
und.
To
use t
erm
s of t
he m
oder
n the
orist
Eug
ene N
arm
our,
Mar
chet
- to
's an
alyt
ic pr
oced
ure i
s one
of "
asce
nt,"
that
is, a
n an
alyt
ic
prog
ress
ion "
from
botto
m to
top.
" In
this
rega
rd, M
arch
etto
re
sem
bles
such
mod
ern t
heor
ists a
s Leo
nard
Mey
er an
d Nar
- m
our,
him
self,
who
sim
ilarl
y pro
ceed
from
fore
grou
nd to
bac
k-
grou
nd, th
at is,
from
indi
vidu
al to
nes t
o lar
ger s
pans
, in co
ntra
st
with
Sche
nker
ians
, who
, acc
ordi
ng to
Nar
mou
r, pr
ocee
d fro
m
back
grou
nd to
for
egro
und i
n th
eir a
pplic
atio
n of t
he U
rsat
z m
odel
.32
Mar
chet
to's i
nter
est in
nar
row
mel
odie
s her
e can
be tr
aced
as fa
r bac
k as t
he
begi
nnin
g of t
he el
even
th ce
ntur
y, w
hen
Bern
o of R
eich
enau
disc
usse
d que
s-
tions
that
arise
from
this
situa
tion (
Ger
bert
, ed.
, Scr
ipto
res E
ccle
siast
ici 2:
60a,
an
d th
e To
nale
Sanc
ti Be
rnar
di di
scus
sed i
n G
iimpe
l, Zur
Inte
rpre
tatio
n der
Tonu
s-D
efin
ition
, 45-4
6.
31Lu
cida
rium
, 11, 4
,248
, pp.
516
-17.
32
See E
ugen
e Nar
mou
r, Be
yond
Sche
nker
ism: T
he N
eed f
orA
ltern
ativ
es in
M
usic
Ana
lysis
(Chi
cago
: Uni
vers
ity of
Chi
cago
Pres
s, 19
77) e
sp. 1
22-6
6.
tise,
Mar
chet
to dr
ives
the p
oint
hom
e aga
in by
stat
ing t
hat "
we
say
the
sam
e of a
ll ot
her m
odes
; con
cern
ing i
nter
rupt
ions
of
othe
r spe
cies
, we d
o not
inte
nd [t
o say
] any
thin
g else
[her
e] ex
- ce
pt th
at th
ey ca
n be p
lace
d in
auth
entic
and p
laga
l mod
es ex
- ce
pt in
the c
ase o
f[an
inte
rrup
tion]
that
cons
ists o
f a si
ngle
inte
r-
val [
i.e.,
a dir
ect le
ap] a
s we h
ave [
alre
ady]
said
" (m
y ita
lics)
.31
Mar
chet
to's T
heor
y of I
nter
rupt
ions
, and I
ssue
s in M
oder
n M
usic
The
ory
Tow
ard t
he ou
tset
of th
is st
udy,
I sa
id th
at M
arch
etto
's ap-
pr
oach
to m
elod
ic an
alys
is see
ms q
uite
mod
ern.
As o
ne g
rap-
pl
es w
ith h
is ac
coun
t of i
nter
rupt
ions
, one
enc
ount
ers is
sues
th
at ar
e cur
rent
ly al
ive i
n m
usic
theo
ry. I
hav
e alr
eady
poin
ted
out t
hat M
arch
etto
is co
ncer
ned w
ith co
nnec
tions
betw
een l
o-
cal,
fore
grou
nd ev
ents
and
glob
al, b
ackg
roun
d var
iabl
es in
a
piec
e. T
he an
alyt
ical
tech
niqu
e im
plic
it in M
arch
etto
's acc
ount
of
inte
rrup
tions
proc
eeds
from
fore
grou
nd to
bac
kgro
und.
To
use t
erm
s of t
he m
oder
n the
orist
Eug
ene N
arm
our,
Mar
chet
- to
's an
alyt
ic pr
oced
ure i
s one
of "
asce
nt,"
that
is, a
n an
alyt
ic
prog
ress
ion "
from
botto
m to
top.
" In
this
rega
rd, M
arch
etto
re
sem
bles
such
mod
ern t
heor
ists a
s Leo
nard
Mey
er an
d Nar
- m
our,
him
self,
who
sim
ilarl
y pro
ceed
from
fore
grou
nd to
bac
k-
grou
nd, th
at is,
from
indi
vidu
al to
nes t
o lar
ger s
pans
, in co
ntra
st
with
Sche
nker
ians
, who
, acc
ordi
ng to
Nar
mou
r, pr
ocee
d fro
m
back
grou
nd to
for
egro
und i
n th
eir a
pplic
atio
n of t
he U
rsat
z m
odel
.32
Mar
chet
to's i
nter
est in
nar
row
mel
odie
s her
e can
be tr
aced
as fa
r bac
k as t
he
begi
nnin
g of t
he el
even
th ce
ntur
y, w
hen
Bern
o of R
eich
enau
disc
usse
d que
s-
tions
that
arise
from
this
situa
tion (
Ger
bert
, ed.
, Scr
ipto
res E
ccle
siast
ici 2:
60a,
an
d th
e To
nale
Sanc
ti Be
rnar
di di
scus
sed i
n G
iimpe
l, Zur
Inte
rpre
tatio
n der
Tonu
s-D
efin
ition
, 45-4
6.
31Lu
cida
rium
, 11, 4
,248
, pp.
516
-17.
32
See E
ugen
e Nar
mou
r, Be
yond
Sche
nker
ism: T
he N
eed f
orA
ltern
ativ
es in
M
usic
Ana
lysis
(Chi
cago
: Uni
vers
ity of
Chi
cago
Pres
s, 19
77) e
sp. 1
22-6
6.
tise,
Mar
chet
to dr
ives
the p
oint
hom
e aga
in by
stat
ing t
hat "
we
say
the
sam
e of a
ll ot
her m
odes
; con
cern
ing i
nter
rupt
ions
of
othe
r spe
cies
, we d
o not
inte
nd [t
o say
] any
thin
g else
[her
e] ex
- ce
pt th
at th
ey ca
n be p
lace
d in
auth
entic
and p
laga
l mod
es ex
- ce
pt in
the c
ase o
f[an
inte
rrup
tion]
that
cons
ists o
f a si
ngle
inte
r-
val [
i.e.,
a dir
ect le
ap] a
s we h
ave [
alre
ady]
said
" (m
y ita
lics)
.31
Mar
chet
to's T
heor
y of I
nter
rupt
ions
, and I
ssue
s in M
oder
n M
usic
The
ory
Tow
ard t
he ou
tset
of th
is st
udy,
I sa
id th
at M
arch
etto
's ap-
pr
oach
to m
elod
ic an
alys
is see
ms q
uite
mod
ern.
As o
ne g
rap-
pl
es w
ith h
is ac
coun
t of i
nter
rupt
ions
, one
enc
ount
ers is
sues
th
at ar
e cur
rent
ly al
ive i
n m
usic
theo
ry. I
hav
e alr
eady
poin
ted
out t
hat M
arch
etto
is co
ncer
ned w
ith co
nnec
tions
betw
een l
o-
cal,
fore
grou
nd ev
ents
and
glob
al, b
ackg
roun
d var
iabl
es in
a
piec
e. T
he an
alyt
ical
tech
niqu
e im
plic
it in M
arch
etto
's acc
ount
of
inte
rrup
tions
proc
eeds
from
fore
grou
nd to
bac
kgro
und.
To
use t
erm
s of t
he m
oder
n the
orist
Eug
ene N
arm
our,
Mar
chet
- to
's an
alyt
ic pr
oced
ure i
s one
of "
asce
nt,"
that
is, a
n an
alyt
ic
prog
ress
ion "
from
botto
m to
top.
" In
this
rega
rd, M
arch
etto
re
sem
bles
such
mod
ern t
heor
ists a
s Leo
nard
Mey
er an
d Nar
- m
our,
him
self,
who
sim
ilarl
y pro
ceed
from
fore
grou
nd to
bac
k-
grou
nd, th
at is,
from
indi
vidu
al to
nes t
o lar
ger s
pans
, in co
ntra
st
with
Sche
nker
ians
, who
, acc
ordi
ng to
Nar
mou
r, pr
ocee
d fro
m
back
grou
nd to
for
egro
und i
n th
eir a
pplic
atio
n of t
he U
rsat
z m
odel
.32
Mar
chet
to's i
nter
est in
nar
row
mel
odie
s her
e can
be tr
aced
as fa
r bac
k as t
he
begi
nnin
g of t
he el
even
th ce
ntur
y, w
hen
Bern
o of R
eich
enau
disc
usse
d que
s-
tions
that
arise
from
this
situa
tion (
Ger
bert
, ed.
, Scr
ipto
res E
ccle
siast
ici 2:
60a,
an
d th
e To
nale
Sanc
ti Be
rnar
di di
scus
sed i
n G
iimpe
l, Zur
Inte
rpre
tatio
n der
Tonu
s-D
efin
ition
, 45-4
6.
31Lu
cida
rium
, 11, 4
,248
, pp.
516
-17.
32
See E
ugen
e Nar
mou
r, Be
yond
Sche
nker
ism: T
he N
eed f
orA
ltern
ativ
es in
M
usic
Ana
lysis
(Chi
cago
: Uni
vers
ity of
Chi
cago
Pres
s, 19
77) e
sp. 1
22-6
6.
tise,
Mar
chet
to dr
ives
the p
oint
hom
e aga
in by
stat
ing t
hat "
we
say
the
sam
e of a
ll ot
her m
odes
; con
cern
ing i
nter
rupt
ions
of
othe
r spe
cies
, we d
o not
inte
nd [t
o say
] any
thin
g else
[her
e] ex
- ce
pt th
at th
ey ca
n be p
lace
d in
auth
entic
and p
laga
l mod
es ex
- ce
pt in
the c
ase o
f[an
inte
rrup
tion]
that
cons
ists o
f a si
ngle
inte
r-
val [
i.e.,
a dir
ect le
ap] a
s we h
ave [
alre
ady]
said
" (m
y ita
lics)
.31
Mar
chet
to's T
heor
y of I
nter
rupt
ions
, and I
ssue
s in M
oder
n M
usic
The
ory
Tow
ard t
he ou
tset
of th
is st
udy,
I sa
id th
at M
arch
etto
's ap-
pr
oach
to m
elod
ic an
alys
is see
ms q
uite
mod
ern.
As o
ne g
rap-
pl
es w
ith h
is ac
coun
t of i
nter
rupt
ions
, one
enc
ount
ers is
sues
th
at ar
e cur
rent
ly al
ive i
n m
usic
theo
ry. I
hav
e alr
eady
poin
ted
out t
hat M
arch
etto
is co
ncer
ned w
ith co
nnec
tions
betw
een l
o-
cal,
fore
grou
nd ev
ents
and
glob
al, b
ackg
roun
d var
iabl
es in
a
piec
e. T
he an
alyt
ical
tech
niqu
e im
plic
it in M
arch
etto
's acc
ount
of
inte
rrup
tions
proc
eeds
from
fore
grou
nd to
bac
kgro
und.
To
use t
erm
s of t
he m
oder
n the
orist
Eug
ene N
arm
our,
Mar
chet
- to
's an
alyt
ic pr
oced
ure i
s one
of "
asce
nt,"
that
is, a
n an
alyt
ic
prog
ress
ion "
from
botto
m to
top.
" In
this
rega
rd, M
arch
etto
re
sem
bles
such
mod
ern t
heor
ists a
s Leo
nard
Mey
er an
d Nar
- m
our,
him
self,
who
sim
ilarl
y pro
ceed
from
fore
grou
nd to
bac
k-
grou
nd, th
at is,
from
indi
vidu
al to
nes t
o lar
ger s
pans
, in co
ntra
st
with
Sche
nker
ians
, who
, acc
ordi
ng to
Nar
mou
r, pr
ocee
d fro
m
back
grou
nd to
for
egro
und i
n th
eir a
pplic
atio
n of t
he U
rsat
z m
odel
.32
Mar
chet
to's i
nter
est in
nar
row
mel
odie
s her
e can
be tr
aced
as fa
r bac
k as t
he
begi
nnin
g of t
he el
even
th ce
ntur
y, w
hen
Bern
o of R
eich
enau
disc
usse
d que
s-
tions
that
arise
from
this
situa
tion (
Ger
bert
, ed.
, Scr
ipto
res E
ccle
siast
ici 2:
60a,
an
d th
e To
nale
Sanc
ti Be
rnar
di di
scus
sed i
n G
iimpe
l, Zur
Inte
rpre
tatio
n der
Tonu
s-D
efin
ition
, 45-4
6.
31Lu
cida
rium
, 11, 4
,248
, pp.
516
-17.
32
See E
ugen
e Nar
mou
r, Be
yond
Sche
nker
ism: T
he N
eed f
orA
ltern
ativ
es in
M
usic
Ana
lysis
(Chi
cago
: Uni
vers
ity of
Chi
cago
Pres
s, 19
77) e
sp. 1
22-6
6.
tise,
Mar
chet
to dr
ives
the p
oint
hom
e aga
in by
stat
ing t
hat "
we
say
the
sam
e of a
ll ot
her m
odes
; con
cern
ing i
nter
rupt
ions
of
othe
r spe
cies
, we d
o not
inte
nd [t
o say
] any
thin
g else
[her
e] ex
- ce
pt th
at th
ey ca
n be p
lace
d in
auth
entic
and p
laga
l mod
es ex
- ce
pt in
the c
ase o
f[an
inte
rrup
tion]
that
cons
ists o
f a si
ngle
inte
r-
val [
i.e.,
a dir
ect le
ap] a
s we h
ave [
alre
ady]
said
" (m
y ita
lics)
.31
Mar
chet
to's T
heor
y of I
nter
rupt
ions
, and I
ssue
s in M
oder
n M
usic
The
ory
Tow
ard t
he ou
tset
of th
is st
udy,
I sa
id th
at M
arch
etto
's ap-
pr
oach
to m
elod
ic an
alys
is see
ms q
uite
mod
ern.
As o
ne g
rap-
pl
es w
ith h
is ac
coun
t of i
nter
rupt
ions
, one
enc
ount
ers is
sues
th
at ar
e cur
rent
ly al
ive i
n m
usic
theo
ry. I
hav
e alr
eady
poin
ted
out t
hat M
arch
etto
is co
ncer
ned w
ith co
nnec
tions
betw
een l
o-
cal,
fore
grou
nd ev
ents
and
glob
al, b
ackg
roun
d var
iabl
es in
a
piec
e. T
he an
alyt
ical
tech
niqu
e im
plic
it in M
arch
etto
's acc
ount
of
inte
rrup
tions
proc
eeds
from
fore
grou
nd to
bac
kgro
und.
To
use t
erm
s of t
he m
oder
n the
orist
Eug
ene N
arm
our,
Mar
chet
- to
's an
alyt
ic pr
oced
ure i
s one
of "
asce
nt,"
that
is, a
n an
alyt
ic
prog
ress
ion "
from
botto
m to
top.
" In
this
rega
rd, M
arch
etto
re
sem
bles
such
mod
ern t
heor
ists a
s Leo
nard
Mey
er an
d Nar
- m
our,
him
self,
who
sim
ilarl
y pro
ceed
from
fore
grou
nd to
bac
k-
grou
nd, th
at is,
from
indi
vidu
al to
nes t
o lar
ger s
pans
, in co
ntra
st
with
Sche
nker
ians
, who
, acc
ordi
ng to
Nar
mou
r, pr
ocee
d fro
m
back
grou
nd to
for
egro
und i
n th
eir a
pplic
atio
n of t
he U
rsat
z m
odel
.32
Mar
chet
to's i
nter
est in
nar
row
mel
odie
s her
e can
be tr
aced
as fa
r bac
k as t
he
begi
nnin
g of t
he el
even
th ce
ntur
y, w
hen
Bern
o of R
eich
enau
disc
usse
d que
s-
tions
that
arise
from
this
situa
tion (
Ger
bert
, ed.
, Scr
ipto
res E
ccle
siast
ici 2:
60a,
an
d th
e To
nale
Sanc
ti Be
rnar
di di
scus
sed i
n G
iimpe
l, Zur
Inte
rpre
tatio
n der
Tonu
s-D
efin
ition
, 45-4
6.
31Lu
cida
rium
, 11, 4
,248
, pp.
516
-17.
32
See E
ugen
e Nar
mou
r, Be
yond
Sche
nker
ism: T
he N
eed f
orA
ltern
ativ
es in
M
usic
Ana
lysis
(Chi
cago
: Uni
vers
ity of
Chi
cago
Pres
s, 19
77) e
sp. 1
22-6
6.
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
132
Mus
ic Th
eory
Spec
trum
13
2 M
usic
Theo
ry Sp
ectr
um
132
Mus
ic Th
eory
Spec
trum
13
2 M
usic
Theo
ry Sp
ectr
um
132
Mus
ic Th
eory
Spec
trum
13
2 M
usic
Theo
ry Sp
ectr
um
In h
is ac
coun
t of i
nter
rupt
ions
, Mar
chet
to pr
ovid
es an
im-
plic
it fra
mew
ork w
ithin
whi
ch ev
ery n
ote o
f a m
elod
y cou
ld, t
o us
e a m
oder
n ter
m ag
ain,
be
"fun
ctio
naliz
ed."
Acc
ordi
ng to
th
e con
cept
s im
plic
it in
Mar
chet
to's p
assa
ge on
inte
rrup
tions
, ev
ery n
ote i
n a m
elod
y is e
ither
a sp
ecia
l not
e or a
non
-spe
cial
no
te (i
.e.,
an or
dina
ry no
te).
A sp
ecia
l not
e is e
ither
a mem
ber
of a
leap
or th
e hig
h- or
low
-poi
nt of
a m
elod
ic pr
ogre
ssio
n. Im
- pl
icit i
n M
arch
etto
's acc
ount
is th
e not
ion
of a
mel
ody a
s a se
- ri
es of
asce
nts a
nd de
scen
ts, a
n ide
a aki
n to t
he w
ides
prea
d me-
di
eval
conc
eptio
n of a
mel
ody
as a
pro
gres
sion p
er a
rsim
et
thes
im (b
y asc
ent a
nd de
scen
t). A
ccor
ding
to M
arch
etto
's for
- m
ulat
ion,
a m
elod
y can
be
segm
ente
d tan
gent
ially
"33 in
to a
s-
cent
s and
desc
ents
such
that
the l
ast, t
op no
te of
an as
cent
is th
e fir
st, t
op n
ote
of th
e fo
llow
ing d
esce
nt, a
nd th
e la
st, b
otto
m
note
of a
des
cent
is th
e fir
st, b
otto
m no
te o
f the
follo
win
g as-
ce
nt. S
uch a
form
ulat
ion o
f a m
elod
y as a
conn
ecte
d ser
ies o
f as
cent
s and
des
cent
s cor
resp
onds
to a
con
cept
ion o
f mel
odic
st
ruct
ure a
dvan
ced b
y a m
odem
anal
yst o
f non
-Wes
tern
mus
ic,
the l
ate M
iecz
ylsla
w K
olin
ski.3
4 In
his
acco
unt o
f int
erru
ptio
ns, M
arch
etto
seem
s to
have
so
ught
a un
iver
sal a
ppro
ach t
o m
elod
ic an
alys
is, al
beit
with
in
the t
radi
tion o
f med
ieva
l mus
ic th
eory
. Fro
m th
e poi
nt of
vie
w
of st
udie
s in th
e fou
ndat
ions
of m
usic
theo
ry, M
arch
etto
's for
- m
ulat
ion i
s par
simon
ious
and s
eem
ingl
y gen
eral
, for M
arch
et-
to's
anal
ytic
tech
niqu
e wou
ld be
com
patib
le w
ith an
y mus
ical
sy
stem
that
incl
uded
in it
s arr
ay of
con
cept
s the
idea
s of o
ne
tone
bei
ng h
ighe
r tha
n an
othe
r and
one
tone
bei
ng ju
st af
ter
33Th
e idea
of "
segm
ent"
used
here
is m
eant
to in
clud
e the
case
whe
re tw
o ad
jace
nt se
gmen
ts sh
are a
note
in co
mm
on, th
at is
, whe
re th
ey ha
ve a
"tan
gen-
tia
l" re
latio
nshi
p (cf
. Jay
Rah
n, A
The
ory fo
r All
Mus
ic [T
oron
to, U
nive
rsity
of
Tor
onto
Pres
s, 19
83] 5
9, on
tang
entia
l span
s).
34C
f. Kol
insk
i's "A
n Apa
che R
abbi
t Dan
ce S
ong C
ycle
as Su
ng by
the I
ro-
quoi
s," E
thno
mus
icol
ogy 1
6/3 (
1972
): 41
5-64
. Kol
insk
i in th
is an
d oth
er st
ud-
ies
goes
on
to c
ateg
oriz
e var
ious
conf
igur
atio
ns of
upw
ard a
nd d
ownw
ard
mov
emen
t.
In h
is ac
coun
t of i
nter
rupt
ions
, Mar
chet
to pr
ovid
es an
im-
plic
it fra
mew
ork w
ithin
whi
ch ev
ery n
ote o
f a m
elod
y cou
ld, t
o us
e a m
oder
n ter
m ag
ain,
be
"fun
ctio
naliz
ed."
Acc
ordi
ng to
th
e con
cept
s im
plic
it in
Mar
chet
to's p
assa
ge on
inte
rrup
tions
, ev
ery n
ote i
n a m
elod
y is e
ither
a sp
ecia
l not
e or a
non
-spe
cial
no
te (i
.e.,
an or
dina
ry no
te).
A sp
ecia
l not
e is e
ither
a mem
ber
of a
leap
or th
e hig
h- or
low
-poi
nt of
a m
elod
ic pr
ogre
ssio
n. Im
- pl
icit i
n M
arch
etto
's acc
ount
is th
e not
ion
of a
mel
ody a
s a se
- ri
es of
asce
nts a
nd de
scen
ts, a
n ide
a aki
n to t
he w
ides
prea
d me-
di
eval
conc
eptio
n of a
mel
ody
as a
pro
gres
sion p
er a
rsim
et
thes
im (b
y asc
ent a
nd de
scen
t). A
ccor
ding
to M
arch
etto
's for
- m
ulat
ion,
a m
elod
y can
be
segm
ente
d tan
gent
ially
"33 in
to a
s-
cent
s and
desc
ents
such
that
the l
ast, t
op no
te of
an as
cent
is th
e fir
st, t
op n
ote
of th
e fo
llow
ing d
esce
nt, a
nd th
e la
st, b
otto
m
note
of a
des
cent
is th
e fir
st, b
otto
m no
te o
f the
follo
win
g as-
ce
nt. S
uch a
form
ulat
ion o
f a m
elod
y as a
conn
ecte
d ser
ies o
f as
cent
s and
des
cent
s cor
resp
onds
to a
con
cept
ion o
f mel
odic
st
ruct
ure a
dvan
ced b
y a m
odem
anal
yst o
f non
-Wes
tern
mus
ic,
the l
ate M
iecz
ylsla
w K
olin
ski.3
4 In
his
acco
unt o
f int
erru
ptio
ns, M
arch
etto
seem
s to
have
so
ught
a un
iver
sal a
ppro
ach t
o m
elod
ic an
alys
is, al
beit
with
in
the t
radi
tion o
f med
ieva
l mus
ic th
eory
. Fro
m th
e poi
nt of
vie
w
of st
udie
s in th
e fou
ndat
ions
of m
usic
theo
ry, M
arch
etto
's for
- m
ulat
ion i
s par
simon
ious
and s
eem
ingl
y gen
eral
, for M
arch
et-
to's
anal
ytic
tech
niqu
e wou
ld be
com
patib
le w
ith an
y mus
ical
sy
stem
that
incl
uded
in it
s arr
ay of
con
cept
s the
idea
s of o
ne
tone
bei
ng h
ighe
r tha
n an
othe
r and
one
tone
bei
ng ju
st af
ter
33Th
e idea
of "
segm
ent"
used
here
is m
eant
to in
clud
e the
case
whe
re tw
o ad
jace
nt se
gmen
ts sh
are a
note
in co
mm
on, th
at is
, whe
re th
ey ha
ve a
"tan
gen-
tia
l" re
latio
nshi
p (cf
. Jay
Rah
n, A
The
ory fo
r All
Mus
ic [T
oron
to, U
nive
rsity
of
Tor
onto
Pres
s, 19
83] 5
9, on
tang
entia
l span
s).
34C
f. Kol
insk
i's "A
n Apa
che R
abbi
t Dan
ce S
ong C
ycle
as Su
ng by
the I
ro-
quoi
s," E
thno
mus
icol
ogy 1
6/3 (
1972
): 41
5-64
. Kol
insk
i in th
is an
d oth
er st
ud-
ies
goes
on
to c
ateg
oriz
e var
ious
conf
igur
atio
ns of
upw
ard a
nd d
ownw
ard
mov
emen
t.
In h
is ac
coun
t of i
nter
rupt
ions
, Mar
chet
to pr
ovid
es an
im-
plic
it fra
mew
ork w
ithin
whi
ch ev
ery n
ote o
f a m
elod
y cou
ld, t
o us
e a m
oder
n ter
m ag
ain,
be
"fun
ctio
naliz
ed."
Acc
ordi
ng to
th
e con
cept
s im
plic
it in
Mar
chet
to's p
assa
ge on
inte
rrup
tions
, ev
ery n
ote i
n a m
elod
y is e
ither
a sp
ecia
l not
e or a
non
-spe
cial
no
te (i
.e.,
an or
dina
ry no
te).
A sp
ecia
l not
e is e
ither
a mem
ber
of a
leap
or th
e hig
h- or
low
-poi
nt of
a m
elod
ic pr
ogre
ssio
n. Im
- pl
icit i
n M
arch
etto
's acc
ount
is th
e not
ion
of a
mel
ody a
s a se
- ri
es of
asce
nts a
nd de
scen
ts, a
n ide
a aki
n to t
he w
ides
prea
d me-
di
eval
conc
eptio
n of a
mel
ody
as a
pro
gres
sion p
er a
rsim
et
thes
im (b
y asc
ent a
nd de
scen
t). A
ccor
ding
to M
arch
etto
's for
- m
ulat
ion,
a m
elod
y can
be
segm
ente
d tan
gent
ially
"33 in
to a
s-
cent
s and
desc
ents
such
that
the l
ast, t
op no
te of
an as
cent
is th
e fir
st, t
op n
ote
of th
e fo
llow
ing d
esce
nt, a
nd th
e la
st, b
otto
m
note
of a
des
cent
is th
e fir
st, b
otto
m no
te o
f the
follo
win
g as-
ce
nt. S
uch a
form
ulat
ion o
f a m
elod
y as a
conn
ecte
d ser
ies o
f as
cent
s and
des
cent
s cor
resp
onds
to a
con
cept
ion o
f mel
odic
st
ruct
ure a
dvan
ced b
y a m
odem
anal
yst o
f non
-Wes
tern
mus
ic,
the l
ate M
iecz
ylsla
w K
olin
ski.3
4 In
his
acco
unt o
f int
erru
ptio
ns, M
arch
etto
seem
s to
have
so
ught
a un
iver
sal a
ppro
ach t
o m
elod
ic an
alys
is, al
beit
with
in
the t
radi
tion o
f med
ieva
l mus
ic th
eory
. Fro
m th
e poi
nt of
vie
w
of st
udie
s in th
e fou
ndat
ions
of m
usic
theo
ry, M
arch
etto
's for
- m
ulat
ion i
s par
simon
ious
and s
eem
ingl
y gen
eral
, for M
arch
et-
to's
anal
ytic
tech
niqu
e wou
ld be
com
patib
le w
ith an
y mus
ical
sy
stem
that
incl
uded
in it
s arr
ay of
con
cept
s the
idea
s of o
ne
tone
bei
ng h
ighe
r tha
n an
othe
r and
one
tone
bei
ng ju
st af
ter
33Th
e idea
of "
segm
ent"
used
here
is m
eant
to in
clud
e the
case
whe
re tw
o ad
jace
nt se
gmen
ts sh
are a
note
in co
mm
on, th
at is
, whe
re th
ey ha
ve a
"tan
gen-
tia
l" re
latio
nshi
p (cf
. Jay
Rah
n, A
The
ory fo
r All
Mus
ic [T
oron
to, U
nive
rsity
of
Tor
onto
Pres
s, 19
83] 5
9, on
tang
entia
l span
s).
34C
f. Kol
insk
i's "A
n Apa
che R
abbi
t Dan
ce S
ong C
ycle
as Su
ng by
the I
ro-
quoi
s," E
thno
mus
icol
ogy 1
6/3 (
1972
): 41
5-64
. Kol
insk
i in th
is an
d oth
er st
ud-
ies
goes
on
to c
ateg
oriz
e var
ious
conf
igur
atio
ns of
upw
ard a
nd d
ownw
ard
mov
emen
t.
In h
is ac
coun
t of i
nter
rupt
ions
, Mar
chet
to pr
ovid
es an
im-
plic
it fra
mew
ork w
ithin
whi
ch ev
ery n
ote o
f a m
elod
y cou
ld, t
o us
e a m
oder
n ter
m ag
ain,
be
"fun
ctio
naliz
ed."
Acc
ordi
ng to
th
e con
cept
s im
plic
it in
Mar
chet
to's p
assa
ge on
inte
rrup
tions
, ev
ery n
ote i
n a m
elod
y is e
ither
a sp
ecia
l not
e or a
non
-spe
cial
no
te (i
.e.,
an or
dina
ry no
te).
A sp
ecia
l not
e is e
ither
a mem
ber
of a
leap
or th
e hig
h- or
low
-poi
nt of
a m
elod
ic pr
ogre
ssio
n. Im
- pl
icit i
n M
arch
etto
's acc
ount
is th
e not
ion
of a
mel
ody a
s a se
- ri
es of
asce
nts a
nd de
scen
ts, a
n ide
a aki
n to t
he w
ides
prea
d me-
di
eval
conc
eptio
n of a
mel
ody
as a
pro
gres
sion p
er a
rsim
et
thes
im (b
y asc
ent a
nd de
scen
t). A
ccor
ding
to M
arch
etto
's for
- m
ulat
ion,
a m
elod
y can
be
segm
ente
d tan
gent
ially
"33 in
to a
s-
cent
s and
desc
ents
such
that
the l
ast, t
op no
te of
an as
cent
is th
e fir
st, t
op n
ote
of th
e fo
llow
ing d
esce
nt, a
nd th
e la
st, b
otto
m
note
of a
des
cent
is th
e fir
st, b
otto
m no
te o
f the
follo
win
g as-
ce
nt. S
uch a
form
ulat
ion o
f a m
elod
y as a
conn
ecte
d ser
ies o
f as
cent
s and
des
cent
s cor
resp
onds
to a
con
cept
ion o
f mel
odic
st
ruct
ure a
dvan
ced b
y a m
odem
anal
yst o
f non
-Wes
tern
mus
ic,
the l
ate M
iecz
ylsla
w K
olin
ski.3
4 In
his
acco
unt o
f int
erru
ptio
ns, M
arch
etto
seem
s to
have
so
ught
a un
iver
sal a
ppro
ach t
o m
elod
ic an
alys
is, al
beit
with
in
the t
radi
tion o
f med
ieva
l mus
ic th
eory
. Fro
m th
e poi
nt of
vie
w
of st
udie
s in th
e fou
ndat
ions
of m
usic
theo
ry, M
arch
etto
's for
- m
ulat
ion i
s par
simon
ious
and s
eem
ingl
y gen
eral
, for M
arch
et-
to's
anal
ytic
tech
niqu
e wou
ld be
com
patib
le w
ith an
y mus
ical
sy
stem
that
incl
uded
in it
s arr
ay of
con
cept
s the
idea
s of o
ne
tone
bei
ng h
ighe
r tha
n an
othe
r and
one
tone
bei
ng ju
st af
ter
33Th
e idea
of "
segm
ent"
used
here
is m
eant
to in
clud
e the
case
whe
re tw
o ad
jace
nt se
gmen
ts sh
are a
note
in co
mm
on, th
at is
, whe
re th
ey ha
ve a
"tan
gen-
tia
l" re
latio
nshi
p (cf
. Jay
Rah
n, A
The
ory fo
r All
Mus
ic [T
oron
to, U
nive
rsity
of
Tor
onto
Pres
s, 19
83] 5
9, on
tang
entia
l span
s).
34C
f. Kol
insk
i's "A
n Apa
che R
abbi
t Dan
ce S
ong C
ycle
as Su
ng by
the I
ro-
quoi
s," E
thno
mus
icol
ogy 1
6/3 (
1972
): 41
5-64
. Kol
insk
i in th
is an
d oth
er st
ud-
ies
goes
on
to c
ateg
oriz
e var
ious
conf
igur
atio
ns of
upw
ard a
nd d
ownw
ard
mov
emen
t.
In h
is ac
coun
t of i
nter
rupt
ions
, Mar
chet
to pr
ovid
es an
im-
plic
it fra
mew
ork w
ithin
whi
ch ev
ery n
ote o
f a m
elod
y cou
ld, t
o us
e a m
oder
n ter
m ag
ain,
be
"fun
ctio
naliz
ed."
Acc
ordi
ng to
th
e con
cept
s im
plic
it in
Mar
chet
to's p
assa
ge on
inte
rrup
tions
, ev
ery n
ote i
n a m
elod
y is e
ither
a sp
ecia
l not
e or a
non
-spe
cial
no
te (i
.e.,
an or
dina
ry no
te).
A sp
ecia
l not
e is e
ither
a mem
ber
of a
leap
or th
e hig
h- or
low
-poi
nt of
a m
elod
ic pr
ogre
ssio
n. Im
- pl
icit i
n M
arch
etto
's acc
ount
is th
e not
ion
of a
mel
ody a
s a se
- ri
es of
asce
nts a
nd de
scen
ts, a
n ide
a aki
n to t
he w
ides
prea
d me-
di
eval
conc
eptio
n of a
mel
ody
as a
pro
gres
sion p
er a
rsim
et
thes
im (b
y asc
ent a
nd de
scen
t). A
ccor
ding
to M
arch
etto
's for
- m
ulat
ion,
a m
elod
y can
be
segm
ente
d tan
gent
ially
"33 in
to a
s-
cent
s and
desc
ents
such
that
the l
ast, t
op no
te of
an as
cent
is th
e fir
st, t
op n
ote
of th
e fo
llow
ing d
esce
nt, a
nd th
e la
st, b
otto
m
note
of a
des
cent
is th
e fir
st, b
otto
m no
te o
f the
follo
win
g as-
ce
nt. S
uch a
form
ulat
ion o
f a m
elod
y as a
conn
ecte
d ser
ies o
f as
cent
s and
des
cent
s cor
resp
onds
to a
con
cept
ion o
f mel
odic
st
ruct
ure a
dvan
ced b
y a m
odem
anal
yst o
f non
-Wes
tern
mus
ic,
the l
ate M
iecz
ylsla
w K
olin
ski.3
4 In
his
acco
unt o
f int
erru
ptio
ns, M
arch
etto
seem
s to
have
so
ught
a un
iver
sal a
ppro
ach t
o m
elod
ic an
alys
is, al
beit
with
in
the t
radi
tion o
f med
ieva
l mus
ic th
eory
. Fro
m th
e poi
nt of
vie
w
of st
udie
s in th
e fou
ndat
ions
of m
usic
theo
ry, M
arch
etto
's for
- m
ulat
ion i
s par
simon
ious
and s
eem
ingl
y gen
eral
, for M
arch
et-
to's
anal
ytic
tech
niqu
e wou
ld be
com
patib
le w
ith an
y mus
ical
sy
stem
that
incl
uded
in it
s arr
ay of
con
cept
s the
idea
s of o
ne
tone
bei
ng h
ighe
r tha
n an
othe
r and
one
tone
bei
ng ju
st af
ter
33Th
e idea
of "
segm
ent"
used
here
is m
eant
to in
clud
e the
case
whe
re tw
o ad
jace
nt se
gmen
ts sh
are a
note
in co
mm
on, th
at is
, whe
re th
ey ha
ve a
"tan
gen-
tia
l" re
latio
nshi
p (cf
. Jay
Rah
n, A
The
ory fo
r All
Mus
ic [T
oron
to, U
nive
rsity
of
Tor
onto
Pres
s, 19
83] 5
9, on
tang
entia
l span
s).
34C
f. Kol
insk
i's "A
n Apa
che R
abbi
t Dan
ce S
ong C
ycle
as Su
ng by
the I
ro-
quoi
s," E
thno
mus
icol
ogy 1
6/3 (
1972
): 41
5-64
. Kol
insk
i in th
is an
d oth
er st
ud-
ies
goes
on
to c
ateg
oriz
e var
ious
conf
igur
atio
ns of
upw
ard a
nd d
ownw
ard
mov
emen
t.
In h
is ac
coun
t of i
nter
rupt
ions
, Mar
chet
to pr
ovid
es an
im-
plic
it fra
mew
ork w
ithin
whi
ch ev
ery n
ote o
f a m
elod
y cou
ld, t
o us
e a m
oder
n ter
m ag
ain,
be
"fun
ctio
naliz
ed."
Acc
ordi
ng to
th
e con
cept
s im
plic
it in
Mar
chet
to's p
assa
ge on
inte
rrup
tions
, ev
ery n
ote i
n a m
elod
y is e
ither
a sp
ecia
l not
e or a
non
-spe
cial
no
te (i
.e.,
an or
dina
ry no
te).
A sp
ecia
l not
e is e
ither
a mem
ber
of a
leap
or th
e hig
h- or
low
-poi
nt of
a m
elod
ic pr
ogre
ssio
n. Im
- pl
icit i
n M
arch
etto
's acc
ount
is th
e not
ion
of a
mel
ody a
s a se
- ri
es of
asce
nts a
nd de
scen
ts, a
n ide
a aki
n to t
he w
ides
prea
d me-
di
eval
conc
eptio
n of a
mel
ody
as a
pro
gres
sion p
er a
rsim
et
thes
im (b
y asc
ent a
nd de
scen
t). A
ccor
ding
to M
arch
etto
's for
- m
ulat
ion,
a m
elod
y can
be
segm
ente
d tan
gent
ially
"33 in
to a
s-
cent
s and
desc
ents
such
that
the l
ast, t
op no
te of
an as
cent
is th
e fir
st, t
op n
ote
of th
e fo
llow
ing d
esce
nt, a
nd th
e la
st, b
otto
m
note
of a
des
cent
is th
e fir
st, b
otto
m no
te o
f the
follo
win
g as-
ce
nt. S
uch a
form
ulat
ion o
f a m
elod
y as a
conn
ecte
d ser
ies o
f as
cent
s and
des
cent
s cor
resp
onds
to a
con
cept
ion o
f mel
odic
st
ruct
ure a
dvan
ced b
y a m
odem
anal
yst o
f non
-Wes
tern
mus
ic,
the l
ate M
iecz
ylsla
w K
olin
ski.3
4 In
his
acco
unt o
f int
erru
ptio
ns, M
arch
etto
seem
s to
have
so
ught
a un
iver
sal a
ppro
ach t
o m
elod
ic an
alys
is, al
beit
with
in
the t
radi
tion o
f med
ieva
l mus
ic th
eory
. Fro
m th
e poi
nt of
vie
w
of st
udie
s in th
e fou
ndat
ions
of m
usic
theo
ry, M
arch
etto
's for
- m
ulat
ion i
s par
simon
ious
and s
eem
ingl
y gen
eral
, for M
arch
et-
to's
anal
ytic
tech
niqu
e wou
ld be
com
patib
le w
ith an
y mus
ical
sy
stem
that
incl
uded
in it
s arr
ay of
con
cept
s the
idea
s of o
ne
tone
bei
ng h
ighe
r tha
n an
othe
r and
one
tone
bei
ng ju
st af
ter
33Th
e idea
of "
segm
ent"
used
here
is m
eant
to in
clud
e the
case
whe
re tw
o ad
jace
nt se
gmen
ts sh
are a
note
in co
mm
on, th
at is
, whe
re th
ey ha
ve a
"tan
gen-
tia
l" re
latio
nshi
p (cf
. Jay
Rah
n, A
The
ory fo
r All
Mus
ic [T
oron
to, U
nive
rsity
of
Tor
onto
Pres
s, 19
83] 5
9, on
tang
entia
l span
s).
34C
f. Kol
insk
i's "A
n Apa
che R
abbi
t Dan
ce S
ong C
ycle
as Su
ng by
the I
ro-
quoi
s," E
thno
mus
icol
ogy 1
6/3 (
1972
): 41
5-64
. Kol
insk
i in th
is an
d oth
er st
ud-
ies
goes
on
to c
ateg
oriz
e var
ious
conf
igur
atio
ns of
upw
ard a
nd d
ownw
ard
mov
emen
t.
anot
her a
s wel
l as t
he n
otio
ns of
qua
ntiz
ing p
itch-
spac
e in sc
ale
degr
ees a
nd gr
oupi
ng co
nsec
utiv
e ton
es to
form
a sin
gle l
ine.
35
In a
mod
ern
form
ulat
ion,
one
coul
d re
gard
ever
y sp
ecia
l no
te as
a ru
ptur
e of "
ordi
nary
"36 st
epw
ise m
otio
n in
a giv
en di
- re
ctio
n. N
otes
that
wer
e "no
n-sp
ecia
l" or
"or
dina
ry" c
ould
be
unde
rsto
od as
"pa
ssin
g not
es,"
not
es th
at "p
ass b
etw
een"
spe-
ci
al no
tes.
From
the p
oint
of v
iew
of o
ne m
oder
n app
roac
h to
anal
ysis,
37 a se
ries
of p
assin
g not
es is
repl
ete w
ith is
omor
phic
re
latio
ns in
the s
ense
that
ever
y not
e in
such
a se
ries
that
is ne
xt
to a
noth
er in
tim
e is a
lso n
ext t
o th
e oth
er in
pitc
h. In
a ri
sing
pass
age o
f pas
sing n
otes
, a no
te th
at is
just
afte
r ano
ther
is al
so
just
high
er th
an th
e oth
er, a
nd in
a de
scen
ding
segm
ent o
f pas
s-
ing n
otes
, a n
ote t
hat i
s jus
t afte
r ano
ther
is ju
st lo
wer
than
the
othe
r. If
a no
te is
a hi
gh- o
r low
-poi
nt of
a ri
se or
fall a
nd/o
r is a
mem
ber o
f a le
ap, t
his i
som
orph
ism of
pitc
h an
d tim
e is b
ro-
ken,
and
the
note
is "
spec
ial."
One
can
say
that
Mar
chet
to's
inte
rpre
tatio
n of s
peci
al no
tes a
s ori
entin
g ton
es re
pres
ents
an
anal
ytic
"com
pens
atio
n," f
or n
otes
that
repr
esen
t a fr
actu
ring
of
the r
elat
ions
in a
step
wise
prog
ress
ion a
re ac
cord
ed a c
entr
al
posit
ion i
n th
e mod
al hi
erar
chy;
such
note
s are
gran
ted a
"co
n-
sola
tion p
rize
," as
it w
ere.
Attr
ibut
ing t
o su
ch no
tes a
cent
ral
posit
ion c
an be
und
erst
ood a
s acc
ordi
ng th
em th
e sta
tus o
f tem
- po
rary
poin
ts of
reso
lutio
n bet
wee
n whi
ch th
ere m
ight
be p
ass-
in
g not
es, t
hat is
, not
es w
hich
"mer
ely p
ass."
Such
an in
terp
re-
tatio
n of
the
conn
ectio
n be
twee
n sp
ecia
l not
es a
nd o
rien
ting
35E.
g., th
e sys
tem
of R
ahn,
A T
heor
y for A
ll M
usic
, 44-
92.
On t
he d
efin
i- tio
n of i
ndiv
idua
l line
s, se
e Jay
Rah
n, "W
here
is th
e Mel
ody?
" In
Theo
ry O
nly,
6/
6 (19
82):
3-19
. Fo
r a sy
stem
atic
func
tiona
lizat
ion o
f ori
entin
g ton
es in
mod
al
mus
ic, c
f. Ja
y Rah
n's "
Con
stru
cts fo
r Mod
ality
, 130
0-15
50,"
Can
adia
n Ass
o-
ciat
ion o
f Uni
vers
ity Sc
hool
s of M
usic
Jour
nal 8
/2 (1
978)
: 5-3
9, a
nd hi
s stu
dy
"Ock
eghe
m's
Thre
e-Se
ctio
n Mot
et S
alve
Reg
ina:
Pro
blem
s in
Coo
rdin
atin
g Pi
tch a
nd T
ime C
onst
ruct
s," M
usic
The
ory S
pect
rum
3:11
7-31
. 36
In a s
truc
tura
l, not
a fr
eque
ncy-
base
d, se
nse o
f "or
dina
ry" (
see a
bove
). 37
E.g.
, as r
epre
sent
ed by
the f
orm
alist
ic ac
coun
t of R
ahn,
"W
here
is th
e M
elod
y?"
anot
her a
s wel
l as t
he n
otio
ns of
qua
ntiz
ing p
itch-
spac
e in sc
ale
degr
ees a
nd gr
oupi
ng co
nsec
utiv
e ton
es to
form
a sin
gle l
ine.
35
In a
mod
ern
form
ulat
ion,
one
coul
d re
gard
ever
y sp
ecia
l no
te as
a ru
ptur
e of "
ordi
nary
"36 st
epw
ise m
otio
n in
a giv
en di
- re
ctio
n. N
otes
that
wer
e "no
n-sp
ecia
l" or
"or
dina
ry" c
ould
be
unde
rsto
od as
"pa
ssin
g not
es,"
not
es th
at "p
ass b
etw
een"
spe-
ci
al no
tes.
From
the p
oint
of v
iew
of o
ne m
oder
n app
roac
h to
anal
ysis,
37 a se
ries
of p
assin
g not
es is
repl
ete w
ith is
omor
phic
re
latio
ns in
the s
ense
that
ever
y not
e in
such
a se
ries
that
is ne
xt
to a
noth
er in
tim
e is a
lso n
ext t
o th
e oth
er in
pitc
h. In
a ri
sing
pass
age o
f pas
sing n
otes
, a no
te th
at is
just
afte
r ano
ther
is al
so
just
high
er th
an th
e oth
er, a
nd in
a de
scen
ding
segm
ent o
f pas
s-
ing n
otes
, a n
ote t
hat i
s jus
t afte
r ano
ther
is ju
st lo
wer
than
the
othe
r. If
a no
te is
a hi
gh- o
r low
-poi
nt of
a ri
se or
fall a
nd/o
r is a
mem
ber o
f a le
ap, t
his i
som
orph
ism of
pitc
h an
d tim
e is b
ro-
ken,
and
the
note
is "
spec
ial."
One
can
say
that
Mar
chet
to's
inte
rpre
tatio
n of s
peci
al no
tes a
s ori
entin
g ton
es re
pres
ents
an
anal
ytic
"com
pens
atio
n," f
or n
otes
that
repr
esen
t a fr
actu
ring
of
the r
elat
ions
in a
step
wise
prog
ress
ion a
re ac
cord
ed a c
entr
al
posit
ion i
n th
e mod
al hi
erar
chy;
such
note
s are
gran
ted a
"co
n-
sola
tion p
rize
," as
it w
ere.
Attr
ibut
ing t
o su
ch no
tes a
cent
ral
posit
ion c
an be
und
erst
ood a
s acc
ordi
ng th
em th
e sta
tus o
f tem
- po
rary
poin
ts of
reso
lutio
n bet
wee
n whi
ch th
ere m
ight
be p
ass-
in
g not
es, t
hat is
, not
es w
hich
"mer
ely p
ass."
Such
an in
terp
re-
tatio
n of
the
conn
ectio
n be
twee
n sp
ecia
l not
es a
nd o
rien
ting
35E.
g., th
e sys
tem
of R
ahn,
A T
heor
y for A
ll M
usic
, 44-
92.
On t
he d
efin
i- tio
n of i
ndiv
idua
l line
s, se
e Jay
Rah
n, "W
here
is th
e Mel
ody?
" In
Theo
ry O
nly,
6/
6 (19
82):
3-19
. Fo
r a sy
stem
atic
func
tiona
lizat
ion o
f ori
entin
g ton
es in
mod
al
mus
ic, c
f. Ja
y Rah
n's "
Con
stru
cts fo
r Mod
ality
, 130
0-15
50,"
Can
adia
n Ass
o-
ciat
ion o
f Uni
vers
ity Sc
hool
s of M
usic
Jour
nal 8
/2 (1
978)
: 5-3
9, a
nd hi
s stu
dy
"Ock
eghe
m's
Thre
e-Se
ctio
n Mot
et S
alve
Reg
ina:
Pro
blem
s in
Coo
rdin
atin
g Pi
tch a
nd T
ime C
onst
ruct
s," M
usic
The
ory S
pect
rum
3:11
7-31
. 36
In a s
truc
tura
l, not
a fr
eque
ncy-
base
d, se
nse o
f "or
dina
ry" (
see a
bove
). 37
E.g.
, as r
epre
sent
ed by
the f
orm
alist
ic ac
coun
t of R
ahn,
"W
here
is th
e M
elod
y?"
anot
her a
s wel
l as t
he n
otio
ns of
qua
ntiz
ing p
itch-
spac
e in sc
ale
degr
ees a
nd gr
oupi
ng co
nsec
utiv
e ton
es to
form
a sin
gle l
ine.
35
In a
mod
ern
form
ulat
ion,
one
coul
d re
gard
ever
y sp
ecia
l no
te as
a ru
ptur
e of "
ordi
nary
"36 st
epw
ise m
otio
n in
a giv
en di
- re
ctio
n. N
otes
that
wer
e "no
n-sp
ecia
l" or
"or
dina
ry" c
ould
be
unde
rsto
od as
"pa
ssin
g not
es,"
not
es th
at "p
ass b
etw
een"
spe-
ci
al no
tes.
From
the p
oint
of v
iew
of o
ne m
oder
n app
roac
h to
anal
ysis,
37 a se
ries
of p
assin
g not
es is
repl
ete w
ith is
omor
phic
re
latio
ns in
the s
ense
that
ever
y not
e in
such
a se
ries
that
is ne
xt
to a
noth
er in
tim
e is a
lso n
ext t
o th
e oth
er in
pitc
h. In
a ri
sing
pass
age o
f pas
sing n
otes
, a no
te th
at is
just
afte
r ano
ther
is al
so
just
high
er th
an th
e oth
er, a
nd in
a de
scen
ding
segm
ent o
f pas
s-
ing n
otes
, a n
ote t
hat i
s jus
t afte
r ano
ther
is ju
st lo
wer
than
the
othe
r. If
a no
te is
a hi
gh- o
r low
-poi
nt of
a ri
se or
fall a
nd/o
r is a
mem
ber o
f a le
ap, t
his i
som
orph
ism of
pitc
h an
d tim
e is b
ro-
ken,
and
the
note
is "
spec
ial."
One
can
say
that
Mar
chet
to's
inte
rpre
tatio
n of s
peci
al no
tes a
s ori
entin
g ton
es re
pres
ents
an
anal
ytic
"com
pens
atio
n," f
or n
otes
that
repr
esen
t a fr
actu
ring
of
the r
elat
ions
in a
step
wise
prog
ress
ion a
re ac
cord
ed a c
entr
al
posit
ion i
n th
e mod
al hi
erar
chy;
such
note
s are
gran
ted a
"co
n-
sola
tion p
rize
," as
it w
ere.
Attr
ibut
ing t
o su
ch no
tes a
cent
ral
posit
ion c
an be
und
erst
ood a
s acc
ordi
ng th
em th
e sta
tus o
f tem
- po
rary
poin
ts of
reso
lutio
n bet
wee
n whi
ch th
ere m
ight
be p
ass-
in
g not
es, t
hat is
, not
es w
hich
"mer
ely p
ass."
Such
an in
terp
re-
tatio
n of
the
conn
ectio
n be
twee
n sp
ecia
l not
es a
nd o
rien
ting
35E.
g., th
e sys
tem
of R
ahn,
A T
heor
y for A
ll M
usic
, 44-
92.
On t
he d
efin
i- tio
n of i
ndiv
idua
l line
s, se
e Jay
Rah
n, "W
here
is th
e Mel
ody?
" In
Theo
ry O
nly,
6/
6 (19
82):
3-19
. Fo
r a sy
stem
atic
func
tiona
lizat
ion o
f ori
entin
g ton
es in
mod
al
mus
ic, c
f. Ja
y Rah
n's "
Con
stru
cts fo
r Mod
ality
, 130
0-15
50,"
Can
adia
n Ass
o-
ciat
ion o
f Uni
vers
ity Sc
hool
s of M
usic
Jour
nal 8
/2 (1
978)
: 5-3
9, a
nd hi
s stu
dy
"Ock
eghe
m's
Thre
e-Se
ctio
n Mot
et S
alve
Reg
ina:
Pro
blem
s in
Coo
rdin
atin
g Pi
tch a
nd T
ime C
onst
ruct
s," M
usic
The
ory S
pect
rum
3:11
7-31
. 36
In a s
truc
tura
l, not
a fr
eque
ncy-
base
d, se
nse o
f "or
dina
ry" (
see a
bove
). 37
E.g.
, as r
epre
sent
ed by
the f
orm
alist
ic ac
coun
t of R
ahn,
"W
here
is th
e M
elod
y?"
anot
her a
s wel
l as t
he n
otio
ns of
qua
ntiz
ing p
itch-
spac
e in sc
ale
degr
ees a
nd gr
oupi
ng co
nsec
utiv
e ton
es to
form
a sin
gle l
ine.
35
In a
mod
ern
form
ulat
ion,
one
coul
d re
gard
ever
y sp
ecia
l no
te as
a ru
ptur
e of "
ordi
nary
"36 st
epw
ise m
otio
n in
a giv
en di
- re
ctio
n. N
otes
that
wer
e "no
n-sp
ecia
l" or
"or
dina
ry" c
ould
be
unde
rsto
od as
"pa
ssin
g not
es,"
not
es th
at "p
ass b
etw
een"
spe-
ci
al no
tes.
From
the p
oint
of v
iew
of o
ne m
oder
n app
roac
h to
anal
ysis,
37 a se
ries
of p
assin
g not
es is
repl
ete w
ith is
omor
phic
re
latio
ns in
the s
ense
that
ever
y not
e in
such
a se
ries
that
is ne
xt
to a
noth
er in
tim
e is a
lso n
ext t
o th
e oth
er in
pitc
h. In
a ri
sing
pass
age o
f pas
sing n
otes
, a no
te th
at is
just
afte
r ano
ther
is al
so
just
high
er th
an th
e oth
er, a
nd in
a de
scen
ding
segm
ent o
f pas
s-
ing n
otes
, a n
ote t
hat i
s jus
t afte
r ano
ther
is ju
st lo
wer
than
the
othe
r. If
a no
te is
a hi
gh- o
r low
-poi
nt of
a ri
se or
fall a
nd/o
r is a
mem
ber o
f a le
ap, t
his i
som
orph
ism of
pitc
h an
d tim
e is b
ro-
ken,
and
the
note
is "
spec
ial."
One
can
say
that
Mar
chet
to's
inte
rpre
tatio
n of s
peci
al no
tes a
s ori
entin
g ton
es re
pres
ents
an
anal
ytic
"com
pens
atio
n," f
or n
otes
that
repr
esen
t a fr
actu
ring
of
the r
elat
ions
in a
step
wise
prog
ress
ion a
re ac
cord
ed a c
entr
al
posit
ion i
n th
e mod
al hi
erar
chy;
such
note
s are
gran
ted a
"co
n-
sola
tion p
rize
," as
it w
ere.
Attr
ibut
ing t
o su
ch no
tes a
cent
ral
posit
ion c
an be
und
erst
ood a
s acc
ordi
ng th
em th
e sta
tus o
f tem
- po
rary
poin
ts of
reso
lutio
n bet
wee
n whi
ch th
ere m
ight
be p
ass-
in
g not
es, t
hat is
, not
es w
hich
"mer
ely p
ass."
Such
an in
terp
re-
tatio
n of
the
conn
ectio
n be
twee
n sp
ecia
l not
es a
nd o
rien
ting
35E.
g., th
e sys
tem
of R
ahn,
A T
heor
y for A
ll M
usic
, 44-
92.
On t
he d
efin
i- tio
n of i
ndiv
idua
l line
s, se
e Jay
Rah
n, "W
here
is th
e Mel
ody?
" In
Theo
ry O
nly,
6/
6 (19
82):
3-19
. Fo
r a sy
stem
atic
func
tiona
lizat
ion o
f ori
entin
g ton
es in
mod
al
mus
ic, c
f. Ja
y Rah
n's "
Con
stru
cts fo
r Mod
ality
, 130
0-15
50,"
Can
adia
n Ass
o-
ciat
ion o
f Uni
vers
ity Sc
hool
s of M
usic
Jour
nal 8
/2 (1
978)
: 5-3
9, a
nd hi
s stu
dy
"Ock
eghe
m's
Thre
e-Se
ctio
n Mot
et S
alve
Reg
ina:
Pro
blem
s in
Coo
rdin
atin
g Pi
tch a
nd T
ime C
onst
ruct
s," M
usic
The
ory S
pect
rum
3:11
7-31
. 36
In a s
truc
tura
l, not
a fr
eque
ncy-
base
d, se
nse o
f "or
dina
ry" (
see a
bove
). 37
E.g.
, as r
epre
sent
ed by
the f
orm
alist
ic ac
coun
t of R
ahn,
"W
here
is th
e M
elod
y?"
anot
her a
s wel
l as t
he n
otio
ns of
qua
ntiz
ing p
itch-
spac
e in sc
ale
degr
ees a
nd gr
oupi
ng co
nsec
utiv
e ton
es to
form
a sin
gle l
ine.
35
In a
mod
ern
form
ulat
ion,
one
coul
d re
gard
ever
y sp
ecia
l no
te as
a ru
ptur
e of "
ordi
nary
"36 st
epw
ise m
otio
n in
a giv
en di
- re
ctio
n. N
otes
that
wer
e "no
n-sp
ecia
l" or
"or
dina
ry" c
ould
be
unde
rsto
od as
"pa
ssin
g not
es,"
not
es th
at "p
ass b
etw
een"
spe-
ci
al no
tes.
From
the p
oint
of v
iew
of o
ne m
oder
n app
roac
h to
anal
ysis,
37 a se
ries
of p
assin
g not
es is
repl
ete w
ith is
omor
phic
re
latio
ns in
the s
ense
that
ever
y not
e in
such
a se
ries
that
is ne
xt
to a
noth
er in
tim
e is a
lso n
ext t
o th
e oth
er in
pitc
h. In
a ri
sing
pass
age o
f pas
sing n
otes
, a no
te th
at is
just
afte
r ano
ther
is al
so
just
high
er th
an th
e oth
er, a
nd in
a de
scen
ding
segm
ent o
f pas
s-
ing n
otes
, a n
ote t
hat i
s jus
t afte
r ano
ther
is ju
st lo
wer
than
the
othe
r. If
a no
te is
a hi
gh- o
r low
-poi
nt of
a ri
se or
fall a
nd/o
r is a
mem
ber o
f a le
ap, t
his i
som
orph
ism of
pitc
h an
d tim
e is b
ro-
ken,
and
the
note
is "
spec
ial."
One
can
say
that
Mar
chet
to's
inte
rpre
tatio
n of s
peci
al no
tes a
s ori
entin
g ton
es re
pres
ents
an
anal
ytic
"com
pens
atio
n," f
or n
otes
that
repr
esen
t a fr
actu
ring
of
the r
elat
ions
in a
step
wise
prog
ress
ion a
re ac
cord
ed a c
entr
al
posit
ion i
n th
e mod
al hi
erar
chy;
such
note
s are
gran
ted a
"co
n-
sola
tion p
rize
," as
it w
ere.
Attr
ibut
ing t
o su
ch no
tes a
cent
ral
posit
ion c
an be
und
erst
ood a
s acc
ordi
ng th
em th
e sta
tus o
f tem
- po
rary
poin
ts of
reso
lutio
n bet
wee
n whi
ch th
ere m
ight
be p
ass-
in
g not
es, t
hat is
, not
es w
hich
"mer
ely p
ass."
Such
an in
terp
re-
tatio
n of
the
conn
ectio
n be
twee
n sp
ecia
l not
es a
nd o
rien
ting
35E.
g., th
e sys
tem
of R
ahn,
A T
heor
y for A
ll M
usic
, 44-
92.
On t
he d
efin
i- tio
n of i
ndiv
idua
l line
s, se
e Jay
Rah
n, "W
here
is th
e Mel
ody?
" In
Theo
ry O
nly,
6/
6 (19
82):
3-19
. Fo
r a sy
stem
atic
func
tiona
lizat
ion o
f ori
entin
g ton
es in
mod
al
mus
ic, c
f. Ja
y Rah
n's "
Con
stru
cts fo
r Mod
ality
, 130
0-15
50,"
Can
adia
n Ass
o-
ciat
ion o
f Uni
vers
ity Sc
hool
s of M
usic
Jour
nal 8
/2 (1
978)
: 5-3
9, a
nd hi
s stu
dy
"Ock
eghe
m's
Thre
e-Se
ctio
n Mot
et S
alve
Reg
ina:
Pro
blem
s in
Coo
rdin
atin
g Pi
tch a
nd T
ime C
onst
ruct
s," M
usic
The
ory S
pect
rum
3:11
7-31
. 36
In a s
truc
tura
l, not
a fr
eque
ncy-
base
d, se
nse o
f "or
dina
ry" (
see a
bove
). 37
E.g.
, as r
epre
sent
ed by
the f
orm
alist
ic ac
coun
t of R
ahn,
"W
here
is th
e M
elod
y?"
anot
her a
s wel
l as t
he n
otio
ns of
qua
ntiz
ing p
itch-
spac
e in sc
ale
degr
ees a
nd gr
oupi
ng co
nsec
utiv
e ton
es to
form
a sin
gle l
ine.
35
In a
mod
ern
form
ulat
ion,
one
coul
d re
gard
ever
y sp
ecia
l no
te as
a ru
ptur
e of "
ordi
nary
"36 st
epw
ise m
otio
n in
a giv
en di
- re
ctio
n. N
otes
that
wer
e "no
n-sp
ecia
l" or
"or
dina
ry" c
ould
be
unde
rsto
od as
"pa
ssin
g not
es,"
not
es th
at "p
ass b
etw
een"
spe-
ci
al no
tes.
From
the p
oint
of v
iew
of o
ne m
oder
n app
roac
h to
anal
ysis,
37 a se
ries
of p
assin
g not
es is
repl
ete w
ith is
omor
phic
re
latio
ns in
the s
ense
that
ever
y not
e in
such
a se
ries
that
is ne
xt
to a
noth
er in
tim
e is a
lso n
ext t
o th
e oth
er in
pitc
h. In
a ri
sing
pass
age o
f pas
sing n
otes
, a no
te th
at is
just
afte
r ano
ther
is al
so
just
high
er th
an th
e oth
er, a
nd in
a de
scen
ding
segm
ent o
f pas
s-
ing n
otes
, a n
ote t
hat i
s jus
t afte
r ano
ther
is ju
st lo
wer
than
the
othe
r. If
a no
te is
a hi
gh- o
r low
-poi
nt of
a ri
se or
fall a
nd/o
r is a
mem
ber o
f a le
ap, t
his i
som
orph
ism of
pitc
h an
d tim
e is b
ro-
ken,
and
the
note
is "
spec
ial."
One
can
say
that
Mar
chet
to's
inte
rpre
tatio
n of s
peci
al no
tes a
s ori
entin
g ton
es re
pres
ents
an
anal
ytic
"com
pens
atio
n," f
or n
otes
that
repr
esen
t a fr
actu
ring
of
the r
elat
ions
in a
step
wise
prog
ress
ion a
re ac
cord
ed a c
entr
al
posit
ion i
n th
e mod
al hi
erar
chy;
such
note
s are
gran
ted a
"co
n-
sola
tion p
rize
," as
it w
ere.
Attr
ibut
ing t
o su
ch no
tes a
cent
ral
posit
ion c
an be
und
erst
ood a
s acc
ordi
ng th
em th
e sta
tus o
f tem
- po
rary
poin
ts of
reso
lutio
n bet
wee
n whi
ch th
ere m
ight
be p
ass-
in
g not
es, t
hat is
, not
es w
hich
"mer
ely p
ass."
Such
an in
terp
re-
tatio
n of
the
conn
ectio
n be
twee
n sp
ecia
l not
es a
nd o
rien
ting
35E.
g., th
e sys
tem
of R
ahn,
A T
heor
y for A
ll M
usic
, 44-
92.
On t
he d
efin
i- tio
n of i
ndiv
idua
l line
s, se
e Jay
Rah
n, "W
here
is th
e Mel
ody?
" In
Theo
ry O
nly,
6/
6 (19
82):
3-19
. Fo
r a sy
stem
atic
func
tiona
lizat
ion o
f ori
entin
g ton
es in
mod
al
mus
ic, c
f. Ja
y Rah
n's "
Con
stru
cts fo
r Mod
ality
, 130
0-15
50,"
Can
adia
n Ass
o-
ciat
ion o
f Uni
vers
ity Sc
hool
s of M
usic
Jour
nal 8
/2 (1
978)
: 5-3
9, a
nd hi
s stu
dy
"Ock
eghe
m's
Thre
e-Se
ctio
n Mot
et S
alve
Reg
ina:
Pro
blem
s in
Coo
rdin
atin
g Pi
tch a
nd T
ime C
onst
ruct
s," M
usic
The
ory S
pect
rum
3:11
7-31
. 36
In a s
truc
tura
l, not
a fr
eque
ncy-
base
d, se
nse o
f "or
dina
ry" (
see a
bove
). 37
E.g.
, as r
epre
sent
ed by
the f
orm
alist
ic ac
coun
t of R
ahn,
"W
here
is th
e M
elod
y?"
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
133
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
133
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
133
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
133
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
133
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
133
note
s wou
ld be
cons
isten
t with
a cu
rren
t vie
w of
mus
ical
stru
c-
ture
as an
inte
rpla
y bet
wee
n "g
ram
mar
" and
"de
sign,
" as a
d-
vanc
ed, fo
r exa
mpl
e, by
the m
usic
al se
mio
ticia
n Dav
id L
idov
.38
In M
arch
etto
's im
plic
it fo
rmul
atio
n, if
a pa
ssag
e im
plie
s a
mod
e oth
er th
an th
e mai
n one
of a
piec
e, on
e sho
uld n
ot re
gard
th
e pas
sage
conc
erne
d as a
dist
inct
segm
ent o
f the
piec
e; ra
ther
on
e sho
uld c
onsid
er th
e pas
sage
as em
bedd
ed in
a la
rger
mod
al
cont
ext.
Ther
e is n
othi
ng in
the r
est o
f Mar
chet
to's t
reat
ise to
su
gges
t tha
t a p
assa
ge in
ano
ther
mod
e is t
o be
cons
true
d as a
se
para
te se
ctio
n.39
Inst
ead,
Mar
chet
to's u
se o
f the
term
com
- m
ixta
sugg
ests
a re
gion
in w
hich
, to em
ploy
a m
etap
hor,
a fo
r-
eign
gran
ular
solid
is h
eld
in su
spen
sion i
n a l
iqui
d rat
her t
han
float
ing s
epar
atel
y (as
wou
ld ha
ppen
in th
e cas
e of o
il an
d wa-
te
r). A
giv
en m
ode i
s con
sider
ed to
be c
omm
ixed
with
, tha
t is,
mix
ed to
geth
er w
ith, a
noth
er m
ode i
n suc
h a w
ay th
at a p
iece
in
first
mod
e doe
s not
ceas
e bei
ng in
firs
t mod
e dur
ing a
pass
age i
n w
hich
anot
her m
ode i
s im
plie
d. In
deed
, Mar
chet
to's e
xam
ples
of
inte
rrup
tions
and
his c
omm
ents
on th
em sh
ow th
at a
give
n pa
ssag
e mig
ht si
mul
tane
ously
impl
y diff
eren
t mod
es in
vary
ing
degr
ees a
nd in
ove
rlap
ping
fash
ion.
In th
is re
spec
t, hi
s ap
- pr
oach
to s
egm
enta
tion d
iffer
s fro
m th
e va
riou
s lay
ered
sys-
te
ms
and
tree
-str
uctu
res o
r hi
erar
chie
s tha
t hav
e be
en a
d-
vanc
ed in
rece
nt ye
ars,
part
icul
arly
by m
usic
theo
rist
s who
have
be
en in
fluen
ced b
y lin
guist
ic th
eory
; at t
he sa
me t
ime,
Mar
- ch
etto
's ap
proa
ch to
seg
men
tatio
n con
form
s, in
a s
truc
tura
l w
ay, w
ith ot
her m
oder
n the
orist
s' use
of m
odel
s tha
t are
con-
ce
ived
as n
etw
orks
rath
er th
an tr
ees.4
0 M
arch
etto
's not
ion
of d
egre
es of
impl
icat
ion i
s also
rath
er
mod
ern,
for i
t car
ries
with
it th
e ide
as of
rela
tivity
and h
iera
r-
chy w
hich
perm
eate
s mod
ern m
usic
al th
ough
t. Par
alle
l to M
ar-
38C
f. Dav
id L
idov
, "Th
e Alle
gret
to o
f Bee
thov
en's
Seve
nth,
" Am
eric
an
Jour
nal o
f Sem
iotic
s 1, n
os. 1
-2 (
1981
): 14
4-66
. 39
See,
for e
xam
ple,
Luc
idar
ium
, 11, 4
,227
-28,
pp.
500-
07 fo
r Mar
chet
to's
prin
cipa
l exam
ples
of co
mm
ixtu
re.
40Se
e the d
iscus
sion i
n N
arm
our,
Beyo
nd Sc
henk
erism
, 122-
66.
note
s wou
ld be
cons
isten
t with
a cu
rren
t vie
w of
mus
ical
stru
c-
ture
as an
inte
rpla
y bet
wee
n "g
ram
mar
" and
"de
sign,
" as a
d-
vanc
ed, fo
r exa
mpl
e, by
the m
usic
al se
mio
ticia
n Dav
id L
idov
.38
In M
arch
etto
's im
plic
it fo
rmul
atio
n, if
a pa
ssag
e im
plie
s a
mod
e oth
er th
an th
e mai
n one
of a
piec
e, on
e sho
uld n
ot re
gard
th
e pas
sage
conc
erne
d as a
dist
inct
segm
ent o
f the
piec
e; ra
ther
on
e sho
uld c
onsid
er th
e pas
sage
as em
bedd
ed in
a la
rger
mod
al
cont
ext.
Ther
e is n
othi
ng in
the r
est o
f Mar
chet
to's t
reat
ise to
su
gges
t tha
t a p
assa
ge in
ano
ther
mod
e is t
o be
cons
true
d as a
se
para
te se
ctio
n.39
Inst
ead,
Mar
chet
to's u
se o
f the
term
com
- m
ixta
sugg
ests
a re
gion
in w
hich
, to em
ploy
a m
etap
hor,
a fo
r-
eign
gran
ular
solid
is h
eld
in su
spen
sion i
n a l
iqui
d rat
her t
han
float
ing s
epar
atel
y (as
wou
ld ha
ppen
in th
e cas
e of o
il an
d wa-
te
r). A
giv
en m
ode i
s con
sider
ed to
be c
omm
ixed
with
, tha
t is,
mix
ed to
geth
er w
ith, a
noth
er m
ode i
n suc
h a w
ay th
at a p
iece
in
first
mod
e doe
s not
ceas
e bei
ng in
firs
t mod
e dur
ing a
pass
age i
n w
hich
anot
her m
ode i
s im
plie
d. In
deed
, Mar
chet
to's e
xam
ples
of
inte
rrup
tions
and
his c
omm
ents
on th
em sh
ow th
at a
give
n pa
ssag
e mig
ht si
mul
tane
ously
impl
y diff
eren
t mod
es in
vary
ing
degr
ees a
nd in
ove
rlap
ping
fash
ion.
In th
is re
spec
t, hi
s ap
- pr
oach
to s
egm
enta
tion d
iffer
s fro
m th
e va
riou
s lay
ered
sys-
te
ms
and
tree
-str
uctu
res o
r hi
erar
chie
s tha
t hav
e be
en a
d-
vanc
ed in
rece
nt ye
ars,
part
icul
arly
by m
usic
theo
rist
s who
have
be
en in
fluen
ced b
y lin
guist
ic th
eory
; at t
he sa
me t
ime,
Mar
- ch
etto
's ap
proa
ch to
seg
men
tatio
n con
form
s, in
a s
truc
tura
l w
ay, w
ith ot
her m
oder
n the
orist
s' use
of m
odel
s tha
t are
con-
ce
ived
as n
etw
orks
rath
er th
an tr
ees.4
0 M
arch
etto
's not
ion
of d
egre
es of
impl
icat
ion i
s also
rath
er
mod
ern,
for i
t car
ries
with
it th
e ide
as of
rela
tivity
and h
iera
r-
chy w
hich
perm
eate
s mod
ern m
usic
al th
ough
t. Par
alle
l to M
ar-
38C
f. Dav
id L
idov
, "Th
e Alle
gret
to o
f Bee
thov
en's
Seve
nth,
" Am
eric
an
Jour
nal o
f Sem
iotic
s 1, n
os. 1
-2 (
1981
): 14
4-66
. 39
See,
for e
xam
ple,
Luc
idar
ium
, 11, 4
,227
-28,
pp.
500-
07 fo
r Mar
chet
to's
prin
cipa
l exam
ples
of co
mm
ixtu
re.
40Se
e the d
iscus
sion i
n N
arm
our,
Beyo
nd Sc
henk
erism
, 122-
66.
note
s wou
ld be
cons
isten
t with
a cu
rren
t vie
w of
mus
ical
stru
c-
ture
as an
inte
rpla
y bet
wee
n "g
ram
mar
" and
"de
sign,
" as a
d-
vanc
ed, fo
r exa
mpl
e, by
the m
usic
al se
mio
ticia
n Dav
id L
idov
.38
In M
arch
etto
's im
plic
it fo
rmul
atio
n, if
a pa
ssag
e im
plie
s a
mod
e oth
er th
an th
e mai
n one
of a
piec
e, on
e sho
uld n
ot re
gard
th
e pas
sage
conc
erne
d as a
dist
inct
segm
ent o
f the
piec
e; ra
ther
on
e sho
uld c
onsid
er th
e pas
sage
as em
bedd
ed in
a la
rger
mod
al
cont
ext.
Ther
e is n
othi
ng in
the r
est o
f Mar
chet
to's t
reat
ise to
su
gges
t tha
t a p
assa
ge in
ano
ther
mod
e is t
o be
cons
true
d as a
se
para
te se
ctio
n.39
Inst
ead,
Mar
chet
to's u
se o
f the
term
com
- m
ixta
sugg
ests
a re
gion
in w
hich
, to em
ploy
a m
etap
hor,
a fo
r-
eign
gran
ular
solid
is h
eld
in su
spen
sion i
n a l
iqui
d rat
her t
han
float
ing s
epar
atel
y (as
wou
ld ha
ppen
in th
e cas
e of o
il an
d wa-
te
r). A
giv
en m
ode i
s con
sider
ed to
be c
omm
ixed
with
, tha
t is,
mix
ed to
geth
er w
ith, a
noth
er m
ode i
n suc
h a w
ay th
at a p
iece
in
first
mod
e doe
s not
ceas
e bei
ng in
firs
t mod
e dur
ing a
pass
age i
n w
hich
anot
her m
ode i
s im
plie
d. In
deed
, Mar
chet
to's e
xam
ples
of
inte
rrup
tions
and
his c
omm
ents
on th
em sh
ow th
at a
give
n pa
ssag
e mig
ht si
mul
tane
ously
impl
y diff
eren
t mod
es in
vary
ing
degr
ees a
nd in
ove
rlap
ping
fash
ion.
In th
is re
spec
t, hi
s ap
- pr
oach
to s
egm
enta
tion d
iffer
s fro
m th
e va
riou
s lay
ered
sys-
te
ms
and
tree
-str
uctu
res o
r hi
erar
chie
s tha
t hav
e be
en a
d-
vanc
ed in
rece
nt ye
ars,
part
icul
arly
by m
usic
theo
rist
s who
have
be
en in
fluen
ced b
y lin
guist
ic th
eory
; at t
he sa
me t
ime,
Mar
- ch
etto
's ap
proa
ch to
seg
men
tatio
n con
form
s, in
a s
truc
tura
l w
ay, w
ith ot
her m
oder
n the
orist
s' use
of m
odel
s tha
t are
con-
ce
ived
as n
etw
orks
rath
er th
an tr
ees.4
0 M
arch
etto
's not
ion
of d
egre
es of
impl
icat
ion i
s also
rath
er
mod
ern,
for i
t car
ries
with
it th
e ide
as of
rela
tivity
and h
iera
r-
chy w
hich
perm
eate
s mod
ern m
usic
al th
ough
t. Par
alle
l to M
ar-
38C
f. Dav
id L
idov
, "Th
e Alle
gret
to o
f Bee
thov
en's
Seve
nth,
" Am
eric
an
Jour
nal o
f Sem
iotic
s 1, n
os. 1
-2 (
1981
): 14
4-66
. 39
See,
for e
xam
ple,
Luc
idar
ium
, 11, 4
,227
-28,
pp.
500-
07 fo
r Mar
chet
to's
prin
cipa
l exam
ples
of co
mm
ixtu
re.
40Se
e the d
iscus
sion i
n N
arm
our,
Beyo
nd Sc
henk
erism
, 122-
66.
note
s wou
ld be
cons
isten
t with
a cu
rren
t vie
w of
mus
ical
stru
c-
ture
as an
inte
rpla
y bet
wee
n "g
ram
mar
" and
"de
sign,
" as a
d-
vanc
ed, fo
r exa
mpl
e, by
the m
usic
al se
mio
ticia
n Dav
id L
idov
.38
In M
arch
etto
's im
plic
it fo
rmul
atio
n, if
a pa
ssag
e im
plie
s a
mod
e oth
er th
an th
e mai
n one
of a
piec
e, on
e sho
uld n
ot re
gard
th
e pas
sage
conc
erne
d as a
dist
inct
segm
ent o
f the
piec
e; ra
ther
on
e sho
uld c
onsid
er th
e pas
sage
as em
bedd
ed in
a la
rger
mod
al
cont
ext.
Ther
e is n
othi
ng in
the r
est o
f Mar
chet
to's t
reat
ise to
su
gges
t tha
t a p
assa
ge in
ano
ther
mod
e is t
o be
cons
true
d as a
se
para
te se
ctio
n.39
Inst
ead,
Mar
chet
to's u
se o
f the
term
com
- m
ixta
sugg
ests
a re
gion
in w
hich
, to em
ploy
a m
etap
hor,
a fo
r-
eign
gran
ular
solid
is h
eld
in su
spen
sion i
n a l
iqui
d rat
her t
han
float
ing s
epar
atel
y (as
wou
ld ha
ppen
in th
e cas
e of o
il an
d wa-
te
r). A
giv
en m
ode i
s con
sider
ed to
be c
omm
ixed
with
, tha
t is,
mix
ed to
geth
er w
ith, a
noth
er m
ode i
n suc
h a w
ay th
at a p
iece
in
first
mod
e doe
s not
ceas
e bei
ng in
firs
t mod
e dur
ing a
pass
age i
n w
hich
anot
her m
ode i
s im
plie
d. In
deed
, Mar
chet
to's e
xam
ples
of
inte
rrup
tions
and
his c
omm
ents
on th
em sh
ow th
at a
give
n pa
ssag
e mig
ht si
mul
tane
ously
impl
y diff
eren
t mod
es in
vary
ing
degr
ees a
nd in
ove
rlap
ping
fash
ion.
In th
is re
spec
t, hi
s ap
- pr
oach
to s
egm
enta
tion d
iffer
s fro
m th
e va
riou
s lay
ered
sys-
te
ms
and
tree
-str
uctu
res o
r hi
erar
chie
s tha
t hav
e be
en a
d-
vanc
ed in
rece
nt ye
ars,
part
icul
arly
by m
usic
theo
rist
s who
have
be
en in
fluen
ced b
y lin
guist
ic th
eory
; at t
he sa
me t
ime,
Mar
- ch
etto
's ap
proa
ch to
seg
men
tatio
n con
form
s, in
a s
truc
tura
l w
ay, w
ith ot
her m
oder
n the
orist
s' use
of m
odel
s tha
t are
con-
ce
ived
as n
etw
orks
rath
er th
an tr
ees.4
0 M
arch
etto
's not
ion
of d
egre
es of
impl
icat
ion i
s also
rath
er
mod
ern,
for i
t car
ries
with
it th
e ide
as of
rela
tivity
and h
iera
r-
chy w
hich
perm
eate
s mod
ern m
usic
al th
ough
t. Par
alle
l to M
ar-
38C
f. Dav
id L
idov
, "Th
e Alle
gret
to o
f Bee
thov
en's
Seve
nth,
" Am
eric
an
Jour
nal o
f Sem
iotic
s 1, n
os. 1
-2 (
1981
): 14
4-66
. 39
See,
for e
xam
ple,
Luc
idar
ium
, 11, 4
,227
-28,
pp.
500-
07 fo
r Mar
chet
to's
prin
cipa
l exam
ples
of co
mm
ixtu
re.
40Se
e the d
iscus
sion i
n N
arm
our,
Beyo
nd Sc
henk
erism
, 122-
66.
note
s wou
ld be
cons
isten
t with
a cu
rren
t vie
w of
mus
ical
stru
c-
ture
as an
inte
rpla
y bet
wee
n "g
ram
mar
" and
"de
sign,
" as a
d-
vanc
ed, fo
r exa
mpl
e, by
the m
usic
al se
mio
ticia
n Dav
id L
idov
.38
In M
arch
etto
's im
plic
it fo
rmul
atio
n, if
a pa
ssag
e im
plie
s a
mod
e oth
er th
an th
e mai
n one
of a
piec
e, on
e sho
uld n
ot re
gard
th
e pas
sage
conc
erne
d as a
dist
inct
segm
ent o
f the
piec
e; ra
ther
on
e sho
uld c
onsid
er th
e pas
sage
as em
bedd
ed in
a la
rger
mod
al
cont
ext.
Ther
e is n
othi
ng in
the r
est o
f Mar
chet
to's t
reat
ise to
su
gges
t tha
t a p
assa
ge in
ano
ther
mod
e is t
o be
cons
true
d as a
se
para
te se
ctio
n.39
Inst
ead,
Mar
chet
to's u
se o
f the
term
com
- m
ixta
sugg
ests
a re
gion
in w
hich
, to em
ploy
a m
etap
hor,
a fo
r-
eign
gran
ular
solid
is h
eld
in su
spen
sion i
n a l
iqui
d rat
her t
han
float
ing s
epar
atel
y (as
wou
ld ha
ppen
in th
e cas
e of o
il an
d wa-
te
r). A
giv
en m
ode i
s con
sider
ed to
be c
omm
ixed
with
, tha
t is,
mix
ed to
geth
er w
ith, a
noth
er m
ode i
n suc
h a w
ay th
at a p
iece
in
first
mod
e doe
s not
ceas
e bei
ng in
firs
t mod
e dur
ing a
pass
age i
n w
hich
anot
her m
ode i
s im
plie
d. In
deed
, Mar
chet
to's e
xam
ples
of
inte
rrup
tions
and
his c
omm
ents
on th
em sh
ow th
at a
give
n pa
ssag
e mig
ht si
mul
tane
ously
impl
y diff
eren
t mod
es in
vary
ing
degr
ees a
nd in
ove
rlap
ping
fash
ion.
In th
is re
spec
t, hi
s ap
- pr
oach
to s
egm
enta
tion d
iffer
s fro
m th
e va
riou
s lay
ered
sys-
te
ms
and
tree
-str
uctu
res o
r hi
erar
chie
s tha
t hav
e be
en a
d-
vanc
ed in
rece
nt ye
ars,
part
icul
arly
by m
usic
theo
rist
s who
have
be
en in
fluen
ced b
y lin
guist
ic th
eory
; at t
he sa
me t
ime,
Mar
- ch
etto
's ap
proa
ch to
seg
men
tatio
n con
form
s, in
a s
truc
tura
l w
ay, w
ith ot
her m
oder
n the
orist
s' use
of m
odel
s tha
t are
con-
ce
ived
as n
etw
orks
rath
er th
an tr
ees.4
0 M
arch
etto
's not
ion
of d
egre
es of
impl
icat
ion i
s also
rath
er
mod
ern,
for i
t car
ries
with
it th
e ide
as of
rela
tivity
and h
iera
r-
chy w
hich
perm
eate
s mod
ern m
usic
al th
ough
t. Par
alle
l to M
ar-
38C
f. Dav
id L
idov
, "Th
e Alle
gret
to o
f Bee
thov
en's
Seve
nth,
" Am
eric
an
Jour
nal o
f Sem
iotic
s 1, n
os. 1
-2 (
1981
): 14
4-66
. 39
See,
for e
xam
ple,
Luc
idar
ium
, 11, 4
,227
-28,
pp.
500-
07 fo
r Mar
chet
to's
prin
cipa
l exam
ples
of co
mm
ixtu
re.
40Se
e the d
iscus
sion i
n N
arm
our,
Beyo
nd Sc
henk
erism
, 122-
66.
note
s wou
ld be
cons
isten
t with
a cu
rren
t vie
w of
mus
ical
stru
c-
ture
as an
inte
rpla
y bet
wee
n "g
ram
mar
" and
"de
sign,
" as a
d-
vanc
ed, fo
r exa
mpl
e, by
the m
usic
al se
mio
ticia
n Dav
id L
idov
.38
In M
arch
etto
's im
plic
it fo
rmul
atio
n, if
a pa
ssag
e im
plie
s a
mod
e oth
er th
an th
e mai
n one
of a
piec
e, on
e sho
uld n
ot re
gard
th
e pas
sage
conc
erne
d as a
dist
inct
segm
ent o
f the
piec
e; ra
ther
on
e sho
uld c
onsid
er th
e pas
sage
as em
bedd
ed in
a la
rger
mod
al
cont
ext.
Ther
e is n
othi
ng in
the r
est o
f Mar
chet
to's t
reat
ise to
su
gges
t tha
t a p
assa
ge in
ano
ther
mod
e is t
o be
cons
true
d as a
se
para
te se
ctio
n.39
Inst
ead,
Mar
chet
to's u
se o
f the
term
com
- m
ixta
sugg
ests
a re
gion
in w
hich
, to em
ploy
a m
etap
hor,
a fo
r-
eign
gran
ular
solid
is h
eld
in su
spen
sion i
n a l
iqui
d rat
her t
han
float
ing s
epar
atel
y (as
wou
ld ha
ppen
in th
e cas
e of o
il an
d wa-
te
r). A
giv
en m
ode i
s con
sider
ed to
be c
omm
ixed
with
, tha
t is,
mix
ed to
geth
er w
ith, a
noth
er m
ode i
n suc
h a w
ay th
at a p
iece
in
first
mod
e doe
s not
ceas
e bei
ng in
firs
t mod
e dur
ing a
pass
age i
n w
hich
anot
her m
ode i
s im
plie
d. In
deed
, Mar
chet
to's e
xam
ples
of
inte
rrup
tions
and
his c
omm
ents
on th
em sh
ow th
at a
give
n pa
ssag
e mig
ht si
mul
tane
ously
impl
y diff
eren
t mod
es in
vary
ing
degr
ees a
nd in
ove
rlap
ping
fash
ion.
In th
is re
spec
t, hi
s ap
- pr
oach
to s
egm
enta
tion d
iffer
s fro
m th
e va
riou
s lay
ered
sys-
te
ms
and
tree
-str
uctu
res o
r hi
erar
chie
s tha
t hav
e be
en a
d-
vanc
ed in
rece
nt ye
ars,
part
icul
arly
by m
usic
theo
rist
s who
have
be
en in
fluen
ced b
y lin
guist
ic th
eory
; at t
he sa
me t
ime,
Mar
- ch
etto
's ap
proa
ch to
seg
men
tatio
n con
form
s, in
a s
truc
tura
l w
ay, w
ith ot
her m
oder
n the
orist
s' use
of m
odel
s tha
t are
con-
ce
ived
as n
etw
orks
rath
er th
an tr
ees.4
0 M
arch
etto
's not
ion
of d
egre
es of
impl
icat
ion i
s also
rath
er
mod
ern,
for i
t car
ries
with
it th
e ide
as of
rela
tivity
and h
iera
r-
chy w
hich
perm
eate
s mod
ern m
usic
al th
ough
t. Par
alle
l to M
ar-
38C
f. Dav
id L
idov
, "Th
e Alle
gret
to o
f Bee
thov
en's
Seve
nth,
" Am
eric
an
Jour
nal o
f Sem
iotic
s 1, n
os. 1
-2 (
1981
): 14
4-66
. 39
See,
for e
xam
ple,
Luc
idar
ium
, 11, 4
,227
-28,
pp.
500-
07 fo
r Mar
chet
to's
prin
cipa
l exam
ples
of co
mm
ixtu
re.
40Se
e the d
iscus
sion i
n N
arm
our,
Beyo
nd Sc
henk
erism
, 122-
66.
chet
to's
dist
inct
ion b
etw
een
vari
ous d
egre
es of
mod
al im
plic
a-
tion,
one
find
s, in
mod
em ti
mes
, at l
east
as ea
rly a
s Don
ald
Fran
cis T
ovey
's w
ritin
gs, a
dist
inct
ion b
etw
een a
pass
age t
hat is
in
and a
pas
sage
that
is m
erel
y on,
a gi
ven t
onal
area
at a
give
n po
int.4
1 How
ever
, Mar
chet
to's o
vera
ll vie
w is
even
mor
e sub
tle
than
Tove
y's in
that
, like
Hei
nric
h Sch
enke
r, he
reco
gniz
es th
at
a pie
ce ca
n stil
l be f
unct
ioni
ng w
ithin
the f
ram
ewor
k of a
give
n ke
y (o
r, in
Mar
chet
to's c
ase,
a g
iven
mod
e) d
espi
te ap
pare
nt
fore
grou
nd de
viat
ions
from
the
cent
ral t
onal
ity (o
r, in
Mar
- ch
etto
's ca
se, m
odal
ity).4
2 In fa
ct, c
rite
rion
9 (a
bove
) rev
eals
Mar
chet
to to
be a
prot
o-Sc
henk
eria
n in hi
s adv
ance
men
t of th
e no
tion
that
two
far-
flung
spec
ial n
otes
of t
he sa
me p
itch
can
serv
e to
orie
nt th
e m
odal
ity of
the
entir
e pas
sage
that
inte
r-
vene
s bet
wee
n th
em m
uch
as tw
o to
nes o
f a m
elod
y tha
t are
su
ppor
ted b
y a
cent
ral h
arm
ony c
an b
e con
sider
ed to
def
ine a
pr
olon
gatio
n of a
sing
le no
te in
the U
rlin
ie.4
3 Th
e for
egoi
ng ob
serv
atio
ns ar
e not
mea
nt to
con
stitu
te an
ex
erci
se in
ant
i-hist
oric
al an
achr
onism
, nor a
re th
ey m
eant
to
deny
that
Mar
chet
to sh
ould
be un
ders
tood
in te
rms o
f the
inte
l- le
ctua
l and
mus
ical
clim
ate i
n w
hich
he w
orke
d; ra
ther
, thes
e re
mar
ks ar
e mea
nt to
poi
nt ou
t tha
t cer
tain
issue
s tha
t ari
se in
M
arch
etto
's for
mul
atio
n of m
odal
ity sh
ould
be o
f int
eres
t to
theo
rist
s tod
ay, a
part
from
any i
nter
est t
hey m
ight
have
hel
d fo
r mus
icia
ns an
d the
orist
s of M
arch
etto
's ow
n tim
e.
41Se
e, fo
r exa
mpl
e, T
ovey
's "T
he C
lass
ical
Con
cert
o," E
ssay
s in
Mus
ical
A
naly
sis (O
xfor
d: O
xfor
d Uni
vers
ity Pr
ess,
3 vol
s., 1
936-
39),
3:19
-21.
42
See,
for e
xam
ple,
Hei
nric
h Sch
enke
r, "M
ozar
t: Sin
foni
e G-M
oll,"
Das
M
eist
erw
erke
in de
rMus
ik 2 (
1926
): A
pp. 7
(rep
r. G
. Olm
s, Hild
eshe
im, 1
971)
, an
d the
disc
ussio
n of t
he fi
rst m
ovem
ent o
f Moz
art's
Sym
phon
y No.
40 in
Alle
n Fo
rte a
nd St
even
E. G
ilber
t, Int
rodu
ctio
n to Sc
henk
eria
n Ana
lysis
(New
Yor
k:
W. W
. Nor
ton,
198
2), 1
03-0
4, b
ut ob
serv
e esp
ecia
lly no
te 1
, p. 1
04.
43C
f. For
te an
d G
ilber
t, Sc
henk
eria
n Ana
lysis
, 144
, in th
eir d
iscus
sion o
f th
e thi
rd ty
pe of
pro
long
atio
n: "m
otio
n abo
ut a
give
n not
e."
chet
to's
dist
inct
ion b
etw
een
vari
ous d
egre
es of
mod
al im
plic
a-
tion,
one
find
s, in
mod
em ti
mes
, at l
east
as ea
rly a
s Don
ald
Fran
cis T
ovey
's w
ritin
gs, a
dist
inct
ion b
etw
een a
pass
age t
hat is
in
and a
pas
sage
that
is m
erel
y on,
a gi
ven t
onal
area
at a
give
n po
int.4
1 How
ever
, Mar
chet
to's o
vera
ll vie
w is
even
mor
e sub
tle
than
Tove
y's in
that
, like
Hei
nric
h Sch
enke
r, he
reco
gniz
es th
at
a pie
ce ca
n stil
l be f
unct
ioni
ng w
ithin
the f
ram
ewor
k of a
give
n ke
y (o
r, in
Mar
chet
to's c
ase,
a g
iven
mod
e) d
espi
te ap
pare
nt
fore
grou
nd de
viat
ions
from
the
cent
ral t
onal
ity (o
r, in
Mar
- ch
etto
's ca
se, m
odal
ity).4
2 In fa
ct, c
rite
rion
9 (a
bove
) rev
eals
Mar
chet
to to
be a
prot
o-Sc
henk
eria
n in hi
s adv
ance
men
t of th
e no
tion
that
two
far-
flung
spec
ial n
otes
of t
he sa
me p
itch
can
serv
e to
orie
nt th
e m
odal
ity of
the
entir
e pas
sage
that
inte
r-
vene
s bet
wee
n th
em m
uch
as tw
o to
nes o
f a m
elod
y tha
t are
su
ppor
ted b
y a
cent
ral h
arm
ony c
an b
e con
sider
ed to
def
ine a
pr
olon
gatio
n of a
sing
le no
te in
the U
rlin
ie.4
3 Th
e for
egoi
ng ob
serv
atio
ns ar
e not
mea
nt to
con
stitu
te an
ex
erci
se in
ant
i-hist
oric
al an
achr
onism
, nor a
re th
ey m
eant
to
deny
that
Mar
chet
to sh
ould
be un
ders
tood
in te
rms o
f the
inte
l- le
ctua
l and
mus
ical
clim
ate i
n w
hich
he w
orke
d; ra
ther
, thes
e re
mar
ks ar
e mea
nt to
poi
nt ou
t tha
t cer
tain
issue
s tha
t ari
se in
M
arch
etto
's for
mul
atio
n of m
odal
ity sh
ould
be o
f int
eres
t to
theo
rist
s tod
ay, a
part
from
any i
nter
est t
hey m
ight
have
hel
d fo
r mus
icia
ns an
d the
orist
s of M
arch
etto
's ow
n tim
e.
41Se
e, fo
r exa
mpl
e, T
ovey
's "T
he C
lass
ical
Con
cert
o," E
ssay
s in
Mus
ical
A
naly
sis (O
xfor
d: O
xfor
d Uni
vers
ity Pr
ess,
3 vol
s., 1
936-
39),
3:19
-21.
42
See,
for e
xam
ple,
Hei
nric
h Sch
enke
r, "M
ozar
t: Sin
foni
e G-M
oll,"
Das
M
eist
erw
erke
in de
rMus
ik 2 (
1926
): A
pp. 7
(rep
r. G
. Olm
s, Hild
eshe
im, 1
971)
, an
d the
disc
ussio
n of t
he fi
rst m
ovem
ent o
f Moz
art's
Sym
phon
y No.
40 in
Alle
n Fo
rte a
nd St
even
E. G
ilber
t, Int
rodu
ctio
n to Sc
henk
eria
n Ana
lysis
(New
Yor
k:
W. W
. Nor
ton,
198
2), 1
03-0
4, b
ut ob
serv
e esp
ecia
lly no
te 1
, p. 1
04.
43C
f. For
te an
d G
ilber
t, Sc
henk
eria
n Ana
lysis
, 144
, in th
eir d
iscus
sion o
f th
e thi
rd ty
pe of
pro
long
atio
n: "m
otio
n abo
ut a
give
n not
e."
chet
to's
dist
inct
ion b
etw
een
vari
ous d
egre
es of
mod
al im
plic
a-
tion,
one
find
s, in
mod
em ti
mes
, at l
east
as ea
rly a
s Don
ald
Fran
cis T
ovey
's w
ritin
gs, a
dist
inct
ion b
etw
een a
pass
age t
hat is
in
and a
pas
sage
that
is m
erel
y on,
a gi
ven t
onal
area
at a
give
n po
int.4
1 How
ever
, Mar
chet
to's o
vera
ll vie
w is
even
mor
e sub
tle
than
Tove
y's in
that
, like
Hei
nric
h Sch
enke
r, he
reco
gniz
es th
at
a pie
ce ca
n stil
l be f
unct
ioni
ng w
ithin
the f
ram
ewor
k of a
give
n ke
y (o
r, in
Mar
chet
to's c
ase,
a g
iven
mod
e) d
espi
te ap
pare
nt
fore
grou
nd de
viat
ions
from
the
cent
ral t
onal
ity (o
r, in
Mar
- ch
etto
's ca
se, m
odal
ity).4
2 In fa
ct, c
rite
rion
9 (a
bove
) rev
eals
Mar
chet
to to
be a
prot
o-Sc
henk
eria
n in hi
s adv
ance
men
t of th
e no
tion
that
two
far-
flung
spec
ial n
otes
of t
he sa
me p
itch
can
serv
e to
orie
nt th
e m
odal
ity of
the
entir
e pas
sage
that
inte
r-
vene
s bet
wee
n th
em m
uch
as tw
o to
nes o
f a m
elod
y tha
t are
su
ppor
ted b
y a
cent
ral h
arm
ony c
an b
e con
sider
ed to
def
ine a
pr
olon
gatio
n of a
sing
le no
te in
the U
rlin
ie.4
3 Th
e for
egoi
ng ob
serv
atio
ns ar
e not
mea
nt to
con
stitu
te an
ex
erci
se in
ant
i-hist
oric
al an
achr
onism
, nor a
re th
ey m
eant
to
deny
that
Mar
chet
to sh
ould
be un
ders
tood
in te
rms o
f the
inte
l- le
ctua
l and
mus
ical
clim
ate i
n w
hich
he w
orke
d; ra
ther
, thes
e re
mar
ks ar
e mea
nt to
poi
nt ou
t tha
t cer
tain
issue
s tha
t ari
se in
M
arch
etto
's for
mul
atio
n of m
odal
ity sh
ould
be o
f int
eres
t to
theo
rist
s tod
ay, a
part
from
any i
nter
est t
hey m
ight
have
hel
d fo
r mus
icia
ns an
d the
orist
s of M
arch
etto
's ow
n tim
e.
41Se
e, fo
r exa
mpl
e, T
ovey
's "T
he C
lass
ical
Con
cert
o," E
ssay
s in
Mus
ical
A
naly
sis (O
xfor
d: O
xfor
d Uni
vers
ity Pr
ess,
3 vol
s., 1
936-
39),
3:19
-21.
42
See,
for e
xam
ple,
Hei
nric
h Sch
enke
r, "M
ozar
t: Sin
foni
e G-M
oll,"
Das
M
eist
erw
erke
in de
rMus
ik 2 (
1926
): A
pp. 7
(rep
r. G
. Olm
s, Hild
eshe
im, 1
971)
, an
d the
disc
ussio
n of t
he fi
rst m
ovem
ent o
f Moz
art's
Sym
phon
y No.
40 in
Alle
n Fo
rte a
nd St
even
E. G
ilber
t, Int
rodu
ctio
n to Sc
henk
eria
n Ana
lysis
(New
Yor
k:
W. W
. Nor
ton,
198
2), 1
03-0
4, b
ut ob
serv
e esp
ecia
lly no
te 1
, p. 1
04.
43C
f. For
te an
d G
ilber
t, Sc
henk
eria
n Ana
lysis
, 144
, in th
eir d
iscus
sion o
f th
e thi
rd ty
pe of
pro
long
atio
n: "m
otio
n abo
ut a
give
n not
e."
chet
to's
dist
inct
ion b
etw
een
vari
ous d
egre
es of
mod
al im
plic
a-
tion,
one
find
s, in
mod
em ti
mes
, at l
east
as ea
rly a
s Don
ald
Fran
cis T
ovey
's w
ritin
gs, a
dist
inct
ion b
etw
een a
pass
age t
hat is
in
and a
pas
sage
that
is m
erel
y on,
a gi
ven t
onal
area
at a
give
n po
int.4
1 How
ever
, Mar
chet
to's o
vera
ll vie
w is
even
mor
e sub
tle
than
Tove
y's in
that
, like
Hei
nric
h Sch
enke
r, he
reco
gniz
es th
at
a pie
ce ca
n stil
l be f
unct
ioni
ng w
ithin
the f
ram
ewor
k of a
give
n ke
y (o
r, in
Mar
chet
to's c
ase,
a g
iven
mod
e) d
espi
te ap
pare
nt
fore
grou
nd de
viat
ions
from
the
cent
ral t
onal
ity (o
r, in
Mar
- ch
etto
's ca
se, m
odal
ity).4
2 In fa
ct, c
rite
rion
9 (a
bove
) rev
eals
Mar
chet
to to
be a
prot
o-Sc
henk
eria
n in hi
s adv
ance
men
t of th
e no
tion
that
two
far-
flung
spec
ial n
otes
of t
he sa
me p
itch
can
serv
e to
orie
nt th
e m
odal
ity of
the
entir
e pas
sage
that
inte
r-
vene
s bet
wee
n th
em m
uch
as tw
o to
nes o
f a m
elod
y tha
t are
su
ppor
ted b
y a
cent
ral h
arm
ony c
an b
e con
sider
ed to
def
ine a
pr
olon
gatio
n of a
sing
le no
te in
the U
rlin
ie.4
3 Th
e for
egoi
ng ob
serv
atio
ns ar
e not
mea
nt to
con
stitu
te an
ex
erci
se in
ant
i-hist
oric
al an
achr
onism
, nor a
re th
ey m
eant
to
deny
that
Mar
chet
to sh
ould
be un
ders
tood
in te
rms o
f the
inte
l- le
ctua
l and
mus
ical
clim
ate i
n w
hich
he w
orke
d; ra
ther
, thes
e re
mar
ks ar
e mea
nt to
poi
nt ou
t tha
t cer
tain
issue
s tha
t ari
se in
M
arch
etto
's for
mul
atio
n of m
odal
ity sh
ould
be o
f int
eres
t to
theo
rist
s tod
ay, a
part
from
any i
nter
est t
hey m
ight
have
hel
d fo
r mus
icia
ns an
d the
orist
s of M
arch
etto
's ow
n tim
e.
41Se
e, fo
r exa
mpl
e, T
ovey
's "T
he C
lass
ical
Con
cert
o," E
ssay
s in
Mus
ical
A
naly
sis (O
xfor
d: O
xfor
d Uni
vers
ity Pr
ess,
3 vol
s., 1
936-
39),
3:19
-21.
42
See,
for e
xam
ple,
Hei
nric
h Sch
enke
r, "M
ozar
t: Sin
foni
e G-M
oll,"
Das
M
eist
erw
erke
in de
rMus
ik 2 (
1926
): A
pp. 7
(rep
r. G
. Olm
s, Hild
eshe
im, 1
971)
, an
d the
disc
ussio
n of t
he fi
rst m
ovem
ent o
f Moz
art's
Sym
phon
y No.
40 in
Alle
n Fo
rte a
nd St
even
E. G
ilber
t, Int
rodu
ctio
n to Sc
henk
eria
n Ana
lysis
(New
Yor
k:
W. W
. Nor
ton,
198
2), 1
03-0
4, b
ut ob
serv
e esp
ecia
lly no
te 1
, p. 1
04.
43C
f. For
te an
d G
ilber
t, Sc
henk
eria
n Ana
lysis
, 144
, in th
eir d
iscus
sion o
f th
e thi
rd ty
pe of
pro
long
atio
n: "m
otio
n abo
ut a
give
n not
e."
chet
to's
dist
inct
ion b
etw
een
vari
ous d
egre
es of
mod
al im
plic
a-
tion,
one
find
s, in
mod
em ti
mes
, at l
east
as ea
rly a
s Don
ald
Fran
cis T
ovey
's w
ritin
gs, a
dist
inct
ion b
etw
een a
pass
age t
hat is
in
and a
pas
sage
that
is m
erel
y on,
a gi
ven t
onal
area
at a
give
n po
int.4
1 How
ever
, Mar
chet
to's o
vera
ll vie
w is
even
mor
e sub
tle
than
Tove
y's in
that
, like
Hei
nric
h Sch
enke
r, he
reco
gniz
es th
at
a pie
ce ca
n stil
l be f
unct
ioni
ng w
ithin
the f
ram
ewor
k of a
give
n ke
y (o
r, in
Mar
chet
to's c
ase,
a g
iven
mod
e) d
espi
te ap
pare
nt
fore
grou
nd de
viat
ions
from
the
cent
ral t
onal
ity (o
r, in
Mar
- ch
etto
's ca
se, m
odal
ity).4
2 In fa
ct, c
rite
rion
9 (a
bove
) rev
eals
Mar
chet
to to
be a
prot
o-Sc
henk
eria
n in hi
s adv
ance
men
t of th
e no
tion
that
two
far-
flung
spec
ial n
otes
of t
he sa
me p
itch
can
serv
e to
orie
nt th
e m
odal
ity of
the
entir
e pas
sage
that
inte
r-
vene
s bet
wee
n th
em m
uch
as tw
o to
nes o
f a m
elod
y tha
t are
su
ppor
ted b
y a
cent
ral h
arm
ony c
an b
e con
sider
ed to
def
ine a
pr
olon
gatio
n of a
sing
le no
te in
the U
rlin
ie.4
3 Th
e for
egoi
ng ob
serv
atio
ns ar
e not
mea
nt to
con
stitu
te an
ex
erci
se in
ant
i-hist
oric
al an
achr
onism
, nor a
re th
ey m
eant
to
deny
that
Mar
chet
to sh
ould
be un
ders
tood
in te
rms o
f the
inte
l- le
ctua
l and
mus
ical
clim
ate i
n w
hich
he w
orke
d; ra
ther
, thes
e re
mar
ks ar
e mea
nt to
poi
nt ou
t tha
t cer
tain
issue
s tha
t ari
se in
M
arch
etto
's for
mul
atio
n of m
odal
ity sh
ould
be o
f int
eres
t to
theo
rist
s tod
ay, a
part
from
any i
nter
est t
hey m
ight
have
hel
d fo
r mus
icia
ns an
d the
orist
s of M
arch
etto
's ow
n tim
e.
41Se
e, fo
r exa
mpl
e, T
ovey
's "T
he C
lass
ical
Con
cert
o," E
ssay
s in
Mus
ical
A
naly
sis (O
xfor
d: O
xfor
d Uni
vers
ity Pr
ess,
3 vol
s., 1
936-
39),
3:19
-21.
42
See,
for e
xam
ple,
Hei
nric
h Sch
enke
r, "M
ozar
t: Sin
foni
e G-M
oll,"
Das
M
eist
erw
erke
in de
rMus
ik 2 (
1926
): A
pp. 7
(rep
r. G
. Olm
s, Hild
eshe
im, 1
971)
, an
d the
disc
ussio
n of t
he fi
rst m
ovem
ent o
f Moz
art's
Sym
phon
y No.
40 in
Alle
n Fo
rte a
nd St
even
E. G
ilber
t, Int
rodu
ctio
n to Sc
henk
eria
n Ana
lysis
(New
Yor
k:
W. W
. Nor
ton,
198
2), 1
03-0
4, b
ut ob
serv
e esp
ecia
lly no
te 1
, p. 1
04.
43C
f. For
te an
d G
ilber
t, Sc
henk
eria
n Ana
lysis
, 144
, in th
eir d
iscus
sion o
f th
e thi
rd ty
pe of
pro
long
atio
n: "m
otio
n abo
ut a
give
n not
e."
chet
to's
dist
inct
ion b
etw
een
vari
ous d
egre
es of
mod
al im
plic
a-
tion,
one
find
s, in
mod
em ti
mes
, at l
east
as ea
rly a
s Don
ald
Fran
cis T
ovey
's w
ritin
gs, a
dist
inct
ion b
etw
een a
pass
age t
hat is
in
and a
pas
sage
that
is m
erel
y on,
a gi
ven t
onal
area
at a
give
n po
int.4
1 How
ever
, Mar
chet
to's o
vera
ll vie
w is
even
mor
e sub
tle
than
Tove
y's in
that
, like
Hei
nric
h Sch
enke
r, he
reco
gniz
es th
at
a pie
ce ca
n stil
l be f
unct
ioni
ng w
ithin
the f
ram
ewor
k of a
give
n ke
y (o
r, in
Mar
chet
to's c
ase,
a g
iven
mod
e) d
espi
te ap
pare
nt
fore
grou
nd de
viat
ions
from
the
cent
ral t
onal
ity (o
r, in
Mar
- ch
etto
's ca
se, m
odal
ity).4
2 In fa
ct, c
rite
rion
9 (a
bove
) rev
eals
Mar
chet
to to
be a
prot
o-Sc
henk
eria
n in hi
s adv
ance
men
t of th
e no
tion
that
two
far-
flung
spec
ial n
otes
of t
he sa
me p
itch
can
serv
e to
orie
nt th
e m
odal
ity of
the
entir
e pas
sage
that
inte
r-
vene
s bet
wee
n th
em m
uch
as tw
o to
nes o
f a m
elod
y tha
t are
su
ppor
ted b
y a
cent
ral h
arm
ony c
an b
e con
sider
ed to
def
ine a
pr
olon
gatio
n of a
sing
le no
te in
the U
rlin
ie.4
3 Th
e for
egoi
ng ob
serv
atio
ns ar
e not
mea
nt to
con
stitu
te an
ex
erci
se in
ant
i-hist
oric
al an
achr
onism
, nor a
re th
ey m
eant
to
deny
that
Mar
chet
to sh
ould
be un
ders
tood
in te
rms o
f the
inte
l- le
ctua
l and
mus
ical
clim
ate i
n w
hich
he w
orke
d; ra
ther
, thes
e re
mar
ks ar
e mea
nt to
poi
nt ou
t tha
t cer
tain
issue
s tha
t ari
se in
M
arch
etto
's for
mul
atio
n of m
odal
ity sh
ould
be o
f int
eres
t to
theo
rist
s tod
ay, a
part
from
any i
nter
est t
hey m
ight
have
hel
d fo
r mus
icia
ns an
d the
orist
s of M
arch
etto
's ow
n tim
e.
41Se
e, fo
r exa
mpl
e, T
ovey
's "T
he C
lass
ical
Con
cert
o," E
ssay
s in
Mus
ical
A
naly
sis (O
xfor
d: O
xfor
d Uni
vers
ity Pr
ess,
3 vol
s., 1
936-
39),
3:19
-21.
42
See,
for e
xam
ple,
Hei
nric
h Sch
enke
r, "M
ozar
t: Sin
foni
e G-M
oll,"
Das
M
eist
erw
erke
in de
rMus
ik 2 (
1926
): A
pp. 7
(rep
r. G
. Olm
s, Hild
eshe
im, 1
971)
, an
d the
disc
ussio
n of t
he fi
rst m
ovem
ent o
f Moz
art's
Sym
phon
y No.
40 in
Alle
n Fo
rte a
nd St
even
E. G
ilber
t, Int
rodu
ctio
n to Sc
henk
eria
n Ana
lysis
(New
Yor
k:
W. W
. Nor
ton,
198
2), 1
03-0
4, b
ut ob
serv
e esp
ecia
lly no
te 1
, p. 1
04.
43C
f. For
te an
d G
ilber
t, Sc
henk
eria
n Ana
lysis
, 144
, in th
eir d
iscus
sion o
f th
e thi
rd ty
pe of
pro
long
atio
n: "m
otio
n abo
ut a
give
n not
e."
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
134
Mus
ic T
heor
y Spe
ctru
m
134
Mus
ic T
heor
y Spe
ctru
m
134
Mus
ic T
heor
y Spe
ctru
m
134
Mus
ic T
heor
y Spe
ctru
m
134
Mus
ic T
heor
y Spe
ctru
m
134
Mus
ic T
heor
y Spe
ctru
m
Mar
chet
to's
Theo
ry o
f Int
erru
ptio
ns in
Its H
istor
ical
Con
text
With
rega
rd to
its i
mm
edia
te h
istor
ical
con
text
, a
num
ber
of
ques
tions
rem
ain
abou
t M
arch
etto
's fo
rmul
atio
n of
int
erru
p-
tions
. In
the
first
pla
ce,
thou
gh it
mig
ht s
eem
cle
ar h
ow h
is im
- pl
icit
anal
ytic
tech
niqu
e m
ight
be
appl
ied
to c
hant
, it i
s not
nec
- es
sari
ly so
cle
ar h
ow it
mig
ht b
e ap
plie
d to
mea
sure
d m
usic
or
poly
phon
y of
the
Mid
dle
Age
s an
d R
enai
ssan
ce.
How
ever
, if
one
exam
ines
Mar
chet
to's
exam
ples
in o
ther
par
ts o
f the
Luc
i- da
rium
, it i
s ev
iden
t th
at h
e al
so c
onsid
ers
repe
ated
not
es o
r lo
ng-h
eld
note
s (n
eith
er o
f whi
ch a
rise
s in
his
disc
ussio
n of
in-
terr
uptio
ns) t
o be
spe
cial
not
es.4
4 One
can
not
e th
at th
is ob
ser-
va
tion
is co
nsist
ent
with
my
earl
ier
form
ulat
ion
of s
peci
al
note
s, fo
r in
a p
air
of r
epea
ted
note
s, th
e se
cond
not
e is
just
af
ter t
he fi
rst b
ut is
nei
ther
just
hig
her t
han,
nor
just
low
er th
an,
the
first
(sin
ce t
hey
are
both
of
the
sam
e pi
tch)
; m
oreo
ver,
lo
ng-h
eld
note
s (e
.g.,
at th
e en
ds o
f phr
ases
) ca
n be
con
sider
ed
to fu
nctio
n te
mpo
rally
as "
tied
repe
ated
not
es."
In
the
case
of m
easu
red
mus
ic, t
here
wou
ld b
e a
dura
tiona
l hi
erar
chy
of s
peci
al-n
ess
acco
rdin
g to
whi
ch v
ario
us n
otes
of a
m
elod
y or
line
cou
ld b
e re
gard
ed a
s mor
e or
less
"sp
ecia
l," o
r to
use
mod
ern
term
s, fo
cal,
wei
ghty
, or
impo
rtan
t. A
nd in
con-
fo
rmity
with
thos
e la
te m
edie
val
and
earl
y R
enai
ssan
ce t
heo-
ri
sts,
who
wer
e la
rgel
y ra
ther
dir
ect f
ollo
wer
s of
Mar
chet
to a
nd
who
reg
arde
d th
e m
odes
of p
olyp
honi
c pi
eces
as
a fu
nctio
n of
th
e m
odes
im
plie
d by
indi
vidu
al li
nes,
one
coul
d ex
tend
Mar
- ch
etto
's co
ncep
tion
of m
odal
impl
icat
ion
to m
uch
mor
e co
mpl
i- ca
ted
text
ures
than
the
mon
opho
ny o
f cha
nt.4
5
44R
epea
ted a
nd lo
ng-h
eld n
otes
arise
in th
e mod
el m
elod
ies t
hat M
arch
etto
em
ploy
s to ill
ustr
ate "
the f
orm
atio
n of m
odes
by sp
ecie
s" in
Luc
idar
ium
, 11, 4
, pa
ssim
, whe
re su
ch no
tes t
end o
verw
helm
ingl
y to co
inci
de w
ith or
ient
ing n
otes
of
the m
elod
y bei
ng ill
ustr
ated
. 45
On
the
appl
icat
ion o
f mod
al id
eas t
o po
lyph
onic
text
ures
, see
Pow
ers,
"Mod
e," e
sp. 3
99-4
06.
Mar
chet
to's
Theo
ry o
f Int
erru
ptio
ns in
Its H
istor
ical
Con
text
With
rega
rd to
its i
mm
edia
te h
istor
ical
con
text
, a
num
ber
of
ques
tions
rem
ain
abou
t M
arch
etto
's fo
rmul
atio
n of
int
erru
p-
tions
. In
the
first
pla
ce,
thou
gh it
mig
ht s
eem
cle
ar h
ow h
is im
- pl
icit
anal
ytic
tech
niqu
e m
ight
be
appl
ied
to c
hant
, it i
s not
nec
- es
sari
ly so
cle
ar h
ow it
mig
ht b
e ap
plie
d to
mea
sure
d m
usic
or
poly
phon
y of
the
Mid
dle
Age
s an
d R
enai
ssan
ce.
How
ever
, if
one
exam
ines
Mar
chet
to's
exam
ples
in o
ther
par
ts o
f the
Luc
i- da
rium
, it i
s ev
iden
t th
at h
e al
so c
onsid
ers
repe
ated
not
es o
r lo
ng-h
eld
note
s (n
eith
er o
f whi
ch a
rise
s in
his
disc
ussio
n of
in-
terr
uptio
ns) t
o be
spe
cial
not
es.4
4 One
can
not
e th
at th
is ob
ser-
va
tion
is co
nsist
ent
with
my
earl
ier
form
ulat
ion
of s
peci
al
note
s, fo
r in
a p
air
of r
epea
ted
note
s, th
e se
cond
not
e is
just
af
ter t
he fi
rst b
ut is
nei
ther
just
hig
her t
han,
nor
just
low
er th
an,
the
first
(sin
ce t
hey
are
both
of
the
sam
e pi
tch)
; m
oreo
ver,
lo
ng-h
eld
note
s (e
.g.,
at th
e en
ds o
f phr
ases
) ca
n be
con
sider
ed
to fu
nctio
n te
mpo
rally
as "
tied
repe
ated
not
es."
In
the
case
of m
easu
red
mus
ic, t
here
wou
ld b
e a
dura
tiona
l hi
erar
chy
of s
peci
al-n
ess
acco
rdin
g to
whi
ch v
ario
us n
otes
of a
m
elod
y or
line
cou
ld b
e re
gard
ed a
s mor
e or
less
"sp
ecia
l," o
r to
use
mod
ern
term
s, fo
cal,
wei
ghty
, or
impo
rtan
t. A
nd in
con-
fo
rmity
with
thos
e la
te m
edie
val
and
earl
y R
enai
ssan
ce t
heo-
ri
sts,
who
wer
e la
rgel
y ra
ther
dir
ect f
ollo
wer
s of
Mar
chet
to a
nd
who
reg
arde
d th
e m
odes
of p
olyp
honi
c pi
eces
as
a fu
nctio
n of
th
e m
odes
im
plie
d by
indi
vidu
al li
nes,
one
coul
d ex
tend
Mar
- ch
etto
's co
ncep
tion
of m
odal
impl
icat
ion
to m
uch
mor
e co
mpl
i- ca
ted
text
ures
than
the
mon
opho
ny o
f cha
nt.4
5
44R
epea
ted a
nd lo
ng-h
eld n
otes
arise
in th
e mod
el m
elod
ies t
hat M
arch
etto
em
ploy
s to ill
ustr
ate "
the f
orm
atio
n of m
odes
by sp
ecie
s" in
Luc
idar
ium
, 11, 4
, pa
ssim
, whe
re su
ch no
tes t
end o
verw
helm
ingl
y to co
inci
de w
ith or
ient
ing n
otes
of
the m
elod
y bei
ng ill
ustr
ated
. 45
On
the
appl
icat
ion o
f mod
al id
eas t
o po
lyph
onic
text
ures
, see
Pow
ers,
"Mod
e," e
sp. 3
99-4
06.
Mar
chet
to's
Theo
ry o
f Int
erru
ptio
ns in
Its H
istor
ical
Con
text
With
rega
rd to
its i
mm
edia
te h
istor
ical
con
text
, a
num
ber
of
ques
tions
rem
ain
abou
t M
arch
etto
's fo
rmul
atio
n of
int
erru
p-
tions
. In
the
first
pla
ce,
thou
gh it
mig
ht s
eem
cle
ar h
ow h
is im
- pl
icit
anal
ytic
tech
niqu
e m
ight
be
appl
ied
to c
hant
, it i
s not
nec
- es
sari
ly so
cle
ar h
ow it
mig
ht b
e ap
plie
d to
mea
sure
d m
usic
or
poly
phon
y of
the
Mid
dle
Age
s an
d R
enai
ssan
ce.
How
ever
, if
one
exam
ines
Mar
chet
to's
exam
ples
in o
ther
par
ts o
f the
Luc
i- da
rium
, it i
s ev
iden
t th
at h
e al
so c
onsid
ers
repe
ated
not
es o
r lo
ng-h
eld
note
s (n
eith
er o
f whi
ch a
rise
s in
his
disc
ussio
n of
in-
terr
uptio
ns) t
o be
spe
cial
not
es.4
4 One
can
not
e th
at th
is ob
ser-
va
tion
is co
nsist
ent
with
my
earl
ier
form
ulat
ion
of s
peci
al
note
s, fo
r in
a p
air
of r
epea
ted
note
s, th
e se
cond
not
e is
just
af
ter t
he fi
rst b
ut is
nei
ther
just
hig
her t
han,
nor
just
low
er th
an,
the
first
(sin
ce t
hey
are
both
of
the
sam
e pi
tch)
; m
oreo
ver,
lo
ng-h
eld
note
s (e
.g.,
at th
e en
ds o
f phr
ases
) ca
n be
con
sider
ed
to fu
nctio
n te
mpo
rally
as "
tied
repe
ated
not
es."
In
the
case
of m
easu
red
mus
ic, t
here
wou
ld b
e a
dura
tiona
l hi
erar
chy
of s
peci
al-n
ess
acco
rdin
g to
whi
ch v
ario
us n
otes
of a
m
elod
y or
line
cou
ld b
e re
gard
ed a
s mor
e or
less
"sp
ecia
l," o
r to
use
mod
ern
term
s, fo
cal,
wei
ghty
, or
impo
rtan
t. A
nd in
con-
fo
rmity
with
thos
e la
te m
edie
val
and
earl
y R
enai
ssan
ce t
heo-
ri
sts,
who
wer
e la
rgel
y ra
ther
dir
ect f
ollo
wer
s of
Mar
chet
to a
nd
who
reg
arde
d th
e m
odes
of p
olyp
honi
c pi
eces
as
a fu
nctio
n of
th
e m
odes
im
plie
d by
indi
vidu
al li
nes,
one
coul
d ex
tend
Mar
- ch
etto
's co
ncep
tion
of m
odal
impl
icat
ion
to m
uch
mor
e co
mpl
i- ca
ted
text
ures
than
the
mon
opho
ny o
f cha
nt.4
5
44R
epea
ted a
nd lo
ng-h
eld n
otes
arise
in th
e mod
el m
elod
ies t
hat M
arch
etto
em
ploy
s to ill
ustr
ate "
the f
orm
atio
n of m
odes
by sp
ecie
s" in
Luc
idar
ium
, 11, 4
, pa
ssim
, whe
re su
ch no
tes t
end o
verw
helm
ingl
y to co
inci
de w
ith or
ient
ing n
otes
of
the m
elod
y bei
ng ill
ustr
ated
. 45
On
the
appl
icat
ion o
f mod
al id
eas t
o po
lyph
onic
text
ures
, see
Pow
ers,
"Mod
e," e
sp. 3
99-4
06.
Mar
chet
to's
Theo
ry o
f Int
erru
ptio
ns in
Its H
istor
ical
Con
text
With
rega
rd to
its i
mm
edia
te h
istor
ical
con
text
, a
num
ber
of
ques
tions
rem
ain
abou
t M
arch
etto
's fo
rmul
atio
n of
int
erru
p-
tions
. In
the
first
pla
ce,
thou
gh it
mig
ht s
eem
cle
ar h
ow h
is im
- pl
icit
anal
ytic
tech
niqu
e m
ight
be
appl
ied
to c
hant
, it i
s not
nec
- es
sari
ly so
cle
ar h
ow it
mig
ht b
e ap
plie
d to
mea
sure
d m
usic
or
poly
phon
y of
the
Mid
dle
Age
s an
d R
enai
ssan
ce.
How
ever
, if
one
exam
ines
Mar
chet
to's
exam
ples
in o
ther
par
ts o
f the
Luc
i- da
rium
, it i
s ev
iden
t th
at h
e al
so c
onsid
ers
repe
ated
not
es o
r lo
ng-h
eld
note
s (n
eith
er o
f whi
ch a
rise
s in
his
disc
ussio
n of
in-
terr
uptio
ns) t
o be
spe
cial
not
es.4
4 One
can
not
e th
at th
is ob
ser-
va
tion
is co
nsist
ent
with
my
earl
ier
form
ulat
ion
of s
peci
al
note
s, fo
r in
a p
air
of r
epea
ted
note
s, th
e se
cond
not
e is
just
af
ter t
he fi
rst b
ut is
nei
ther
just
hig
her t
han,
nor
just
low
er th
an,
the
first
(sin
ce t
hey
are
both
of
the
sam
e pi
tch)
; m
oreo
ver,
lo
ng-h
eld
note
s (e
.g.,
at th
e en
ds o
f phr
ases
) ca
n be
con
sider
ed
to fu
nctio
n te
mpo
rally
as "
tied
repe
ated
not
es."
In
the
case
of m
easu
red
mus
ic, t
here
wou
ld b
e a
dura
tiona
l hi
erar
chy
of s
peci
al-n
ess
acco
rdin
g to
whi
ch v
ario
us n
otes
of a
m
elod
y or
line
cou
ld b
e re
gard
ed a
s mor
e or
less
"sp
ecia
l," o
r to
use
mod
ern
term
s, fo
cal,
wei
ghty
, or
impo
rtan
t. A
nd in
con-
fo
rmity
with
thos
e la
te m
edie
val
and
earl
y R
enai
ssan
ce t
heo-
ri
sts,
who
wer
e la
rgel
y ra
ther
dir
ect f
ollo
wer
s of
Mar
chet
to a
nd
who
reg
arde
d th
e m
odes
of p
olyp
honi
c pi
eces
as
a fu
nctio
n of
th
e m
odes
im
plie
d by
indi
vidu
al li
nes,
one
coul
d ex
tend
Mar
- ch
etto
's co
ncep
tion
of m
odal
impl
icat
ion
to m
uch
mor
e co
mpl
i- ca
ted
text
ures
than
the
mon
opho
ny o
f cha
nt.4
5
44R
epea
ted a
nd lo
ng-h
eld n
otes
arise
in th
e mod
el m
elod
ies t
hat M
arch
etto
em
ploy
s to ill
ustr
ate "
the f
orm
atio
n of m
odes
by sp
ecie
s" in
Luc
idar
ium
, 11, 4
, pa
ssim
, whe
re su
ch no
tes t
end o
verw
helm
ingl
y to co
inci
de w
ith or
ient
ing n
otes
of
the m
elod
y bei
ng ill
ustr
ated
. 45
On
the
appl
icat
ion o
f mod
al id
eas t
o po
lyph
onic
text
ures
, see
Pow
ers,
"Mod
e," e
sp. 3
99-4
06.
Mar
chet
to's
Theo
ry o
f Int
erru
ptio
ns in
Its H
istor
ical
Con
text
With
rega
rd to
its i
mm
edia
te h
istor
ical
con
text
, a
num
ber
of
ques
tions
rem
ain
abou
t M
arch
etto
's fo
rmul
atio
n of
int
erru
p-
tions
. In
the
first
pla
ce,
thou
gh it
mig
ht s
eem
cle
ar h
ow h
is im
- pl
icit
anal
ytic
tech
niqu
e m
ight
be
appl
ied
to c
hant
, it i
s not
nec
- es
sari
ly so
cle
ar h
ow it
mig
ht b
e ap
plie
d to
mea
sure
d m
usic
or
poly
phon
y of
the
Mid
dle
Age
s an
d R
enai
ssan
ce.
How
ever
, if
one
exam
ines
Mar
chet
to's
exam
ples
in o
ther
par
ts o
f the
Luc
i- da
rium
, it i
s ev
iden
t th
at h
e al
so c
onsid
ers
repe
ated
not
es o
r lo
ng-h
eld
note
s (n
eith
er o
f whi
ch a
rise
s in
his
disc
ussio
n of
in-
terr
uptio
ns) t
o be
spe
cial
not
es.4
4 One
can
not
e th
at th
is ob
ser-
va
tion
is co
nsist
ent
with
my
earl
ier
form
ulat
ion
of s
peci
al
note
s, fo
r in
a p
air
of r
epea
ted
note
s, th
e se
cond
not
e is
just
af
ter t
he fi
rst b
ut is
nei
ther
just
hig
her t
han,
nor
just
low
er th
an,
the
first
(sin
ce t
hey
are
both
of
the
sam
e pi
tch)
; m
oreo
ver,
lo
ng-h
eld
note
s (e
.g.,
at th
e en
ds o
f phr
ases
) ca
n be
con
sider
ed
to fu
nctio
n te
mpo
rally
as "
tied
repe
ated
not
es."
In
the
case
of m
easu
red
mus
ic, t
here
wou
ld b
e a
dura
tiona
l hi
erar
chy
of s
peci
al-n
ess
acco
rdin
g to
whi
ch v
ario
us n
otes
of a
m
elod
y or
line
cou
ld b
e re
gard
ed a
s mor
e or
less
"sp
ecia
l," o
r to
use
mod
ern
term
s, fo
cal,
wei
ghty
, or
impo
rtan
t. A
nd in
con-
fo
rmity
with
thos
e la
te m
edie
val
and
earl
y R
enai
ssan
ce t
heo-
ri
sts,
who
wer
e la
rgel
y ra
ther
dir
ect f
ollo
wer
s of
Mar
chet
to a
nd
who
reg
arde
d th
e m
odes
of p
olyp
honi
c pi
eces
as
a fu
nctio
n of
th
e m
odes
im
plie
d by
indi
vidu
al li
nes,
one
coul
d ex
tend
Mar
- ch
etto
's co
ncep
tion
of m
odal
impl
icat
ion
to m
uch
mor
e co
mpl
i- ca
ted
text
ures
than
the
mon
opho
ny o
f cha
nt.4
5
44R
epea
ted a
nd lo
ng-h
eld n
otes
arise
in th
e mod
el m
elod
ies t
hat M
arch
etto
em
ploy
s to ill
ustr
ate "
the f
orm
atio
n of m
odes
by sp
ecie
s" in
Luc
idar
ium
, 11, 4
, pa
ssim
, whe
re su
ch no
tes t
end o
verw
helm
ingl
y to co
inci
de w
ith or
ient
ing n
otes
of
the m
elod
y bei
ng ill
ustr
ated
. 45
On
the
appl
icat
ion o
f mod
al id
eas t
o po
lyph
onic
text
ures
, see
Pow
ers,
"Mod
e," e
sp. 3
99-4
06.
Mar
chet
to's
Theo
ry o
f Int
erru
ptio
ns in
Its H
istor
ical
Con
text
With
rega
rd to
its i
mm
edia
te h
istor
ical
con
text
, a
num
ber
of
ques
tions
rem
ain
abou
t M
arch
etto
's fo
rmul
atio
n of
int
erru
p-
tions
. In
the
first
pla
ce,
thou
gh it
mig
ht s
eem
cle
ar h
ow h
is im
- pl
icit
anal
ytic
tech
niqu
e m
ight
be
appl
ied
to c
hant
, it i
s not
nec
- es
sari
ly so
cle
ar h
ow it
mig
ht b
e ap
plie
d to
mea
sure
d m
usic
or
poly
phon
y of
the
Mid
dle
Age
s an
d R
enai
ssan
ce.
How
ever
, if
one
exam
ines
Mar
chet
to's
exam
ples
in o
ther
par
ts o
f the
Luc
i- da
rium
, it i
s ev
iden
t th
at h
e al
so c
onsid
ers
repe
ated
not
es o
r lo
ng-h
eld
note
s (n
eith
er o
f whi
ch a
rise
s in
his
disc
ussio
n of
in-
terr
uptio
ns) t
o be
spe
cial
not
es.4
4 One
can
not
e th
at th
is ob
ser-
va
tion
is co
nsist
ent
with
my
earl
ier
form
ulat
ion
of s
peci
al
note
s, fo
r in
a p
air
of r
epea
ted
note
s, th
e se
cond
not
e is
just
af
ter t
he fi
rst b
ut is
nei
ther
just
hig
her t
han,
nor
just
low
er th
an,
the
first
(sin
ce t
hey
are
both
of
the
sam
e pi
tch)
; m
oreo
ver,
lo
ng-h
eld
note
s (e
.g.,
at th
e en
ds o
f phr
ases
) ca
n be
con
sider
ed
to fu
nctio
n te
mpo
rally
as "
tied
repe
ated
not
es."
In
the
case
of m
easu
red
mus
ic, t
here
wou
ld b
e a
dura
tiona
l hi
erar
chy
of s
peci
al-n
ess
acco
rdin
g to
whi
ch v
ario
us n
otes
of a
m
elod
y or
line
cou
ld b
e re
gard
ed a
s mor
e or
less
"sp
ecia
l," o
r to
use
mod
ern
term
s, fo
cal,
wei
ghty
, or
impo
rtan
t. A
nd in
con-
fo
rmity
with
thos
e la
te m
edie
val
and
earl
y R
enai
ssan
ce t
heo-
ri
sts,
who
wer
e la
rgel
y ra
ther
dir
ect f
ollo
wer
s of
Mar
chet
to a
nd
who
reg
arde
d th
e m
odes
of p
olyp
honi
c pi
eces
as
a fu
nctio
n of
th
e m
odes
im
plie
d by
indi
vidu
al li
nes,
one
coul
d ex
tend
Mar
- ch
etto
's co
ncep
tion
of m
odal
impl
icat
ion
to m
uch
mor
e co
mpl
i- ca
ted
text
ures
than
the
mon
opho
ny o
f cha
nt.4
5
44R
epea
ted a
nd lo
ng-h
eld n
otes
arise
in th
e mod
el m
elod
ies t
hat M
arch
etto
em
ploy
s to ill
ustr
ate "
the f
orm
atio
n of m
odes
by sp
ecie
s" in
Luc
idar
ium
, 11, 4
, pa
ssim
, whe
re su
ch no
tes t
end o
verw
helm
ingl
y to co
inci
de w
ith or
ient
ing n
otes
of
the m
elod
y bei
ng ill
ustr
ated
. 45
On
the
appl
icat
ion o
f mod
al id
eas t
o po
lyph
onic
text
ures
, see
Pow
ers,
"Mod
e," e
sp. 3
99-4
06.
Just
whe
re M
arch
etto
der
ived
his
cent
ral
notio
ns o
f co
m-
mix
ture
and
inte
rrup
tions
fro
m,
and
wha
t w
as t
heir
fat
e, a
re
som
ewha
t di
fficu
lt to
det
erm
ine.
The
idea
that
a c
hang
e m
ight
be
mod
ally
het
erog
eneo
us
had
been
in th
e ai
r for
qui
te a
whi
le
and
the
term
com
mix
ture
(as
wel
l as
its
part
ner
mix
ture
) ha
d be
en i
ntro
duce
d be
fore
Mar
chet
to w
rote
the
Luc
idar
ium
.46
How
ever
, M
arch
etto
's hi
ghly
det
aile
d,
albe
it la
coni
c,
trea
t- m
ent o
f mod
al im
plic
atio
n is
unpr
eced
ente
d as
such
in th
e m
u-
sic th
eore
tical
lite
ratu
re. A
lthou
gh h
is id
ea o
f sys
tem
atic
ally
us-
in
g se
gmen
ts o
f th
e ga
mut
as
exam
ples
of
inte
rrup
tions
mig
ht
have
bee
n de
rive
d fr
om v
ario
us o
f th
e sin
ging
exe
rcise
s th
at
one
finds
in e
arlie
r tr
eatis
es o
n ch
ant,
his
use
of m
elod
ic f
rag-
m
ents
to
illus
trat
e sp
ecifi
c po
ints
abo
ut m
odal
ity i
n pa
rtic
ular
se
ems
to h
ave
been
his
own
inve
ntio
n.
Whe
reas
M
arch
etto
's do
ctri
ne
of c
omm
ixtu
re
lived
on
am
ong
man
y m
ajor
theo
rist
s,47 h
is de
taile
d ex
posit
ion
of in
ter-
ru
ptio
ns se
ems
not t
o ha
ve e
njoy
ed a
s gre
at a
succ
ess.
Cer
tain
ly
the
maj
ority
of t
he m
any
copi
es t
hat w
ere
mad
e of
the
Luci
da-
rium
inc
lude
d th
e pa
ssag
e on
int
erru
ptio
ns.4
8 Fu
rthe
rmor
e,
som
e of
the
anon
ymou
s di
gest
s th
at w
ere
mad
e of
Mar
chet
to's
mod
al t
heor
y in
clud
e th
e m
ater
ial
on i
nter
rupt
ions
.49
How
- ev
er, f
ew m
ajor
theo
rist
s-U
golin
o of
Orv
ieto
is a
n im
port
ant
46Se
e not
e 3, a
bove
. 47
See n
ote 6
, abo
ve, a
nd th
e oth
er th
eori
sts c
ited i
n Pow
ers,
"Mod
e," 3
92-
406.
48Se
e Her
linge
r's L
ucid
ariu
m, 21
-62,
for
desc
ript
ions
of th
e fift
een c
entr
al
man
uscr
ipts
and
p. 5
09 fo
r a li
st o
f the
thir
teen
man
uscr
ipts
that
cont
ain t
he
sect
ion o
n in
terr
uptio
ns.
49E.
g., M
S Be
rgam
o, B
iblio
teca
Civ
ica A
ngel
o M
ai, E
4.37
, fol
s, 69
-106
, fo
l. 84
, cha
p. 31
; MS R
ome,
Bib
liote
ca V
allic
ellia
na, B
83,
fols.
18-
29v,
fol
s. 26
v-27
v; M
S Flo
renc
e Plu
teus
, XX
IX 48
, fol
s. 93
-97v
, fo
ls. 9
6v-9
7; a
nd M
S Fl
oren
ce, B
iblio
teca
Med
icea
Lau
renz
iana
, Ash
burn
ham
1119
, fol
s. 33
-51v
, fo
ls. 4
4-44
v, a
ll of
whi
ch fo
rm an
inte
r-re
late
d gro
up of
ver
sions
of a
sing
le
trea
tise.
Just
whe
re M
arch
etto
der
ived
his
cent
ral
notio
ns o
f co
m-
mix
ture
and
inte
rrup
tions
fro
m,
and
wha
t w
as t
heir
fat
e, a
re
som
ewha
t di
fficu
lt to
det
erm
ine.
The
idea
that
a c
hang
e m
ight
be
mod
ally
het
erog
eneo
us
had
been
in th
e ai
r for
qui
te a
whi
le
and
the
term
com
mix
ture
(as
wel
l as
its
part
ner
mix
ture
) ha
d be
en i
ntro
duce
d be
fore
Mar
chet
to w
rote
the
Luc
idar
ium
.46
How
ever
, M
arch
etto
's hi
ghly
det
aile
d,
albe
it la
coni
c,
trea
t- m
ent o
f mod
al im
plic
atio
n is
unpr
eced
ente
d as
such
in th
e m
u-
sic th
eore
tical
lite
ratu
re. A
lthou
gh h
is id
ea o
f sys
tem
atic
ally
us-
in
g se
gmen
ts o
f th
e ga
mut
as
exam
ples
of
inte
rrup
tions
mig
ht
have
bee
n de
rive
d fr
om v
ario
us o
f th
e sin
ging
exe
rcise
s th
at
one
finds
in e
arlie
r tr
eatis
es o
n ch
ant,
his
use
of m
elod
ic f
rag-
m
ents
to
illus
trat
e sp
ecifi
c po
ints
abo
ut m
odal
ity i
n pa
rtic
ular
se
ems
to h
ave
been
his
own
inve
ntio
n.
Whe
reas
M
arch
etto
's do
ctri
ne
of c
omm
ixtu
re
lived
on
am
ong
man
y m
ajor
theo
rist
s,47 h
is de
taile
d ex
posit
ion
of in
ter-
ru
ptio
ns se
ems
not t
o ha
ve e
njoy
ed a
s gre
at a
succ
ess.
Cer
tain
ly
the
maj
ority
of t
he m
any
copi
es t
hat w
ere
mad
e of
the
Luci
da-
rium
inc
lude
d th
e pa
ssag
e on
int
erru
ptio
ns.4
8 Fu
rthe
rmor
e,
som
e of
the
anon
ymou
s di
gest
s th
at w
ere
mad
e of
Mar
chet
to's
mod
al t
heor
y in
clud
e th
e m
ater
ial
on i
nter
rupt
ions
.49
How
- ev
er, f
ew m
ajor
theo
rist
s-U
golin
o of
Orv
ieto
is a
n im
port
ant
46Se
e not
e 3, a
bove
. 47
See n
ote 6
, abo
ve, a
nd th
e oth
er th
eori
sts c
ited i
n Pow
ers,
"Mod
e," 3
92-
406.
48Se
e Her
linge
r's L
ucid
ariu
m, 21
-62,
for
desc
ript
ions
of th
e fift
een c
entr
al
man
uscr
ipts
and
p. 5
09 fo
r a li
st o
f the
thir
teen
man
uscr
ipts
that
cont
ain t
he
sect
ion o
n in
terr
uptio
ns.
49E.
g., M
S Be
rgam
o, B
iblio
teca
Civ
ica A
ngel
o M
ai, E
4.37
, fol
s, 69
-106
, fo
l. 84
, cha
p. 31
; MS R
ome,
Bib
liote
ca V
allic
ellia
na, B
83,
fols.
18-
29v,
fol
s. 26
v-27
v; M
S Flo
renc
e Plu
teus
, XX
IX 48
, fol
s. 93
-97v
, fo
ls. 9
6v-9
7; a
nd M
S Fl
oren
ce, B
iblio
teca
Med
icea
Lau
renz
iana
, Ash
burn
ham
1119
, fol
s. 33
-51v
, fo
ls. 4
4-44
v, a
ll of
whi
ch fo
rm an
inte
r-re
late
d gro
up of
ver
sions
of a
sing
le
trea
tise.
Just
whe
re M
arch
etto
der
ived
his
cent
ral
notio
ns o
f co
m-
mix
ture
and
inte
rrup
tions
fro
m,
and
wha
t w
as t
heir
fat
e, a
re
som
ewha
t di
fficu
lt to
det
erm
ine.
The
idea
that
a c
hang
e m
ight
be
mod
ally
het
erog
eneo
us
had
been
in th
e ai
r for
qui
te a
whi
le
and
the
term
com
mix
ture
(as
wel
l as
its
part
ner
mix
ture
) ha
d be
en i
ntro
duce
d be
fore
Mar
chet
to w
rote
the
Luc
idar
ium
.46
How
ever
, M
arch
etto
's hi
ghly
det
aile
d,
albe
it la
coni
c,
trea
t- m
ent o
f mod
al im
plic
atio
n is
unpr
eced
ente
d as
such
in th
e m
u-
sic th
eore
tical
lite
ratu
re. A
lthou
gh h
is id
ea o
f sys
tem
atic
ally
us-
in
g se
gmen
ts o
f th
e ga
mut
as
exam
ples
of
inte
rrup
tions
mig
ht
have
bee
n de
rive
d fr
om v
ario
us o
f th
e sin
ging
exe
rcise
s th
at
one
finds
in e
arlie
r tr
eatis
es o
n ch
ant,
his
use
of m
elod
ic f
rag-
m
ents
to
illus
trat
e sp
ecifi
c po
ints
abo
ut m
odal
ity i
n pa
rtic
ular
se
ems
to h
ave
been
his
own
inve
ntio
n.
Whe
reas
M
arch
etto
's do
ctri
ne
of c
omm
ixtu
re
lived
on
am
ong
man
y m
ajor
theo
rist
s,47 h
is de
taile
d ex
posit
ion
of in
ter-
ru
ptio
ns se
ems
not t
o ha
ve e
njoy
ed a
s gre
at a
succ
ess.
Cer
tain
ly
the
maj
ority
of t
he m
any
copi
es t
hat w
ere
mad
e of
the
Luci
da-
rium
inc
lude
d th
e pa
ssag
e on
int
erru
ptio
ns.4
8 Fu
rthe
rmor
e,
som
e of
the
anon
ymou
s di
gest
s th
at w
ere
mad
e of
Mar
chet
to's
mod
al t
heor
y in
clud
e th
e m
ater
ial
on i
nter
rupt
ions
.49
How
- ev
er, f
ew m
ajor
theo
rist
s-U
golin
o of
Orv
ieto
is a
n im
port
ant
46Se
e not
e 3, a
bove
. 47
See n
ote 6
, abo
ve, a
nd th
e oth
er th
eori
sts c
ited i
n Pow
ers,
"Mod
e," 3
92-
406.
48Se
e Her
linge
r's L
ucid
ariu
m, 21
-62,
for
desc
ript
ions
of th
e fift
een c
entr
al
man
uscr
ipts
and
p. 5
09 fo
r a li
st o
f the
thir
teen
man
uscr
ipts
that
cont
ain t
he
sect
ion o
n in
terr
uptio
ns.
49E.
g., M
S Be
rgam
o, B
iblio
teca
Civ
ica A
ngel
o M
ai, E
4.37
, fol
s, 69
-106
, fo
l. 84
, cha
p. 31
; MS R
ome,
Bib
liote
ca V
allic
ellia
na, B
83,
fols.
18-
29v,
fol
s. 26
v-27
v; M
S Flo
renc
e Plu
teus
, XX
IX 48
, fol
s. 93
-97v
, fo
ls. 9
6v-9
7; a
nd M
S Fl
oren
ce, B
iblio
teca
Med
icea
Lau
renz
iana
, Ash
burn
ham
1119
, fol
s. 33
-51v
, fo
ls. 4
4-44
v, a
ll of
whi
ch fo
rm an
inte
r-re
late
d gro
up of
ver
sions
of a
sing
le
trea
tise.
Just
whe
re M
arch
etto
der
ived
his
cent
ral
notio
ns o
f co
m-
mix
ture
and
inte
rrup
tions
fro
m,
and
wha
t w
as t
heir
fat
e, a
re
som
ewha
t di
fficu
lt to
det
erm
ine.
The
idea
that
a c
hang
e m
ight
be
mod
ally
het
erog
eneo
us
had
been
in th
e ai
r for
qui
te a
whi
le
and
the
term
com
mix
ture
(as
wel
l as
its
part
ner
mix
ture
) ha
d be
en i
ntro
duce
d be
fore
Mar
chet
to w
rote
the
Luc
idar
ium
.46
How
ever
, M
arch
etto
's hi
ghly
det
aile
d,
albe
it la
coni
c,
trea
t- m
ent o
f mod
al im
plic
atio
n is
unpr
eced
ente
d as
such
in th
e m
u-
sic th
eore
tical
lite
ratu
re. A
lthou
gh h
is id
ea o
f sys
tem
atic
ally
us-
in
g se
gmen
ts o
f th
e ga
mut
as
exam
ples
of
inte
rrup
tions
mig
ht
have
bee
n de
rive
d fr
om v
ario
us o
f th
e sin
ging
exe
rcise
s th
at
one
finds
in e
arlie
r tr
eatis
es o
n ch
ant,
his
use
of m
elod
ic f
rag-
m
ents
to
illus
trat
e sp
ecifi
c po
ints
abo
ut m
odal
ity i
n pa
rtic
ular
se
ems
to h
ave
been
his
own
inve
ntio
n.
Whe
reas
M
arch
etto
's do
ctri
ne
of c
omm
ixtu
re
lived
on
am
ong
man
y m
ajor
theo
rist
s,47 h
is de
taile
d ex
posit
ion
of in
ter-
ru
ptio
ns se
ems
not t
o ha
ve e
njoy
ed a
s gre
at a
succ
ess.
Cer
tain
ly
the
maj
ority
of t
he m
any
copi
es t
hat w
ere
mad
e of
the
Luci
da-
rium
inc
lude
d th
e pa
ssag
e on
int
erru
ptio
ns.4
8 Fu
rthe
rmor
e,
som
e of
the
anon
ymou
s di
gest
s th
at w
ere
mad
e of
Mar
chet
to's
mod
al t
heor
y in
clud
e th
e m
ater
ial
on i
nter
rupt
ions
.49
How
- ev
er, f
ew m
ajor
theo
rist
s-U
golin
o of
Orv
ieto
is a
n im
port
ant
46Se
e not
e 3, a
bove
. 47
See n
ote 6
, abo
ve, a
nd th
e oth
er th
eori
sts c
ited i
n Pow
ers,
"Mod
e," 3
92-
406.
48Se
e Her
linge
r's L
ucid
ariu
m, 21
-62,
for
desc
ript
ions
of th
e fift
een c
entr
al
man
uscr
ipts
and
p. 5
09 fo
r a li
st o
f the
thir
teen
man
uscr
ipts
that
cont
ain t
he
sect
ion o
n in
terr
uptio
ns.
49E.
g., M
S Be
rgam
o, B
iblio
teca
Civ
ica A
ngel
o M
ai, E
4.37
, fol
s, 69
-106
, fo
l. 84
, cha
p. 31
; MS R
ome,
Bib
liote
ca V
allic
ellia
na, B
83,
fols.
18-
29v,
fol
s. 26
v-27
v; M
S Flo
renc
e Plu
teus
, XX
IX 48
, fol
s. 93
-97v
, fo
ls. 9
6v-9
7; a
nd M
S Fl
oren
ce, B
iblio
teca
Med
icea
Lau
renz
iana
, Ash
burn
ham
1119
, fol
s. 33
-51v
, fo
ls. 4
4-44
v, a
ll of
whi
ch fo
rm an
inte
r-re
late
d gro
up of
ver
sions
of a
sing
le
trea
tise.
Just
whe
re M
arch
etto
der
ived
his
cent
ral
notio
ns o
f co
m-
mix
ture
and
inte
rrup
tions
fro
m,
and
wha
t w
as t
heir
fat
e, a
re
som
ewha
t di
fficu
lt to
det
erm
ine.
The
idea
that
a c
hang
e m
ight
be
mod
ally
het
erog
eneo
us
had
been
in th
e ai
r for
qui
te a
whi
le
and
the
term
com
mix
ture
(as
wel
l as
its
part
ner
mix
ture
) ha
d be
en i
ntro
duce
d be
fore
Mar
chet
to w
rote
the
Luc
idar
ium
.46
How
ever
, M
arch
etto
's hi
ghly
det
aile
d,
albe
it la
coni
c,
trea
t- m
ent o
f mod
al im
plic
atio
n is
unpr
eced
ente
d as
such
in th
e m
u-
sic th
eore
tical
lite
ratu
re. A
lthou
gh h
is id
ea o
f sys
tem
atic
ally
us-
in
g se
gmen
ts o
f th
e ga
mut
as
exam
ples
of
inte
rrup
tions
mig
ht
have
bee
n de
rive
d fr
om v
ario
us o
f th
e sin
ging
exe
rcise
s th
at
one
finds
in e
arlie
r tr
eatis
es o
n ch
ant,
his
use
of m
elod
ic f
rag-
m
ents
to
illus
trat
e sp
ecifi
c po
ints
abo
ut m
odal
ity i
n pa
rtic
ular
se
ems
to h
ave
been
his
own
inve
ntio
n.
Whe
reas
M
arch
etto
's do
ctri
ne
of c
omm
ixtu
re
lived
on
am
ong
man
y m
ajor
theo
rist
s,47 h
is de
taile
d ex
posit
ion
of in
ter-
ru
ptio
ns se
ems
not t
o ha
ve e
njoy
ed a
s gre
at a
succ
ess.
Cer
tain
ly
the
maj
ority
of t
he m
any
copi
es t
hat w
ere
mad
e of
the
Luci
da-
rium
inc
lude
d th
e pa
ssag
e on
int
erru
ptio
ns.4
8 Fu
rthe
rmor
e,
som
e of
the
anon
ymou
s di
gest
s th
at w
ere
mad
e of
Mar
chet
to's
mod
al t
heor
y in
clud
e th
e m
ater
ial
on i
nter
rupt
ions
.49
How
- ev
er, f
ew m
ajor
theo
rist
s-U
golin
o of
Orv
ieto
is a
n im
port
ant
46Se
e not
e 3, a
bove
. 47
See n
ote 6
, abo
ve, a
nd th
e oth
er th
eori
sts c
ited i
n Pow
ers,
"Mod
e," 3
92-
406.
48Se
e Her
linge
r's L
ucid
ariu
m, 21
-62,
for
desc
ript
ions
of th
e fift
een c
entr
al
man
uscr
ipts
and
p. 5
09 fo
r a li
st o
f the
thir
teen
man
uscr
ipts
that
cont
ain t
he
sect
ion o
n in
terr
uptio
ns.
49E.
g., M
S Be
rgam
o, B
iblio
teca
Civ
ica A
ngel
o M
ai, E
4.37
, fol
s, 69
-106
, fo
l. 84
, cha
p. 31
; MS R
ome,
Bib
liote
ca V
allic
ellia
na, B
83,
fols.
18-
29v,
fol
s. 26
v-27
v; M
S Flo
renc
e Plu
teus
, XX
IX 48
, fol
s. 93
-97v
, fo
ls. 9
6v-9
7; a
nd M
S Fl
oren
ce, B
iblio
teca
Med
icea
Lau
renz
iana
, Ash
burn
ham
1119
, fol
s. 33
-51v
, fo
ls. 4
4-44
v, a
ll of
whi
ch fo
rm an
inte
r-re
late
d gro
up of
ver
sions
of a
sing
le
trea
tise.
Just
whe
re M
arch
etto
der
ived
his
cent
ral
notio
ns o
f co
m-
mix
ture
and
inte
rrup
tions
fro
m,
and
wha
t w
as t
heir
fat
e, a
re
som
ewha
t di
fficu
lt to
det
erm
ine.
The
idea
that
a c
hang
e m
ight
be
mod
ally
het
erog
eneo
us
had
been
in th
e ai
r for
qui
te a
whi
le
and
the
term
com
mix
ture
(as
wel
l as
its
part
ner
mix
ture
) ha
d be
en i
ntro
duce
d be
fore
Mar
chet
to w
rote
the
Luc
idar
ium
.46
How
ever
, M
arch
etto
's hi
ghly
det
aile
d,
albe
it la
coni
c,
trea
t- m
ent o
f mod
al im
plic
atio
n is
unpr
eced
ente
d as
such
in th
e m
u-
sic th
eore
tical
lite
ratu
re. A
lthou
gh h
is id
ea o
f sys
tem
atic
ally
us-
in
g se
gmen
ts o
f th
e ga
mut
as
exam
ples
of
inte
rrup
tions
mig
ht
have
bee
n de
rive
d fr
om v
ario
us o
f th
e sin
ging
exe
rcise
s th
at
one
finds
in e
arlie
r tr
eatis
es o
n ch
ant,
his
use
of m
elod
ic f
rag-
m
ents
to
illus
trat
e sp
ecifi
c po
ints
abo
ut m
odal
ity i
n pa
rtic
ular
se
ems
to h
ave
been
his
own
inve
ntio
n.
Whe
reas
M
arch
etto
's do
ctri
ne
of c
omm
ixtu
re
lived
on
am
ong
man
y m
ajor
theo
rist
s,47 h
is de
taile
d ex
posit
ion
of in
ter-
ru
ptio
ns se
ems
not t
o ha
ve e
njoy
ed a
s gre
at a
succ
ess.
Cer
tain
ly
the
maj
ority
of t
he m
any
copi
es t
hat w
ere
mad
e of
the
Luci
da-
rium
inc
lude
d th
e pa
ssag
e on
int
erru
ptio
ns.4
8 Fu
rthe
rmor
e,
som
e of
the
anon
ymou
s di
gest
s th
at w
ere
mad
e of
Mar
chet
to's
mod
al t
heor
y in
clud
e th
e m
ater
ial
on i
nter
rupt
ions
.49
How
- ev
er, f
ew m
ajor
theo
rist
s-U
golin
o of
Orv
ieto
is a
n im
port
ant
46Se
e not
e 3, a
bove
. 47
See n
ote 6
, abo
ve, a
nd th
e oth
er th
eori
sts c
ited i
n Pow
ers,
"Mod
e," 3
92-
406.
48Se
e Her
linge
r's L
ucid
ariu
m, 21
-62,
for
desc
ript
ions
of th
e fift
een c
entr
al
man
uscr
ipts
and
p. 5
09 fo
r a li
st o
f the
thir
teen
man
uscr
ipts
that
cont
ain t
he
sect
ion o
n in
terr
uptio
ns.
49E.
g., M
S Be
rgam
o, B
iblio
teca
Civ
ica A
ngel
o M
ai, E
4.37
, fol
s, 69
-106
, fo
l. 84
, cha
p. 31
; MS R
ome,
Bib
liote
ca V
allic
ellia
na, B
83,
fols.
18-
29v,
fol
s. 26
v-27
v; M
S Flo
renc
e Plu
teus
, XX
IX 48
, fol
s. 93
-97v
, fo
ls. 9
6v-9
7; a
nd M
S Fl
oren
ce, B
iblio
teca
Med
icea
Lau
renz
iana
, Ash
burn
ham
1119
, fol
s. 33
-51v
, fo
ls. 4
4-44
v, a
ll of
whi
ch fo
rm an
inte
r-re
late
d gro
up of
ver
sions
of a
sing
le
trea
tise.
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
135
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
135
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
135
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
135
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
135
Mar
chet
to's T
heor
y of C
omm
ixtu
re and I
nter
rupt
ions
135
exce
ptio
n50-
seem
to h
ave b
een
draw
n to
the i
dea o
f int
erru
p-
tion.
A n
umbe
r of e
xpla
natio
ns m
ight
be o
ffere
d: 1)
the p
as-
sage
on in
terr
uptio
ns m
ight
have
been
very
diffi
cult f
or re
ader
s to
und
erst
and (
espe
cial
ly in
view
of th
e num
erou
s cor
rupt
ions
th
at w
ere
intr
oduc
ed in
to th
e m
anus
crip
t trad
ition
);51
2) t
o ju
dge f
rom
the l
arge
num
ber a
nd w
ide d
isper
sion i
n sp
ace a
nd
time o
f the
ext
ant m
anus
crip
t copi
es in
whi
ch it
app
ears
, the
sect
ion o
n in
terr
uptio
ns m
ight
wel
l hav
e bee
n so
read
ily av
aila
- bl
e in
its o
rigi
nal f
orm
that
expo
sitio
n by
late
r, a
nd p
ossib
ly
less
er, t
heor
ists w
ould
hav
e bee
n re
dund
ant;5
2 3) th
e id
ea o
f sp
ecia
l not
es, w
hich
is ce
ntra
l to a
n un
ders
tand
ing o
f the
pas
- sa
ge o
n in
terr
uptio
ns, m
ight
wel
l hav
e bee
n as
simila
ted,
con-
sc
ious
ly or
unco
nsci
ously
, by l
ater
theo
rist
s, and
thus
mig
ht no
t ha
ve re
quir
ed se
para
te tr
eatm
ent, f
or to
judg
e fro
m th
eir t
rea-
tis
es, t
heor
ists w
ho fo
llow
ed M
arch
etto
seem
to h
ave e
xpec
ted
50Se
e Ugo
lino
of O
rvie
to, D
ecla
ratio
Mus
icae
Disc
iplin
ae, e
d. A
lber
t Sea
y (R
ome:
Am
eric
an In
stitu
te of
Mus
icol
ogy,
3 vo
ls., 1
959 [
Cor
pus S
crip
toru
m
Mus
icae
, 7]),
bk.
1, c
hap.
46, 1
7-24
(Se
ay ed
ition
, 1:8
3).
51Se
e esp
ecia
lly no
te 27
abov
e.
52Se
e not
e 48 a
bove
.
exce
ptio
n50-
seem
to h
ave b
een
draw
n to
the i
dea o
f int
erru
p-
tion.
A n
umbe
r of e
xpla
natio
ns m
ight
be o
ffere
d: 1)
the p
as-
sage
on in
terr
uptio
ns m
ight
have
been
very
diffi
cult f
or re
ader
s to
und
erst
and (
espe
cial
ly in
view
of th
e num
erou
s cor
rupt
ions
th
at w
ere
intr
oduc
ed in
to th
e m
anus
crip
t trad
ition
);51
2) t
o ju
dge f
rom
the l
arge
num
ber a
nd w
ide d
isper
sion i
n sp
ace a
nd
time o
f the
ext
ant m
anus
crip
t copi
es in
whi
ch it
app
ears
, the
sect
ion o
n in
terr
uptio
ns m
ight
wel
l hav
e bee
n so
read
ily av
aila
- bl
e in
its o
rigi
nal f
orm
that
expo
sitio
n by
late
r, a
nd p
ossib
ly
less
er, t
heor
ists w
ould
hav
e bee
n re
dund
ant;5
2 3) th
e id
ea o
f sp
ecia
l not
es, w
hich
is ce
ntra
l to a
n un
ders
tand
ing o
f the
pas
- sa
ge o
n in
terr
uptio
ns, m
ight
wel
l hav
e bee
n as
simila
ted,
con-
sc
ious
ly or
unco
nsci
ously
, by l
ater
theo
rist
s, and
thus
mig
ht no
t ha
ve re
quir
ed se
para
te tr
eatm
ent, f
or to
judg
e fro
m th
eir t
rea-
tis
es, t
heor
ists w
ho fo
llow
ed M
arch
etto
seem
to h
ave e
xpec
ted
50Se
e Ugo
lino
of O
rvie
to, D
ecla
ratio
Mus
icae
Disc
iplin
ae, e
d. A
lber
t Sea
y (R
ome:
Am
eric
an In
stitu
te of
Mus
icol
ogy,
3 vo
ls., 1
959 [
Cor
pus S
crip
toru
m
Mus
icae
, 7]),
bk.
1, c
hap.
46, 1
7-24
(Se
ay ed
ition
, 1:8
3).
51Se
e esp
ecia
lly no
te 27
abov
e.
52Se
e not
e 48 a
bove
.
exce
ptio
n50-
seem
to h
ave b
een
draw
n to
the i
dea o
f int
erru
p-
tion.
A n
umbe
r of e
xpla
natio
ns m
ight
be o
ffere
d: 1)
the p
as-
sage
on in
terr
uptio
ns m
ight
have
been
very
diffi
cult f
or re
ader
s to
und
erst
and (
espe
cial
ly in
view
of th
e num
erou
s cor
rupt
ions
th
at w
ere
intr
oduc
ed in
to th
e m
anus
crip
t trad
ition
);51
2) t
o ju
dge f
rom
the l
arge
num
ber a
nd w
ide d
isper
sion i
n sp
ace a
nd
time o
f the
ext
ant m
anus
crip
t copi
es in
whi
ch it
app
ears
, the
sect
ion o
n in
terr
uptio
ns m
ight
wel
l hav
e bee
n so
read
ily av
aila
- bl
e in
its o
rigi
nal f
orm
that
expo
sitio
n by
late
r, a
nd p
ossib
ly
less
er, t
heor
ists w
ould
hav
e bee
n re
dund
ant;5
2 3) th
e id
ea o
f sp
ecia
l not
es, w
hich
is ce
ntra
l to a
n un
ders
tand
ing o
f the
pas
- sa
ge o
n in
terr
uptio
ns, m
ight
wel
l hav
e bee
n as
simila
ted,
con-
sc
ious
ly or
unco
nsci
ously
, by l
ater
theo
rist
s, and
thus
mig
ht no
t ha
ve re
quir
ed se
para
te tr
eatm
ent, f
or to
judg
e fro
m th
eir t
rea-
tis
es, t
heor
ists w
ho fo
llow
ed M
arch
etto
seem
to h
ave e
xpec
ted
50Se
e Ugo
lino
of O
rvie
to, D
ecla
ratio
Mus
icae
Disc
iplin
ae, e
d. A
lber
t Sea
y (R
ome:
Am
eric
an In
stitu
te of
Mus
icol
ogy,
3 vo
ls., 1
959 [
Cor
pus S
crip
toru
m
Mus
icae
, 7]),
bk.
1, c
hap.
46, 1
7-24
(Se
ay ed
ition
, 1:8
3).
51Se
e esp
ecia
lly no
te 27
abov
e.
52Se
e not
e 48 a
bove
.
exce
ptio
n50-
seem
to h
ave b
een
draw
n to
the i
dea o
f int
erru
p-
tion.
A n
umbe
r of e
xpla
natio
ns m
ight
be o
ffere
d: 1)
the p
as-
sage
on in
terr
uptio
ns m
ight
have
been
very
diffi
cult f
or re
ader
s to
und
erst
and (
espe
cial
ly in
view
of th
e num
erou
s cor
rupt
ions
th
at w
ere
intr
oduc
ed in
to th
e m
anus
crip
t trad
ition
);51
2) t
o ju
dge f
rom
the l
arge
num
ber a
nd w
ide d
isper
sion i
n sp
ace a
nd
time o
f the
ext
ant m
anus
crip
t copi
es in
whi
ch it
app
ears
, the
sect
ion o
n in
terr
uptio
ns m
ight
wel
l hav
e bee
n so
read
ily av
aila
- bl
e in
its o
rigi
nal f
orm
that
expo
sitio
n by
late
r, a
nd p
ossib
ly
less
er, t
heor
ists w
ould
hav
e bee
n re
dund
ant;5
2 3) th
e id
ea o
f sp
ecia
l not
es, w
hich
is ce
ntra
l to a
n un
ders
tand
ing o
f the
pas
- sa
ge o
n in
terr
uptio
ns, m
ight
wel
l hav
e bee
n as
simila
ted,
con-
sc
ious
ly or
unco
nsci
ously
, by l
ater
theo
rist
s, and
thus
mig
ht no
t ha
ve re
quir
ed se
para
te tr
eatm
ent, f
or to
judg
e fro
m th
eir t
rea-
tis
es, t
heor
ists w
ho fo
llow
ed M
arch
etto
seem
to h
ave e
xpec
ted
50Se
e Ugo
lino
of O
rvie
to, D
ecla
ratio
Mus
icae
Disc
iplin
ae, e
d. A
lber
t Sea
y (R
ome:
Am
eric
an In
stitu
te of
Mus
icol
ogy,
3 vo
ls., 1
959 [
Cor
pus S
crip
toru
m
Mus
icae
, 7]),
bk.
1, c
hap.
46, 1
7-24
(Se
ay ed
ition
, 1:8
3).
51Se
e esp
ecia
lly no
te 27
abov
e.
52Se
e not
e 48 a
bove
.
exce
ptio
n50-
seem
to h
ave b
een
draw
n to
the i
dea o
f int
erru
p-
tion.
A n
umbe
r of e
xpla
natio
ns m
ight
be o
ffere
d: 1)
the p
as-
sage
on in
terr
uptio
ns m
ight
have
been
very
diffi
cult f
or re
ader
s to
und
erst
and (
espe
cial
ly in
view
of th
e num
erou
s cor
rupt
ions
th
at w
ere
intr
oduc
ed in
to th
e m
anus
crip
t trad
ition
);51
2) t
o ju
dge f
rom
the l
arge
num
ber a
nd w
ide d
isper
sion i
n sp
ace a
nd
time o
f the
ext
ant m
anus
crip
t copi
es in
whi
ch it
app
ears
, the
sect
ion o
n in
terr
uptio
ns m
ight
wel
l hav
e bee
n so
read
ily av
aila
- bl
e in
its o
rigi
nal f
orm
that
expo
sitio
n by
late
r, a
nd p
ossib
ly
less
er, t
heor
ists w
ould
hav
e bee
n re
dund
ant;5
2 3) th
e id
ea o
f sp
ecia
l not
es, w
hich
is ce
ntra
l to a
n un
ders
tand
ing o
f the
pas
- sa
ge o
n in
terr
uptio
ns, m
ight
wel
l hav
e bee
n as
simila
ted,
con-
sc
ious
ly or
unco
nsci
ously
, by l
ater
theo
rist
s, and
thus
mig
ht no
t ha
ve re
quir
ed se
para
te tr
eatm
ent, f
or to
judg
e fro
m th
eir t
rea-
tis
es, t
heor
ists w
ho fo
llow
ed M
arch
etto
seem
to h
ave e
xpec
ted
50Se
e Ugo
lino
of O
rvie
to, D
ecla
ratio
Mus
icae
Disc
iplin
ae, e
d. A
lber
t Sea
y (R
ome:
Am
eric
an In
stitu
te of
Mus
icol
ogy,
3 vo
ls., 1
959 [
Cor
pus S
crip
toru
m
Mus
icae
, 7]),
bk.
1, c
hap.
46, 1
7-24
(Se
ay ed
ition
, 1:8
3).
51Se
e esp
ecia
lly no
te 27
abov
e.
52Se
e not
e 48 a
bove
.
exce
ptio
n50-
seem
to h
ave b
een
draw
n to
the i
dea o
f int
erru
p-
tion.
A n
umbe
r of e
xpla
natio
ns m
ight
be o
ffere
d: 1)
the p
as-
sage
on in
terr
uptio
ns m
ight
have
been
very
diffi
cult f
or re
ader
s to
und
erst
and (
espe
cial
ly in
view
of th
e num
erou
s cor
rupt
ions
th
at w
ere
intr
oduc
ed in
to th
e m
anus
crip
t trad
ition
);51
2) t
o ju
dge f
rom
the l
arge
num
ber a
nd w
ide d
isper
sion i
n sp
ace a
nd
time o
f the
ext
ant m
anus
crip
t copi
es in
whi
ch it
app
ears
, the
sect
ion o
n in
terr
uptio
ns m
ight
wel
l hav
e bee
n so
read
ily av
aila
- bl
e in
its o
rigi
nal f
orm
that
expo
sitio
n by
late
r, a
nd p
ossib
ly
less
er, t
heor
ists w
ould
hav
e bee
n re
dund
ant;5
2 3) th
e id
ea o
f sp
ecia
l not
es, w
hich
is ce
ntra
l to a
n un
ders
tand
ing o
f the
pas
- sa
ge o
n in
terr
uptio
ns, m
ight
wel
l hav
e bee
n as
simila
ted,
con-
sc
ious
ly or
unco
nsci
ously
, by l
ater
theo
rist
s, and
thus
mig
ht no
t ha
ve re
quir
ed se
para
te tr
eatm
ent, f
or to
judg
e fro
m th
eir t
rea-
tis
es, t
heor
ists w
ho fo
llow
ed M
arch
etto
seem
to h
ave e
xpec
ted
50Se
e Ugo
lino
of O
rvie
to, D
ecla
ratio
Mus
icae
Disc
iplin
ae, e
d. A
lber
t Sea
y (R
ome:
Am
eric
an In
stitu
te of
Mus
icol
ogy,
3 vo
ls., 1
959 [
Cor
pus S
crip
toru
m
Mus
icae
, 7]),
bk.
1, c
hap.
46, 1
7-24
(Se
ay ed
ition
, 1:8
3).
51Se
e esp
ecia
lly no
te 27
abov
e.
52Se
e not
e 48 a
bove
.
thei
r rea
ders
to co
mpr
ehen
d the
not
ion o
f a sp
ecia
l not
e in
or-
der t
o un
ders
tand
the e
xam
ples
of c
omm
ixtu
re th
at th
ey pr
e-
sent
ed.5
3 W
hate
ver m
ight
have
bee
n th
e rea
son f
or th
e app
aren
t ne-
gl
ect o
f M
arch
etto
's do
ctri
ne of
inte
rrup
tions
, a n
umbe
r of
poin
ts re
mai
n cle
ar. F
irst
, Mar
chet
to's a
ccou
nt of
inte
rrup
tions
co
nstit
utes
the
key
that
ope
ns th
e do
or to
a d
etai
led
unde
r-
stan
ding
of c
omm
ixtu
re. S
econ
dly,
the i
deas
of s
peci
al no
tes
and o
rien
ting n
otes
, cen
tral
to, b
ut on
ly im
plic
it in,
Mar
chet
- to
's ac
coun
t of i
nter
rupt
ions
, open
the d
oor t
o a
note
-by-
note
fu
nctio
nal a
naly
sis of
med
ieva
l and
Ren
aiss
ance
mus
ic. A
nd
final
ly, th
e con
cept
ion o
f mus
ic th
at se
ems i
mpl
icit i
n Mar
chet
- to
's ac
coun
t of i
nter
rupt
ions
is ve
ry m
oder
n. In
add
ition
to it
s im
port
ance
in th
e hi
stor
y of l
ate
med
ieva
l and
earl
y Ren
ais-
sa
nce m
odal
theo
ry, M
arch
etto
's doc
trin
e of i
nter
rupt
ions
pos-
se
sses
an im
port
ance
in th
e bro
ader
hist
ory o
f mus
ic th
eory
in
gene
ral, t
hat is
, in t
he hi
stor
y of m
usic
theo
ry su
b spe
cie a
eter
ni-
tatis
.
thei
r rea
ders
to co
mpr
ehen
d the
not
ion o
f a sp
ecia
l not
e in
or-
der t
o un
ders
tand
the e
xam
ples
of c
omm
ixtu
re th
at th
ey pr
e-
sent
ed.5
3 W
hate
ver m
ight
have
bee
n th
e rea
son f
or th
e app
aren
t ne-
gl
ect o
f M
arch
etto
's do
ctri
ne of
inte
rrup
tions
, a n
umbe
r of
poin
ts re
mai
n cle
ar. F
irst
, Mar
chet
to's a
ccou
nt of
inte
rrup
tions
co
nstit
utes
the
key
that
ope
ns th
e do
or to
a d
etai
led
unde
r-
stan
ding
of c
omm
ixtu
re. S
econ
dly,
the i
deas
of s
peci
al no
tes
and o
rien
ting n
otes
, cen
tral
to, b
ut on
ly im
plic
it in,
Mar
chet
- to
's ac
coun
t of i
nter
rupt
ions
, open
the d
oor t
o a
note
-by-
note
fu
nctio
nal a
naly
sis of
med
ieva
l and
Ren
aiss
ance
mus
ic. A
nd
final
ly, th
e con
cept
ion o
f mus
ic th
at se
ems i
mpl
icit i
n Mar
chet
- to
's ac
coun
t of i
nter
rupt
ions
is ve
ry m
oder
n. In
add
ition
to it
s im
port
ance
in th
e hi
stor
y of l
ate
med
ieva
l and
earl
y Ren
ais-
sa
nce m
odal
theo
ry, M
arch
etto
's doc
trin
e of i
nter
rupt
ions
pos-
se
sses
an im
port
ance
in th
e bro
ader
hist
ory o
f mus
ic th
eory
in
gene
ral, t
hat is
, in t
he hi
stor
y of m
usic
theo
ry su
b spe
cie a
eter
ni-
tatis
.
thei
r rea
ders
to co
mpr
ehen
d the
not
ion o
f a sp
ecia
l not
e in
or-
der t
o un
ders
tand
the e
xam
ples
of c
omm
ixtu
re th
at th
ey pr
e-
sent
ed.5
3 W
hate
ver m
ight
have
bee
n th
e rea
son f
or th
e app
aren
t ne-
gl
ect o
f M
arch
etto
's do
ctri
ne of
inte
rrup
tions
, a n
umbe
r of
poin
ts re
mai
n cle
ar. F
irst
, Mar
chet
to's a
ccou
nt of
inte
rrup
tions
co
nstit
utes
the
key
that
ope
ns th
e do
or to
a d
etai
led
unde
r-
stan
ding
of c
omm
ixtu
re. S
econ
dly,
the i
deas
of s
peci
al no
tes
and o
rien
ting n
otes
, cen
tral
to, b
ut on
ly im
plic
it in,
Mar
chet
- to
's ac
coun
t of i
nter
rupt
ions
, open
the d
oor t
o a
note
-by-
note
fu
nctio
nal a
naly
sis of
med
ieva
l and
Ren
aiss
ance
mus
ic. A
nd
final
ly, th
e con
cept
ion o
f mus
ic th
at se
ems i
mpl
icit i
n Mar
chet
- to
's ac
coun
t of i
nter
rupt
ions
is ve
ry m
oder
n. In
add
ition
to it
s im
port
ance
in th
e hi
stor
y of l
ate
med
ieva
l and
earl
y Ren
ais-
sa
nce m
odal
theo
ry, M
arch
etto
's doc
trin
e of i
nter
rupt
ions
pos-
se
sses
an im
port
ance
in th
e bro
ader
hist
ory o
f mus
ic th
eory
in
gene
ral, t
hat is
, in t
he hi
stor
y of m
usic
theo
ry su
b spe
cie a
eter
ni-
tatis
.
thei
r rea
ders
to co
mpr
ehen
d the
not
ion o
f a sp
ecia
l not
e in
or-
der t
o un
ders
tand
the e
xam
ples
of c
omm
ixtu
re th
at th
ey pr
e-
sent
ed.5
3 W
hate
ver m
ight
have
bee
n th
e rea
son f
or th
e app
aren
t ne-
gl
ect o
f M
arch
etto
's do
ctri
ne of
inte
rrup
tions
, a n
umbe
r of
poin
ts re
mai
n cle
ar. F
irst
, Mar
chet
to's a
ccou
nt of
inte
rrup
tions
co
nstit
utes
the
key
that
ope
ns th
e do
or to
a d
etai
led
unde
r-
stan
ding
of c
omm
ixtu
re. S
econ
dly,
the i
deas
of s
peci
al no
tes
and o
rien
ting n
otes
, cen
tral
to, b
ut on
ly im
plic
it in,
Mar
chet
- to
's ac
coun
t of i
nter
rupt
ions
, open
the d
oor t
o a
note
-by-
note
fu
nctio
nal a
naly
sis of
med
ieva
l and
Ren
aiss
ance
mus
ic. A
nd
final
ly, th
e con
cept
ion o
f mus
ic th
at se
ems i
mpl
icit i
n Mar
chet
- to
's ac
coun
t of i
nter
rupt
ions
is ve
ry m
oder
n. In
add
ition
to it
s im
port
ance
in th
e hi
stor
y of l
ate
med
ieva
l and
earl
y Ren
ais-
sa
nce m
odal
theo
ry, M
arch
etto
's doc
trin
e of i
nter
rupt
ions
pos-
se
sses
an im
port
ance
in th
e bro
ader
hist
ory o
f mus
ic th
eory
in
gene
ral, t
hat is
, in t
he hi
stor
y of m
usic
theo
ry su
b spe
cie a
eter
ni-
tatis
.
thei
r rea
ders
to co
mpr
ehen
d the
not
ion o
f a sp
ecia
l not
e in
or-
der t
o un
ders
tand
the e
xam
ples
of c
omm
ixtu
re th
at th
ey pr
e-
sent
ed.5
3 W
hate
ver m
ight
have
bee
n th
e rea
son f
or th
e app
aren
t ne-
gl
ect o
f M
arch
etto
's do
ctri
ne of
inte
rrup
tions
, a n
umbe
r of
poin
ts re
mai
n cle
ar. F
irst
, Mar
chet
to's a
ccou
nt of
inte
rrup
tions
co
nstit
utes
the
key
that
ope
ns th
e do
or to
a d
etai
led
unde
r-
stan
ding
of c
omm
ixtu
re. S
econ
dly,
the i
deas
of s
peci
al no
tes
and o
rien
ting n
otes
, cen
tral
to, b
ut on
ly im
plic
it in,
Mar
chet
- to
's ac
coun
t of i
nter
rupt
ions
, open
the d
oor t
o a
note
-by-
note
fu
nctio
nal a
naly
sis of
med
ieva
l and
Ren
aiss
ance
mus
ic. A
nd
final
ly, th
e con
cept
ion o
f mus
ic th
at se
ems i
mpl
icit i
n Mar
chet
- to
's ac
coun
t of i
nter
rupt
ions
is ve
ry m
oder
n. In
add
ition
to it
s im
port
ance
in th
e hi
stor
y of l
ate
med
ieva
l and
earl
y Ren
ais-
sa
nce m
odal
theo
ry, M
arch
etto
's doc
trin
e of i
nter
rupt
ions
pos-
se
sses
an im
port
ance
in th
e bro
ader
hist
ory o
f mus
ic th
eory
in
gene
ral, t
hat is
, in t
he hi
stor
y of m
usic
theo
ry su
b spe
cie a
eter
ni-
tatis
.
thei
r rea
ders
to co
mpr
ehen
d the
not
ion o
f a sp
ecia
l not
e in
or-
der t
o un
ders
tand
the e
xam
ples
of c
omm
ixtu
re th
at th
ey pr
e-
sent
ed.5
3 W
hate
ver m
ight
have
bee
n th
e rea
son f
or th
e app
aren
t ne-
gl
ect o
f M
arch
etto
's do
ctri
ne of
inte
rrup
tions
, a n
umbe
r of
poin
ts re
mai
n cle
ar. F
irst
, Mar
chet
to's a
ccou
nt of
inte
rrup
tions
co
nstit
utes
the
key
that
ope
ns th
e do
or to
a d
etai
led
unde
r-
stan
ding
of c
omm
ixtu
re. S
econ
dly,
the i
deas
of s
peci
al no
tes
and o
rien
ting n
otes
, cen
tral
to, b
ut on
ly im
plic
it in,
Mar
chet
- to
's ac
coun
t of i
nter
rupt
ions
, open
the d
oor t
o a
note
-by-
note
fu
nctio
nal a
naly
sis of
med
ieva
l and
Ren
aiss
ance
mus
ic. A
nd
final
ly, th
e con
cept
ion o
f mus
ic th
at se
ems i
mpl
icit i
n Mar
chet
- to
's ac
coun
t of i
nter
rupt
ions
is ve
ry m
oder
n. In
add
ition
to it
s im
port
ance
in th
e hi
stor
y of l
ate
med
ieva
l and
earl
y Ren
ais-
sa
nce m
odal
theo
ry, M
arch
etto
's doc
trin
e of i
nter
rupt
ions
pos-
se
sses
an im
port
ance
in th
e bro
ader
hist
ory o
f mus
ic th
eory
in
gene
ral, t
hat is
, in t
he hi
stor
y of m
usic
theo
ry su
b spe
cie a
eter
ni-
tatis
.
53Se
e, fo
r exa
mpl
e, T
inct
oris,
Ope
ra Th
eore
tica,
chap
s. 13
-18,
pp.
16-
20.
53Se
e, fo
r exa
mpl
e, T
inct
oris,
Ope
ra Th
eore
tica,
chap
s. 13
-18,
pp.
16-
20.
53Se
e, fo
r exa
mpl
e, T
inct
oris,
Ope
ra Th
eore
tica,
chap
s. 13
-18,
pp.
16-
20.
53Se
e, fo
r exa
mpl
e, T
inct
oris,
Ope
ra Th
eore
tica,
chap
s. 13
-18,
pp.
16-
20.
53Se
e, fo
r exa
mpl
e, T
inct
oris,
Ope
ra Th
eore
tica,
chap
s. 13
-18,
pp.
16-
20.
53Se
e, fo
r exa
mpl
e, T
inct
oris,
Ope
ra Th
eore
tica,
chap
s. 13
-18,
pp.
16-
20.
This
cont
ent d
ownl
oade
d fro
m 1
30.6
3.18
0.14
7 on
Thu
, 21
May
201
5 03
:21:
26 U
TCA
ll us
e su
bjec
t to
JSTO
R Te
rms a
nd C
ondi
tions
