Goodman and the Score (pre-print)

STEFANO PREDELLI – GOODMAN AND THE SCORE

Goodman and the Score

Stefano Predelli

According to the view presented in the central chapters of

Nelson Goodman’s Languages of Art, an event qualifies as a

performance of a musical work w only if it complies with

the score for w. One of the starting points for Goodman’s

analysis is his conviction that in music there is

… a theoretically decisive test for compliance; and

a performance … is or is not strictly a performance

of [a certain] work, according as it does or does

not pass this test. No historical information

concerning the production of the performance can

affect the result.1

Goodman’s assumption of the irrelevance of the historical

and causal profile of a performance has been rightly

questioned in the recent literature on the ontology of

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music. This criticism is often tacitly accompanied by the

conviction that Goodman’s notational analysis of the work-

performance relation is intimately linked to his anti-

historical stance. Jerrold Levinson, for instance, has

commented that

Goodman … has proposed that only strictly

notationally expressible properties of a musical

composition—i.e. roughly just pitches and rhythms—

should be considered definitive of it, but this is

highly counterintuitive and contrary to musical

practice.2

In this essay, I argue that such an identification of

notationally expressible properties with sheer aural

qualities, such as pitches and rhythms, is resistible. I

develop an account of the relationships holding between a

musical work and its performances, which is sensitive to

the performances’ historical and causal properties, and

which conforms to Goodman’s analysis of the role played by

scores as characters in a notational system.

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In the first section of this paper, I present the

central tenets in the analysis of the work-performance

relation in Languages of Art. In the second section, I focus

on Goodman’s brief discussion of instrument specifications,

and I propose an amendment of Goodman’s view, which is

consistent with widespread intuitions regarding the

importance of the means of production involved in a

performance. In section three, I develop Goodman’s

framework so as to account for the idea that a performance

is of a given work only if it participates in an

appropriate causal and historical relation, terminating in

events suitably related to a relevant act of composition.

1. The Score and Notational Systems

According to Goodman, the relationship between a

performance and a musical work is mediated by the score for

that work, in the sense that the score “has as a primary

function the authoritative identification of a work from

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performance to performance.”3 A score may perform such a

primary function only if both of the following conditions

are satisfied: firstly, a score for a work w must

determine the class of events which count as performances

of w; secondly, given a performance (and a particular

notational system), a score must be uniquely recoverable.

These requirements ensure that if we proceed stepwise from

a performance to the score it determines, and from that

score to any performance complying with it, we may never be

able to “pass from a performance to another that is not of

the same work.”4

Such a strong connection between scores and

performances is for Goodman guaranteed by the fact that

scores are characters in a notational system. A notational

system is a syntactic object of a suitable kind, correlated

to its semantic counterparts by a “field of reference.”

Given a field of reference, a character is typically

associated with a class of objects, its compliants. The

relationship between a character and its compliants is

regulated by three constraints, i.e., roughly,

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(i) nonambiguity: tokens of a character may not by

associated with distinct classes of compliants;

(ii) disjointness: the compliance classes of distinct

characters may not intersect;

(iii) decidability: given an object, it must be theoretically

possible to decide whether it belongs to the compliance

class of a character.5

An apparently dramatic violation of the requirement of

disjointness is exemplified by redundant systems, i.e.,

systems in which two characters are associated with the

same compliance class. However, Goodman points out,

redundancy is a relatively minor problem with respect to

the role supposedly played by musical scores: on the

assumption that any two scores determining the same class

of performances are associated with a unique work, the loss

of unique recoverability of a score from a performance

becomes of secondary importance. Moreover, “redundancy in a

system is easily removed by discarding all but one of any

set of coextensive terms.”6

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Goodman’s theory of notation is primarily a theory of

ideal scores. It is a theory of scores, in the sense that

the essential features of notationality are closely modeled

on the basis of the function a score is supposed to serve.

A notational system in the appropriate semantic relation to

musical performances must be such that each character in

the system determines a class of performances, and is

uniquely recoverable from any suitable performance. On the

other hand, Goodman’s theory of notation is a theory of

ideal scores, because it does not directly tackle the

question whether what we ordinarily label as scores may

indeed be considered as characters in a notational system.

In fact, as Goodman points out, a non irrelevant number of

indications frequently present on ordinary scores must be

considered as inessential, if such objects are to play the

appropriate role with respect to the work-performance

relationship. For instance,

… the verbal language of tempos is not notational.

The tempo words cannot be integral parts of a score

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insofar as the score serves the function of

identifying a work from performance to

performance.7

On the other hand, given Goodman’s insistence that even

“the most brilliant performance with a single wrong note”

does not count as a performance of the relevant work, it is

to be expected that the indications of pitch and relative

duration contained in an ordinary score must be relevant

with respect to the relation between the work associated

with that score and its instances.8 In the following

sections of this paper, I shall evaluate whether other

directions contained in ordinary scores conform to

Goodman’s requirements of notationality, and consequently

qualify as indicative of a musical work’s identifying

properties.

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2. Instrument Specifications

With the exception of indications of pitch, relative

duration, and metronomic specifications, the only aspect of

an ordinary score explicitly considered in Languages of Art is

the specification of the instruments on which the

appropriate tones are to be performed. But, as we shall

see, instrument specifications enter the picture only as

part of Goodman’s solution of a problem apparently

affecting our customary system of pitch indications.

As Goodman points out, the traditional system of

musical notation is redundant, given that certain sound-

events may comply with, say, characters for C sharp and D

flat in a score for keyboard. This problem is of secondary

importance, since, as we have seen, non-redundancy is not

crucial for Goodman’s project. However, this feature of the

traditional notation for keyboard scores apparently

generates problematic consequences when the customary

notation for, say, violin scores, is taken into

consideration. In such scores, one may point out,

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… the characters for c-sharp and d-flat have no

compliants in common. Now if two characters thus

have some compliants jointly (in piano scores) and

others severally, the two compliance-classes

properly intersect, flagrantly violating the

requirement of semantic disjointness.9

Take a sound-occurrence a, obtained by striking the

appropriate black key on a piano, and two sound-occurrences

b and c, obtained by producing vibrations on a violin

string which comply, respectively, with C sharp and D flat

indications on a violin score. It would seem that the

character for C sharp contains a and b among its

compliants, and that a and c comply with the character for

D flat. Thus, at least one item, the sound event a, occurs

in the compliance classes for distinct characters, in

violation of the requirements for a notational system.

Goodman is however not troubled by this objection:

What this account misses … is that since every

performance is on one instrument or another, each

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of the two characters can be considered a vacant

atomic character that combines with different

specifications of instruments to form different

prime characters.10

So, according to the passage just cited, pitch indications

in the customary system of musical notation are incomplete

symbols, which lack semantic counterparts in the field of

reference. But such symbols interact with instrument

specifications, thereby yielding composite characters which

pick up sound events in the intuitively desired fashion.

So, the simplest denoting unit in the traditional system

may be represented as a syntactic complex of the form x(y),

where x is the specification of an instrument, and y the

indication of pitch in the customary format.

Instrument specifications thus qualify as essential

components of a score. Note however that, if such

specifications are analyzed solely as necessarily

ancillaries in a system of pitch indications, they need not

at all conform to our pre-theoretic and intuitive

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understanding of them. In particular, the intuitive

relationship holding between instrument specifications,

actual instruments, and their timbres plays no role in

Goodman’s analysis. If instrument specifications must occur

in a score only insofar as they complement the system of

pitch indications in the required manner, any distinction

between different instruments becomes irrelevant, as long

as such instruments behave in a similar fashion with

respect to the conventions of equal temperament. For

instance, nothing in the above argument for the

essentiality of instrument specifications indicates that

one must distinguish between sounds produced by a modern

piano, by a harpsichord, or by a fretted bass guitar.

Indeed, in a different context, Goodman gives explicit

indication that timbre is not to be considered among a

work’s essential properties:

… performances that comply with the score may

differ appreciably in such musical features as

tempo, timbre, phrasing, and expressiveness.11

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On the other hand, once instrument specifications are

recognized as important components in an ordinary score,

there seems to be no need to interpret them merely as

necessary supplements in a notational system for

indications of pitch. In fact, instrument specifications

should be recognized as essential parts of a score

independently from issues of pitch, by giving due

recognition to the pre-theoretic assumption that, pace

Goodman, timbre is a parameter relevant for the

identification of a musical work. Intuitively, a certain

sequence of sounds qualifies as a performance of, say, a

violin sonata only if a certain quality of tone is present,

associated with the sounds typically produced by common

violins. So, if a score is to identify a work “from

performance to performance,” characters suitably related to

aspects of timbre must be admitted in an intuitively

adequate symbolic system. Moreover, and most importantly

for Goodman’s project, there seems to be no reason why a

system containing instrument specifications suitably

correlated to indications of timbre should fail to meet the

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requirements of notationality. Perhaps, such a system may

even be mapped to the minimal notational system devised for

indications of pitch, if specifications of timbre may be

appropriately correlated to patterns of overtones.

So, it is not only the case that Goodman is explicitly

willing to include instrument specifications among the

essential components of a score. It is also the case that,

independently of Goodman’s own intentions, the theory of

notation in Languages of Art permits that such specifications

be interpreted in the intuitively desired fashion, as

indicating features of timbre among the constitutive

properties of a work. It may however be pointed out that,

although conforming to a certain timbre may well be an

intuitively necessary condition for a tone’s compliance

with an instrument indication, it is by no means a

sufficient condition. Pre-theoretically, in order for a

performance to comply with a score containing, say, the

specification of an oboe, such a performance must not only

consist of the appropriate sequence of oboe-sounding tones.

As Levinson points out

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[w]hen Beethoven writes a middle C for the oboe, he

has done more than require an oboe-like sound at a

certain pitch—he has called for such a sound as

emanating from that quaint reed we call an “oboe.”12

This intuitive requirement is importantly different from

those discussed thus far. Considerations of pitch,

duration, and timbre address parameters of the sound structure

associated with a work, namely the pattern of what Levinson

calls “purely aural” properties.13 On the other hand, the

requirement that the relevant sound-events originate from

objects of a certain kind, and be the result of appropriate

means of production, pertains to extra-structural, non

aural properties. Besides for instantiating the indicated

sound sequence, the tones produced during a performance

must be causally related in the appropriate fashion to

objects of a suitable kind. They must, for instance,

originate from the act of operating in a traditionally

acceptable manner on an object which conforms, to a

suitable degree, to the blueprint for modern oboes.

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The intuition described in the above quoted passage

from Levinson is thus apparently inconsistent with

Goodman’s assumption that “no historical information

concerning the production of the performance can affect the

result.” However, the re-interpretation of instrument

specifications as characters associated with classes of

instruments, rather than as mere indications of tone, does

not entail an obvious violation of any requirement for

notationality. Modulo minor adjustments, the customary

system of instrument specifications may be associated with

the traditional instrument types, in the intuitively

adequate fashion. Characters of the form x(y), x an

instrument specification and y an indication of pitch, may

then be associated with a compliance class containing

sounds produced by an instrument of the type indicated by

x, having the frequency indicated by y.

In fact, it may well be the case that the proposal I

sketched above clashes with Goodman’s non-historical

presupposition in a relatively harmless fashion. Goodman’s

insistence on the irrelevance of historical facts is

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related to his conviction that, in allographic arts such as

music, “the distinction between original and forgery of it

is [not] significant.”14 When it comes to autographic

works, Goodman claims, authenticity is determined by taking

into account the causal relationships between the object

under analysis and a certain artist, or a certain event of

artistic creation. For instance,

[t]he only way of ascertaining that the Lucretia

before us is genuine is thus to establish the

historical fact that it is the actual object made

by Rembrandt.15

It is such a historical chain ending with the original act

of composition which must play no role in music, according

to the analysis of the autographic-allographic distinction

proposed in Languages of Art. Such an analysis, however, does

not entail the irrelevance of different kinds of causal

properties, such as those having to do with the means of

production generating the relevant sound sequence. As we

shall see in the next section, however, there are

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compelling reasons for supposing that, pace Goodman, even

the causal links between a performance and a composer must

enter the analysis of constitutive properties of a work.

Yet, even though Goodman’s anti-historical presupposition

must then be definitively abandoned, the notational account

of the relationship between a work and a performance need

not be relinquished.

3. A More Demanding Criterion

According to the proposal of section two, the score,

conceived of as a character in a notational system,

contains indications of the relevant aural properties, such

as pitch, duration, and timbre, together with causal

requirements concerning the production of the relevant

sounds. Given Goodman’s analysis of the relationship

between a score, a work, and its performances, it follows

that facts regarding the “production means” involved in a

performance are relevant for determining whether a certain

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sound event qualifies as an instance of a certain work.

However, even though this conception of a musical work’s

important properties is already more demanding than the

minimal view of a score’s properties in Languages of Art, it

still does not provide a set of intuitively sufficient

criteria for the work-performance relation. For, as

Levinson argues,

[i]t seems that, in order for a performance to be a

performance of [a musical work] W … there must also

be some connection, more or less direct, between the

sound event produced and [the composer’s] creative

activity.16

Now, as I already indicated in connection with the issue of

instrumentation, the requirements of notationality are not

inconsistent with the presence, in the field of reference,

of items sorted out according to their causal or historical

properties. It is thus interesting to investigate whether a

notational system may be devised, which addresses the

required connection between sound events and compositional

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acts, and whether parts of ordinary scores may be

interpreted as elements of such a system.

It is customary, at least in the tradition associated

with a certain kind of music, to assign to musical works

titles (“Waldstein”, “Symphonie Fantastique”), numbers (“opus

111”, “K 622”), or other kinds of expressions. Such

expressions, possibly together with the composer’s name,

seem to yield a reasonably efficient system for indicating

musical works. For instance, we apparently refer to musical

works by appropriately employing expressions such as

“Mozart’s Concerto for Clarinet and Orchestra in A,”

“Beethoven’s opus 109,” or “K 622.” It may be controversial

whether expressions of this kind do refer to musical works.

But the language comprising them may also be interpreted

with respect to an alternative field of reference, which

associates such expressions with entities, or events, of

the kind required for a causally adequate identification of

musical works. For instance, the inscription “K 622” may be

correlated to a suitable event, comprising Mozart’s actions

and mental states while composing the work we normally

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associate with that inscription. The resulting symbolic

system fails to meet the requirements of notationality only

to a minor extent. It is, to begin with, a redundant

system: the compliance class for, say, the character “K

622,” namely the unit class containing a certain act of

creation, is identical with, for instance, the compliance

class for the distinct character “Mozart’s Concerto for

Clarinet and Orchestra in A.” It may well also be an

ambiguous system, if, for instance, composers bearing the

same name write works typically associated with the same

label. Regimentation is however a trivial enterprise, and

the system may be fairly considered to “come as near to

meeting the theoretical requirements for notationality as

might reasonably be expected of any traditional system in

constant actual use ….”17

Inscriptions from the above envisioned system typically

occur on the copies of actual scores, often as parts of

their titles.18 There thus seems to be no principled

reasons for refusing to accept the indication provided by

(suitably regimented) titles as essential parts of the

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score, on a par with instrument specifications and

indications of pitch and duration. The resulting system may

then be interpreted along the following lines. Consider a

score S, consisting of a title T, an instrument indication

I, and indications of pitch p1, p2, p3. Assume that T, I,

and p1 … p3 are simple characters in a notational system,

and suppose that T is associated with a unique

compositional event as its only compliant, and that I is

thus associated with a certain instrument-type. The

compliance-classes for p1 … p3 include sound-events of the

appropriate frequency. The compound character S is then

taken to denote a sound-event e iff: (i) e consists of a

sound sequence appropriately made up of compliants of p1 …

p3; (ii) e is a sound event produced by an instrument of

the type complying with I; (iii) e is a sound event in the

appropriate relation to the event complying with T. So, for

instance, performances complying with the score for

Beethoven’s Hammerklavier sonata must be sound events made

up of the “right notes,” produced on a traditional piano by

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a performer suitably related to a certain event in XIX

century Austria.19

For Goodman, a score for a work w determines the class

of performances of w, and hence identifies w’s constitutive

properties. According to the account of a musical work’s

constitutive properties which emerges from the foregoing

analysis of scores, such a work consists of a certain

sound-sequence, paired with the indications of appropriate

performing means and of an appropriate event, occurring at

a given time and involving a certain composer in the

suitable fashion. This view of what a musical work is

closely approximates an influential suggestion put forth by

Levinson, according to which a musical work is uniquely

identified by a sound structure, a performing-means

structure, and a condition referring to a composer X and a

time t, i.e., in short, by an “S/PM structure-as-indicated-

by-X-at-t.”20 In my development of Goodman’s notational

theory, I tacitly appealed to Levinson’s explanation of our

intuitions concerning the identity criteria for musical

works, because it is a well known and well developed

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example of a position antagonist to an analysis of musical

works as sheer sound structures. Other proposals in the

same vein should be compatible with my modified Goodmanian

theory, given appropriate adjustments.

4. Conclusion

Goodman begun his investigation of the work-performance

relation by assuming the irrelevance of causal and

historical information. It is probably such an assumption

which motivated his investigation of the properties of

notational systems: if causal relations are neither

necessary nor sufficient, so one may reason, a set of

prescriptions must be provided, so as to obtain a

satisfactory “decisive test for compliance.” It may then be

tempting to conclude that the rejection of Goodman’s anti-

historical presupposition entails the abandonment of a

notational approach to the ontology of musical works. In

this essay, I have argued that such a temptation must be

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resisted: Goodman’s fundamental thesis that an event is a

performance of a work w iff it complies with the

notational character associated with w as its score is

consistent with our intuitions about the relevance of non

structural parameters, such as the means of production

involved in that performance, or the historical chains

linking performer and composer.

I accompanied this main thesis with the additional

tenet that actual scores may be considered, within

acceptable limits, as instances in a notational system

which conforms to our intuitions concerning the identity

criteria for musical works. This tenet should not be

interpreted as the strong empirical claim that ordinary

musical notation satisfactorily conforms to the criteria

for ideal scores provided in Languages of Art. My concern has

rather been to point out that, if elements in an ordinary

score are interpreted as indicating “extra-aural”

properties, such as specifications of means of productions

and of compositional acts, the resulting system need not in

principle be farther from the ideal of notationality than

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the minimal picture of scores suggested by Goodman. For

Goodman, our everyday system for indicating pitches and

relative duration

… comes as near to meeting the theoretical

requirements for notationality as might reasonably

be expected of any traditional system in constant

actual use ….21

No more demanding conformity to those requirements need be

required from the richer conception of scores I proposed.

Stefano PredelliFilosofisk institutt, Universitetet i OsloBoks 1020, Blindern0315 Oslo, [email protected]

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1. Nelson Goodman, Languages of Art: An Approach to a Theory of Symbols

(Indianapolis: Hackett Publishing Company, second edition, 1976), pp.

117-8.

2. Jerrold Levinson, ‘Music’, in Hans Burkhardt and Barry Smith

(eds.), Handbook of Metaphysics and Ontology (Philosophia, 1991), p. 584.

3. Languages of Art, p. 128.

4. Ibid, p. 129.

5. For a more precise characterization of these constraints, see

Languages of Art, pp. 148-154.

6. Ibid., p. 151.

7. Ibid., p. 185. On the other hand, “[m]etronomic specifications of

tempo do, under obvious restrictions and under a system universally

requiring them, qualify as notational and may be taken as belonging

to the score as such.” (Ibid, pp. 185-6)

8. Ibid., p. 186.

9. Ibid., pp. 181-2.

10. Ibid., p. 182.

11. Ibid., 117.

12. Jerrold Levinson, ‘What a Musical Work Is’, The Journal of Philosophy,

Vol. 77 (1980), p. 15.

13. Ibid., p. 6, footnote 3.

14. Languages of Art, 113. Jerrold Levinson has suggested the

distinction between referential and inventive forgeries (see Jerrold

Levinson, Autographic and Allographic Art Revisited’, Philosophical

Studies, Vol. 38 (1980). It is the alleged impossibility of

referential musical forgery which intrigues Goodman: although there

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may be “compositions falsely purporting to be by Haydn … there can be

no forgeries [of the London Symphony]” (Languages of Art,, p. 112).

15. Ibid., p. 116.

16. Levinson. ‘Work’,, p. 25.

17. Languages of Art, p. 186.

18. So, my interpretation of inscriptions such as “opus 109” on a

score slightly differs from our pre-theoretic understanding of these

expressions as indicating the work itself, rather than the relevant

act of composition.

19. The specification of such a “suitable relation” is not a peculiar

task for the framework I am suggesting. For concreteness sake, one

may think at the causal relationship obtaining between the performer

and Beethoven’s compositional act if the former is attentively

following a score appropriately reproducing Beethoven’s manuscript.

20. Levinson, ‘Works’, p. 20.

21. Languages of Art., p. 186.

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Goodman and the Score (pre-print)

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