Tonic Arpeggiation and Successive Equal Third Relations as Elements of Tonal Evolution in the Music...

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Tonic Arpeggiation and Successive Equal Third Relations as Elements of Tonal Evolution in theMusic of Franz LisztAuthor(s): Howard CinnamonSource: Music Theory Spectrum, Vol. 8 (Spring, 1986), pp. 1-24Published by: on behalf of the Society for Music TheoryStable URL: http://www.jstor.org/stable/746067 .

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Tonic Arpeggiation and Successive Equal Third

Relations as Elements of Tonal Evolution in the

Music of Franz Liszt

Howard Cinnamon

During the nineteenth century, composers began to explore methods of tonal organization that involve successions of similar harmonic relationships which divide musical space into equal segments, producing structures that are distinctly un- characteristic of conventional tonal practice. This paper ex- plores the nature of one of these new methods of tonal organization, equal division of the octave by successive thirds, its relationship to earlier practice, and its role in the evolution of tonality that is evident within the music of the nineteenth century. It focuses on certain works of Franz Liszt, illustrating within these pieces tonal procedures that may also be found in the music of other nineteenth-century composers.

Liszt enjoys a unique position within the musical history of the nineteenth century. Not only did his life (1811-86) span the Romantic era, his music exhibits a range of the styles that developed during the century as well. While Liszt's early music clearly shows the influence of eighteenth-century style and harmonic language, his late works (particularly his songs and works for solo piano) have often been cited for their "anticipation" of twentieth-century structural procedures.l This study

'See, for example, Alan Walker's comments on the pieces of the Annees de P&lerinage Book III, the "Csardas Macabre," and the "Bagatelle Ohne

examines a selection of pieces that range in dates of composition from 1838 to 1882: two excerpts from the Annees de Pe- lerinage, Book II that date (in their earliest versions) from 1838-39, the introduction to, and first movement of, the Faust Symphony (1854), and the late piano piece "Die Trauer- Gondel I," also known as "La lugubre gondola I" (1882). These analyses demonstrate a continuity of tonal practice and development, suggesting the degree to which structural procedures found in these pieces may be characteristic of Liszt's com- positional style specifically, and that of nineteenth-century music in general. Before dealing with these pieces, however, a discussion of some applicable theoretical principles will be

helpful. The diatonic tonal system is based predominantly upon har-

monic relationships that divide the octave unequally. Its most

Tonart," in Liszt (New York: Thomas Y. Crowell, 1971), 88-91, and in "Liszt and the Twentieth Century," in Franz Liszt: The Man and His Music, ed. Alan Walker (New York: Taplinger Publishing Co. Inc., 1970), 350-364; Hum- phrey Searle's comments on the late piano pieces in his The Music of Franz Liszt (London: Williams and Norgate Ltd., 1954), 108-123, especially 120- 123; and Sacheverell Sitwell, Liszt, revised ed. (London: Cassell and Com- pany, Ltd., 1955), 278.



2 Music Theory Spectrum

fundamental harmonic progression, I-V, and the more foreground progressions that imitate it to form the hierarchy of relationships that extends from it (e.g., II-V, I-IV, VI-II, III- VI) each divide an octave into a perfect fourth plus a perfect fifth. The intervals that result from these unequal divisions of the octave are, likewise, diatonically subdivided unequally. This consistent unequal division of the octave is a primary factor in the establishment of the scale-step function and identity of each member of the diatonic collection, and thus in that collection's ability to define a tonic.2 In the context of the chromatic tonal system, the potential for combining harmonies into progressions that employ mixture and the resulting availability of harmonies built upon every note of the chromatic scale make it possible to exploit relationships based on conventional diatonic functions in order to divide the octave into equal segments.3

2The intervallic content of the diatonic set and its role in defining a tonic have been discussed by a number of theorists. Their primary interest has been in comparing the diatonic set with the total chromatic and its other subsets, and with distinguishing the use of the diatonic set in tonal music from that of the total chromatic and its other subsets as the basis of pitch structure in twentieth- century music. See, for example, Richmond Browne, "Tonal Implications of the Diatonic Set," In Theory Only 5, no. 6-7 (July-August 1981): 3-21; John Clough, "Aspects of Diatonic Sets," Journal of Music Theory 23 (1979): 45- 61; Heinrich Schenker, Neue Musikalisches Theoren und Fantasien, vol. 1, Harmonielehre (Stuttgart: J. G. Cotta'sche Buchhandlung Nachfolger, 1906), sections 64-71. In regard to the last, Schenker clearly anticipates many of the observations made by later theorists. Unfortunately, many of these passages are omitted from the popular English translation by Elisabeth Mann Borgese (Harmony, edited and annotated by Oswald Jones [Chicago and London: The University of Chicago Press, 1954]).

3The term mixture, as used here, refers to three related, but distinct chromatic operations: 1) the replacement of a diatonic scale-degree and/or the triad built upon it with the corresponding pitch or triad from the parallel mode shar- ing the same tonic (primary mixture); 2) a change in chord quality (from major to minor, minor to major, diminished to minor, etc.) to produce a harmony that is not diatonic in either mode but which retains its function through the scale-step identity of its root (secondary mixture); and 3) the application of sec-

The unique properties of the octave enable it to be a primary basis of prolongation. Within the diatonic tonal system, the unequal division of the octave becomes a fundamental harmonic relationship that reverberates throughout that system to produce the hierarchy of harmonic relationships upon which it is based. Similarly, in a tonal system where the equal division of musical space becomes a standard practice, the octave becomes a primary object of such divisions, and the equal division of the octave becomes an important procedure by which prolongation can be achieved. The principles that govern the equal division of the octave, however, are no different than those which govern the equal division of other musical spaces.

Of the intervals that can divide the octave equally, only thirds (both major and minor) can also represent a conventional harmonic relationship.4 For this reason, they are the most useful intervals within the context of a chromatic tonal system that is based upon the exploitation of conventional

ondary mixture to a harmony that itself resulted from primary mixture or within the prolongation of a harmony so derived (double mixture). These con-

cepts may be familiar from discussions of chromatic harmony in most harmony texts, but descriptions of mixture that most directly correlate with the approach taken here may be found in Edward Aldwell and Carl Schachter, Harmony and Voice Leading, vol. 2 (New York: Harcourt, Brace, Jovanovich, Inc., 1979), 47-57 and 186-193; and Schenker, Harmony, 84- 115 (see preceding note). A detailed discussion of mixture as related to the pieces discussed here may be found in my unpublished Ph.D. dissertation "Third-Relations as Structural El- ements in Book II of Liszt's Annees de Pelerinage and Three Later Works," (The University of Michigan, 1984; Ann Arbor: University Microfilms Inter-

national), 32-78. 4This assumes, as Schenker does, that relationships by step are primarily

contrapuntal rather than harmonic. In a II6-V or IV-V progression, for ex-

ample, the relationship between the II6 or IV and the V harmony is primarily based upon the conjunct melodic motion that occurs between the bass tones rather than any relationship between the roots of the harmonies, as opposed to the II of a II- V progression, in which the fifth (harmonic) relationship to the V that follows is expressed overtly in the bass (see in particular Schenker, New Musical Theories and Fantasies, vol. 3, Free Composition, trans. and ed. by Ernst Oster, [New York: Longman, 1979], 29-31).



Elements of Tonal Evolution in the Music of Franz Liszt 3

diatonic relationships. While equal divisions by other intervals can occur, they most commonly appear as the result of successions of smaller intervals or as subdivisions of larger ones. Equal divisions by major or minor seconds, for example, result in stepwise motion (which is essentially a melodic [i.e., contrapuntal] rather than harmonic relationship) and/or undifferentiated segments of the total chromatic. They are, therefore, meaningful primarily as subdivisions of larger intervals, which themselves may divide still larger ones.

Equal division of musical space into major or minor thirds is usually founded on successive duplications of specific harmonic relationships. In the division of an octave into major thirds, for example, the chord-to-chord progressions are usually based upon repeating relationships (I-(t)III# in the case of ascending thirds, I- ,VI in the case of descending thirds). These relationships overlap, with each succeeding J III# or b VI becoming I of the next progression. On a more background level, however, these harmonies may be identified in a way that reflects diatonically-based relationships to the underlying harmony that is being prolonged. Thus, the third harmony of a progression based on successive ascending major thirds may also be thought of as ,VI (the enharmonic equivalent of IIItt/II IIIt).

Equal division of the octave by successive thirds represents a type of prolongation in which the foreground harmonic relationships that generate it are not referential to the middleground harmony being prolonged. It may, thus, be viewed as a fusion of contrapuntal and harmonic procedures: contrapuntal in terms of the harmony being prolonged, harmonic in terms of the more foreground chord-to-chord successions within it. For this reason, Roman-numeral identification of the harmonies involved in such progressions is often problematic and can rarely reflect the enharmonic relationships that make them possible. Were the harmonic relationships inherent in such a progression to be more completely displayed, a Roman-numeral analysis of a progression based on successive ascending thirds might appear as follows:

I--III(() I-IIII()

I---III(,)

( I--III(p)--4VI-I)

In his dissertation, "Technical Bases of Nineteenth-Century Chromatic Tonality: A Study in Chromaticism," Gregory Proctor draws a useful distinction between chromatic procedures that employ the transposition operation and those that do not.5 The transposition operation takes place when literal transposition forms the basis of tonal organization in a passage. This results in a procedure by which an individual harmony (or prolonging progression) is transposed more or less literally at successive intervals.6 Such a procedure gives the impression of an extended elaborated sequence that is dependent for its coherence on a repeating pattern of relationships. Example 1 illustrates two levels of voice leading that may form the basis of an application of the transposition operation to an equal division of an octave by successive ascending major thirds.

A significant and distinctive feature of the transposition operation is the discontinuity of voice leading between each of the

5Gregory Proctor, "Technical Bases of Nineteenth-Century Chromatic To- nality: A Study in Chromaticism" (Ph.D. dissertation, Princeton University, 1978; Ann Arbor: University Microfilms International), 159-219, particularly 159-170.

6Proctor makes the clear and valid point that the transposition operation is independent of equal divisions of musical space and may occur at unequal and even diatonic intervals. For the purposes of this study, however, this concept is most relevant as a component of the structural procedures that organize the tonal structure of highly chromatic music and take part in the equal division of musical space.




Example 1. The transposition operation as the basis of an equal division of musical space

Example 2. Equal division of musical space exclusive of the transposition operation

II IIII

I III# < t

(=I III bVI I)

,.ImII<- III

I mIII/

I I -I III# II I~~~~~II

IIIt bVI I)

elements of the procedure (indicated by vertical lines between staves in the example). Structures employing equal divisions of musical space without the transposition operation, however, as illustrated in Example 2, usually exhibit a greater continuity of voice leading and melodic motion that contributes to large-

scale coherence in ways unavailable within the former procedure.

Under the transposition operation, all the intermediate harmonies may be of equal structural significance, with the first and last assuming hierarchic primacy more for their positions within the procedure and the larger context than for any hierarchic priority that may exist among the individual harmonies. Because of their closer similarity to conventional tonal practice, however, equal divisions that do not employ the transposition operation offer the potential for both the employment of conventional voice-leading procedures and the establishment of a tonal hierarchy among the individual harmonies.

Example 3 illustrates how voice leading may influence such hierarchic relationships within an equal division of an octave. In Example 3a, the neighboring note in the upper voice (7), which functions to prolong the more structural tone (i), is un-

(=I

I

I




Example 3. Hierarchy of relationships generated by voice leading within equal divisions of an octave not employing the transposition operation

N

-> ". Liv

I III# b I I

I bVI I

I

N

I IIIt bVI I

1.- R -- g, .J-- - -;

I IIIt I I~~~~~~~~~~~~~~-? I

derstood to indicate that the harmony which supports it (IIIp) is also of a lesser hierarchic significance, hence more foreground, than the other intermediate harmony (bVI). The descending I-I VI major third is thus understood to be inverted, becoming a minor sixth that is divided equally into two major thirds.

In Example 3b, the role of the neighboring note (7) is considered more prominent as is that of the harmony which supports it (III#). Here, the 1 VI chord is considered a more foreground contrapuntal approach to I, and the underlying progression is understood to be I-III# -I with the IIIl -I major third inverted to form a minor sixth that is subdivided into two

major thirds. The decision as to which (if either) hierarchy is operative in any given piece must be made on the basis of other factors (design, motivic relationships, etc.) since the harmonic relationships themselves cannot determine this. The hierarchic potential (one not available under the transposition operation) is there, however.

In some of the pieces to be discussed here, equal divisions of the octave of both types replace more diatonic procedures. The employment of these equiproportional structures based on successive third relations may be seen to develop in an evolutionary manner. At first, they appear in incipient form as embellish-

a.




ments of tonic-arpeggiating I-III-V-I progressions. Ulti- mately, however, they replace this diatonically based procedure as an alternative means of prolongation.

Measures 30-77 of "Sposalizio," the first piece of the An- nees de Pelerinage, Book II, could be considered a passage

based on a succession of ascending minor thirds that divide a I-I octave into equal segments (a division not based on the transposition operation). Each of the last three successive thirds is preceded by its own dominant, a feature that emphasizes the sequential nature of the passage. Example 4 illustrates this view of the voice leading.

Example 4. "Sposalizio," mm. 30-77, interpreted in terms of an equal division of the octave

mm. 30

3

38 52 60 64

0III <

III

77

I bIII

I b'II

,iii1 __

I

VI# (=I I)




The main problem with this analysis stems from its treat- ment of the prolonged V (mm. 67-76) as equivalent in structural status only to the other (applied) dominants, not elevating it to its normal structural position within the tonal hierarchy. The analysis preferred here sees that V as the penultimate goal of tonal motion, part of a middleground arpeggiation of the tonic (see Example 5). In this context the B b major harmony of

measure 60 is seen as a passing harmony that links t III with

#VI#, an upper-neighbor harmony to V. This view maintains the normative hierarchic positions and diatonically based functions of each of the principal harmonies and corresponds more closely to the perception of the operation of conventional tonality within this passage.

A similar passage may be found in mm. 16-61 of "Sonetto

Example 5. "Sposalizio," mm. 30-77: voice leading

30 38 52 60 64 67 77

V

V

1II bI III,

iIII < VI#

~III

-'1 1/ 'I --1

I




123 del Petrarca," no. 6 of the Annees de Pelerinage, Book II. There, a tonic-to-tonic octave appears initially to be divided into three descending major thirds (rather than four ascending minor thirds, as in the example from "Sposalizio"). Example 6 shows one possible interpretation of the voice leading underlying this passage.

This view illustrates how the initial tonic (m. 16) is ex-

panded, then prolonged via a motion to its dominant. A tonicization of G6, (IVII) follows (mm. 23-29) eventually leading to VI (Fb major, spelled enharmonically as E major, m. 39) via

two descending thirds (El,, mm. 30-35, and Cl, enharmonically spelled as B~, m. 37) the last of which functions as an applied dominant to 1,VI (Et(Fl,)). In the larger context, 6VII (Gb) serves as a passing harmony subdividing the I-l,VI major third

Example 6. "Sonetto 123 del Petrarca," mm. 16-61: interpretation in terms of an equal division of the octave

11111I. 16 29 39 41 48 61 68 73 77

v

I bvI IIh-- b I

I




into two major seconds. The I VI harmony is then followed directly by its own VI (C major, enharmonically III~ ) in m. 41, resulting in a middleground succession of descending major thirds (I-4 VI-IIIt). This succession is continued, arriving at I (m. 61) through its'own dominant, thereby extending the pattern that controls the preceding progression and completing a division of the octave into a series of descending major thirds:

I-/ VI

/ I-4 VI

(= I-- VI-IIIB-I)

I

The one serious flaw in this analysis (like that in the first analysis of the excerpt from "Sposalizio" in Example 4) derives from its relegation of the prolonged V harmony (mm. 48-60) to a relatively foreground level. In this respect it contradicts the conventional hierarchic position of the tonic-dominant relationship and the role of that relationship as the most basic form of tonic arpeggiation. Example 7 presents an alternative analysis of the voice leading of this passage, which interprets the role of the descending thirds in the context of a more background tonic-dominant axis. In this view, the V of measures 48-60 is seen as the dominant of a I-III -V tonic arpeggiation in which the III harmony of m. 41 is the mediant. The I-IIIt major third is considered to be inverted, becoming a minor sixth that is itself divided into two major thirds by the intervening IVI harmony. The hierarchy of structural relationships that results elevates the first two descending major thirds to a more foreground position than the I-III progression that frames them, and that I-III; progression is, in turn, viewed as part of a larger

I-III-V progression that spans 45 measures of the piece (mm. 16-60).7

Here, as in the earlier excerpt from "Sposalizio," the pre- vailing I-V progression eclipses the successive thirds and pre- vents the equal division of the octave that they produce from becoming a controlling feature of the tonal structure. Like that of the excerpt from "Sposalizio," the equal division of the octave that could have resulted here (had the V not been present) would not have been the result of the transposition operation. The procedures employed in these two excerpts are not, strictly speaking, equal divisions of the octave, but they are informa- tive about such structures in three ways:

1. They illustrate the primacy of the tonic-dominant relationship and the determinative role played by V in differentiat- ing between equiproportional structures and those based on elaborations of more conventional structural patterns. In situations like these, the presence of a root position V harmony, the context produced by its prolongation, and the structural emphasis given the other member harmonies of the tonic arpeggiation (through their respective prolongations) define that arpeggiation as the structural basis of this passage.

2. They show how easily equal divisions of the octave can be produced through extensions of standard diatonic procedures. In either of these cases, the omission of the dominant harmony,

7The V harmony of measures 48- 60, a dividing dominant, supports the so-

prano pitch, 2, in a middleground interruption and closes off the large-scale unfolding of the initial tonic that spans mm. 16-60. The tonic of m. 61 (a harmony that functions as V/IV on only the most foreground level) reasserts the

primary melodic tone, 3, and leads ultimately to the structural close in mm. 74- 75. The presence of this interruption further mitigates against an interpretation that favors the descending thirds. The interruption at this point closes off both the voice leading and harmonic progressions, isolating the I of measure 61 from the progressions that precede it. In an interpretation that accepts the successive descending thirds as the controlling feature, the V of mm. 48-60 would have to be seen to resolve to the I of m. 61 and the 2 of the upper voice would have to be seen to resolve to 1 in some voice, on some middleground level.




Example 7. "Sonetto 123 del Petrarca," mm. 16-61: interpretation in terms of an arpeggiation of the tonic triad

mm. 16 29 39 41 48 60 61 68 73 75

A A A A A

3_______ ________________2 || 3 2 1

A ^'

' _ rA^^ rr T: _

bb r

3rd as 6th

I Illb------- v I v I div.

or its replacement by a passing harmony (even an inversion of conventional practice that unfolds structural harmonies via ar- V or V7), would have necessitated an interpretation in terms of peggiation in the bass. an equal division of the octave. Because the equal divisions of the octave do not fully realize

3. They demonstrate how structures based on equal division their potential as controlling elements in these passages, they of the octave by successive thirds (both ascending and descend- are termed incipient equal divisions, while similar passage in

ing) are related to, and may be seen to grow out of, the more which the penultimate V is omitted (or replaced) are termed




true equal divisions. An example of one such true equal division of the octave by successive thirds does occur as the middleground basis of the first movement of a large portion of the Faust Symphony.

The three "Character Pictures" (as Liszt termed them) that make up the Faust Symphony (1854), "Faust," "Gretchen," and "Mephistopheles," have been the objects of considerable scrutiny over the years, but most of the analytical attention paid these movements has focused on their thematic content and the relationships among the themes of the various movements.8 Example 8 presents the middleground voice leading of a portion of this sonata-form movement (mm. 1-424: the introduction, exposition, development, and the beginning of the recapitulation). This example illustrates some important similarities and differences between tonal procedures employed here and the incipient equal divisions of the octave just discussed.

Large-scale tonal procedure in the major portion of this movement, involves the prolongation of a C minor harmony, one that is based upon a true equal division of a C-C octave not employing the transposition operation. This procedure is considered a true equal division of the octave, because there is no penultimate dominant to complete the tonic arpeggiation. In- stead, the motion from l VI(5) to I is achieved through a succession of contrapuntal harmonies.

The movement begins with the extended prolongation of an Al augmented chord (to be discussed in detail below). After the prolongation of the Al6 augmented chord is completed (m. 22), the tonic (C) is approached contrapuntally, in large part

8See, for example, the representative discussions of the symphony in Hum-

phrey Searle, "Franz Liszt," in The Symphony, vol. 1, Haydn to Dvorak, ed. Robert Simpson (Baltimore: Penguin, 1966), 262-270; and Edward Downes, Guide to Symphonic Music (New York: Walker and Company, 1976), 500- 504.

through the arpeggiation of its diminished-seventh chord (Ab - B-D-F, mm. 24-71: see Example 8) of which Al is part. The arrival of tonic in mm. 71-74 begins an extended and elabo- rately chromaticized unfolding of that harmony which spans 107 measures. This unfolding is guided by complementary arpeggiations in the outer voices. The harmonies produced in conjunction with these complementary contrapuntal lines function in passing roles and often undergo substantial elaborations and expansions in their own rights. (Note, for example, the expansions of the passing B major harmony in mm. 105-111 and of the 6 built over B > in mm. 111-142.)

When B t is added to the C harmony, in m. 167, it turns the tonic harmony (now major) into a dominant seventh sonority that is reinterpreted as an augmented sixth chord. This augmented sixth chord resolves to V of E major in m. 179, a V/4 III that is prolonged through m. 224 where it resolves to E major (m. 225). This resolution establishes III, the second tonal area of the sonata-form procedure, and completes the first stage of the equal division of the C-C octave. As part of the V/t III, harmony, the primary melodic tone, l 3 (El), is reinterpreted as D", the leading tone of E major. It resolves to E~ with the change of harmony, replacing l 3 with ~ 3, at least tem- porarily.

Despite the elaborate chromaticisms and substantial expansions that are applied to some of the transitional harmonies, the large-scale tonal structure through m. 318 corresponds, within acceptable limits, to the conventions of sonata form as they were practiced during the nineteenth century. The portions of the movement involved with the establishment and expansion of the tonic (mm. 71-178) correspond to what would tradition- ally be termed the "first theme" and the beginning of the transi- tion. The portion in which V/b III# is prolonged (mm. 179- 224), which has, at times, been referred to as the "second theme," is best thought of as a "transitional theme," since the second tonal area, t III#, is not established until the cadence of m. 225. The balance of the exposition (mm. 225-318) makes up




Example 8. Faust Symphony, movement I, middleground voice leading, mm. 1-424: introduction, exposition, development, and beginning of recapitulation

m11111. 22 23 71 87 146 163 179 225 250 272 319 335 343 359 381 382

K -- -- -- -- '9 %I, ?- Lb?

J "t - -

J - -J

Vl V

i1s

5

I111#

what convention would call the "second theme" proper (mm. 225-280) and the concluding material.

The prolongation of III# continues into the development section, which begins at m. 319 with a transient tonicization of

Ct minor (VI of E major). This leads ultimately to a dividing dominant (B major: mm. 343-352) through a chromatically passing augmented sixth harmony built on C~ (mm. 335-342). Bt, the root of this dividing dominant, becomes the bass of a

410 414 420

I K - - --- - -

I I I I

I




diminished seventh chord (mm. 353-355) that is then arpeggiated, leading to a unison Al, at mm. 355-358. This Al,, in turn, becomes the bass of an augmented AN -C-E harmony and is prolonged by a literal reprise of the opening Lento assai (mm. 359-381).

Here as in the introduction, this augmented chord is prolonged by means of conventionally based contrapuntal procedures that establish Al', its bass, as a stable and functional bass tone and the augmented chord itself as a relatively stable middleground harmony. At m. 382, the Al is reinterpreted as G( and is led chromatically up to B , which arrives at m. 414. This B at first supports a 4 chord that seems to imply a cadential 6 - 5 resolution and an ultimate cadence on E major. The 6 chord is altered contrapuntally, however (with G# (Al ) and B ~ maintained as common tones), to become a diminished seventh chord built on F (VIIi 3of C). This voice-leading chord leads directly to a contrapuntally expanded I (C minor) at m. 422 without even the most transient appearance of V.

The procedure through m. 353 (the arrival of the diminished seventh chord on B) could be reconciled with the conventions of tonal organization in a sonata-form movement, but the appearance of the Al augmented chord, the chromatic contrapuntal motion leading to and from it, and its role as middleground structural harmony are decidedly unconventional. More typically, the tIII( harmony would continue (possibly through a passing dominant-preparation harmony) to a middleground dividing dominant that would coincide with an interruption in the upper voice (in this case, this would take the form of a G major harmony with D in the soprano). Even the arrival of the dominant would, thus, complete a tonic-arpeggiating I- IIIIf-V progression that would form the middleground basis

of tonal organization in the first two-thirds of the movement. The appearance, at m. 355, of a harmony built on Al could be reconciled with this conventional procedure, if it were to resolve to a V harmony before continuing on to I (this would, of course, produce an incipient equal division of the octave like

those found earlier in "Sposalizio" and "Sonetto 123"), but the omission of that penultimate dominant leaves the equal division of the octave as the controlling factor, replacing the tonic arpeggiation as the primary force for tonal organization.

Like other equal divisions of the octave not employing the transposition operation, the procedure here implies a hierarchy among the third-related harmonies (see Example 9). The tJIIIj -I major third is understood to be inverted, becoming a minor sixth that is divided equally by the Al' augmented harmony. This view correlates with the augmented character of the Ab harmony (and its relatively unstable nature within the con-

Example 9. Faust Symphony, introduction, mm. 71-424: hierarchy of relationships among middleground third-related harmonies

I J---jr- -- -J

I l Ili) bvi 5 1

I

@ ^ --- -J

I ~IIIp I

i




ventional tonal system) and with the structural emphasis given I and i III throughout the movement.

This excerpt from the Faust Symphony demonstrates how passing harmonies can provide a smooth and convincing transi- tion linking , VIP5 with I. But the elimination of the final member of the tonic arpeggiation has even more far-reaching implications for our understanding of the further evolution of tonality. With the omission of the penultimate dominant, the arpeggiation, and with it the middleground unfolding of the underlying harmony, is also eliminated. This fundamentally alters the structural basis of the middleground. No longer can such a passage be said to unfold the harmony it prolongs. No longer is there a correlation between the harmony that is being prolonged and the linear procedure that prolongs it. Instead, a dichotomy is generated between the harmonic and linear dimensions.

In place of the conventional rationale based upon the correlation between dimensions inherent in earlier practice, the sequential nature of the harmonic progressions, the continuity of the voice leading, and the systematic consistency of the successive third relations and equal divisions of the octave combine to produce a new type of prolongational procedure that does not correspond to conventional tonal practice. This dichotomy between the harmonic and linear elements in an equal division of the octave is often overlooked or misunderstood by analysts who refer to procedures like that employed in the Faust Sym- phony as "arpeggiations" without considering whether the harmony being "arpeggiated" is in any way referential.9

9A typical example that deals specifically with the music of Liszt may be found in Harold Adams Thompson, "The Evolution of Whole-Tone Sound in Liszt's Original Piano Works," (Ph.D., Louisiana State University, 1974; Ann Arbor: University Microfilms International), 119-123, where the author dis- cusses the opening passage from the "Sonetto 104 del Petrarca" (no. 5 from the Annees de Pelerinage Book II). For a detailed comparison of Thompson's in-

terpretation with one that coincides with the approach taken here, see Cinna- mon, "Third-Relations," (note 3 above), 176-179 and 184-185.

While the relationship between tonal procedures in each of the examples discussed thus far and that of earlier practice may be clearly shown, the introduction to the Faust Symphony employs procedures (and prolongs a harmony) that more sharply distinguish it from those earlier practices. Although the successive arpeggiations of augmented chords that make up the "main theme" of the symphony, have scarcely eluded the attention of most analysts, the only study of which I am aware that suggests a relationship between these augmented chords and the middleground tonal structure of the opening of the introduction is presented in an article by Robert P. Morgan.10

Morgan astutely points out that the Lento assai of the introduction (mm. 1-22) is based upon a prolongation of an Al -C- E augmented chord. This harmony is prolonged over the course of these 22 measures via an Al -C-E-Al bass arpeggiation that is paralleled by similar arpeggiations in the other voices. Example 10 presents an interpretation of the voice leading in this passage that is based in part on Morgan's interpretation.

This passage is based upon an equal division of the octave by successive major thirds that employs the transposition operation. Despite the obvious similarities, there is a significant dif- ference between this introduction and the middleground of the larger portion of the Faust Symphony's first movement. Unlike the large-scale equal divisions discussed earlier, wherein there is a dichotomy between the harmonic and linear dimensions, there is here a correlation between those dimensions much as there would be in a conventional tonic-arpeggiating progression. The equal division found here may thus be said to unfold the augmented harmony being prolonged, and may properly be said to arpeggiate that harmony in the same way a I-III-V-I progression arpeggiates a major or minor harmony it prolongs.

W1Robert P. Morgan, "Dissonant Prolongation: Theoretical and Composi- tional Precedents," Journal of Music Theory 20 (1976): 49-91, specifically 60- 62.




Example 10. Faust Symphony, introduction, mm. 1-22: two levels of middleground voice leading

4 12

A I

15

-I1--- I

7J. I\ - .. .

_ _-r?

An important realization regarding the opening of the Faust

Symphony is that context can determine the structural roles

played by particular harmonies and can produce a hierarchy of

relationships that is quite different from that of conventional

tonality. In this instance, for example, apparent triadic structures do not play the normative roles (those of stable and po- tentially structural harmonies) that they would in conventional tonal music. Instead, context establishes the augmented AN -C-E chord as a stable and referential structural harmony. Morgan makes this same point quite clearly:

It is noteworthy, nonetheless, that only one of the four [augmented chords] serves as the basis for a prolongation: C-E-A-flat is always present as a referential sonority. But within this basic frame- work there are both passing chords [e.g., mm. 1-2] and neighbor chords [mm. 4-5], as well as a number of nonharmonic tones. The latter are interesting in that they occasionally create the appearance of stable harmonies. Within the context of this section, however, they are neither stable nor even true harmonies, since they result from secondary voice-leading motions. For example, the "minor chord" in m. 5 results from the suspension of the C-sharp in the top voice. Al- though the real meaning of these "chords" is perhaps clear enough

'~~~~~~~~'Iy ~~~~~~~~~~~~~~~~~~O~~`




within the relatively simple closed system established by Liszt, such Scheinharmonien often occasion misreadings. Their structural meaning is here determined entirely by contextual means unrelated to [in fact running directly counter to] the conventions of the tonal system.1

Another aspect of this passage that is particularly interesting is the relationship between tonal structure and design (i.e., thematic organization, rhythmic structure, dynamics, etc.). While the tonal structure of the passage would most readily be divided into three segments corresponding to the three major thirds of the bass descent, design is divided into two parts (the second of which is a modified repeat of the first). The two sections of design, measures 1-11 and 12-22, consist of three phrases each: the string unison, in which four augmented chords, each a half- step below the last, are arpeggiated (mm. 1-3); the woodwind chorale in which the Al -C-E augmented chord is prolonged via a neighbor motion (mm. 4-7); and the clarinet and bassoon unison in which the A, -C-E augmented chord is arpeggiated with each tone of the arpeggiation embellished by a half-step upper neighbor (mm. 8-11). Example 11 illustrates how the two sections (and six subsections) of design are distributed in terms of the tonal structure.

As this example shows, the second section of this passage is not the literal transposition of the first that it seems initially to be. While the first phrase of the second section is transposed one major third below that of the first section, the second and third phrases are transposed down an additional major third, completing the tonal structure much more rapidly than would be expected on the basis of the opening three phrases. Were the design and tonal structure to correspond, the passage would consist of three sections, with the second and third each repre- senting literal transpositions of the first (see Example 12). The fact that this does not occur produces a conflict between design and tonal structure that helps to avoid the monotony of three successive nearly identical sections.

Example 12. Faust Symphony, introduction, mm. 1-22: unre- alized correspondence of design and tonal structure

design

A A A I It 11 1 a b c a b c a b c

I I r iI- 3 I 11 l 'I --- --I I I

V9 ' bi ~ >

Example 11. Faust Symphony, introduction, mm. 1-22: relationship between sections of design and tonal structure

A A

design I iI I design a b c a b c I IJ 11 11- 11 I

9 d~~~~~~~~~l- -1'

tonal structure

- _T

-9: '" :__ -r - r7

l1Ibid., 60-61.

tonal structure

The mere appearance of such a passage within the introduction to a symphonic movement would be reason enough for substantial comment, but a particularly fascinating aspect of this piece derives from the relationship of mm. 1-22 to the tonal structure of the movement as a whole. Conventional wis- dom might attempt to find a relationship between the structure of the introduction and that of the movement as a whole by




pointing out that both structures arpeggiate the same augmented chord. As has been maintained earlier, however, a procedure like that which organizes the middleground structure in the larger portion of the movement is not an arpeggiation, but a prolongation by means of a succession of third-related harmonies that divides the octave equally, while the procedure that organizes the tonal structure in the introduction is an arpeggiation of the augmented harmony it prolongs. If there is a relationship between these two structures, it is motivic rather than structural. Throughout the movement, successions of three major thirds, and the harmonies which can be thereby arpeggiated, play motivic roles on virtually every level. The tonal organization in the introductory Lento and in the movement as a whole are, therefore, simply two examples of this motive and illustrate rather dramatically the degree to which it saturates this piece, serving as the basis, not only of design material, but of tonally structural material as well.

This movement from one of Liszt's most popular and large- scale pieces impressively illustrates the potential of equal division of the octave as the basis for musical structure in pieces of substantial length. While the equal division of the octave does not function as the background structure of this movement (a conventional 3 \ close to the background, one which is consistent with the essentially conventional tonal syntax of the majority of the movement, occurs within the recapitulation) the role of this procedure as the basis of tonal organization within the introduction demonstrates the possibility for such a background quite effectively.

Towards the end of his life (circa 1880-86), Liszt wrote various works, many for solo piano, that appear to abandon the conventions of the common-practice tonal system. Among these pieces are "In festo transfigurationis Domini nostri Jesu Christi" (1880), "Recueillement" (after 1880), "Nuages gris" (1881), "Die Trauer-Gondel" I and II (1882), "Richard

Wagner. Venizia" (1883), "Am Grabe Richard Wagner" (1883), "Schlaflos! Frage und Antwort" (1883), and others. Some of these works, often grouped together and referred to as "The Late Piano Pieces," have been described in terms like

a very odd, peculiar piece of music, of strangely haunting character. ... of experimental nature as though the composer was reaching out towards some untraversed world of harmony. It is not like any other piece of music.12

(as Sitwell describes "Die Truaer-Gondel I"), or (as Searle sees these pieces) as representative of

Liszt . . . striking out into new and uncharted ways at a time of life when he could have well rested on his laurels.13

The following examination of one of these pieces, "Die Trauer-Gondel I," demonstrates that, for this piece at least, precisely the opposite is true. It shows that, rather than "striking out into new and uncharted ways," the piece employs structural procedures exhibited prominently in numerous earlier pieces, and that, rather than being "unlike any other piece of music," it is very much like these earlier pieces in many ways. While in some sense "Die Trauer-Gondel I" might represent an experiment, it is an experiment based on practices developed and perfected throughout Liszt's career.

"Die Trauer-Gondel I" presents an example of an entire piece based upon an equal division of the octave by successive major thirds, and bears a striking resemblance to the introduction to the Faust Symphony written nearly 30 years earlier. Like that in the earlier piece, tonal organization in "Die Trauer- Gondel I" is based on the prolongation of an augmented chord, E-C-Abl. This prolongation is achieved through the unfolding of that augmented chord via an equal division of the octave that produces an arpeggiation of that harmony in the bass.

2Sitwell, 312. 3Searle, The Music of Liszt, 122.




Design in "Die Trauer-Gondel I" may be divided into three roughly equal sections, mm. 1-38, 39-76, and 77-120. When examined for design only, these sections form an AAB pattern. Tonal organization in the first section is comprised of the establishment of the stable (i.e., tonic) augmented sonority and a contrapuntal motion to a similar augmented chord a major second below (see Example 13). The initial establishment and prolongation of this tonic sonority (mm. 1-19) employs two unfolding procedures to project this harmony. The repeating pattern in the left hand is based on a straightforward arpeggiation, which provides the accompaniment for a melody that is itself based upon an extended unfolding of the harmony being prolonged. The arpeggiation that forms the basis of this melody is embellished by upper and lower neighbor tones (Al as a

chromatic neighbor to Al in mm. 6-7, El and Gl, as neighbors to E t [spelled enharmonically as Fl ] in mm. 9-10, and B l as a chormatic lower neighbor to C in mm. 12, 16, and 18) and by passing tones (Gb, m. 8 and Dlb-El mm. 12-13). All of these melodic elaborations help to extend this arpeggiation, enabling it to encompass the first nineteen measures of the piece.

The Db ' harmonies of mm. 19-20 and 23-24 are illusory. The C~ of the upper voice is a motivically associated incom- plete upper neighbor to B (CK ), functioning much as the A of mm. 6-7 does in relation to Al. This Bt is, in turn, a middleground passing tone between Ct (m. 3) and A# (m. 37) and is itself part of a contrapuntally motivated ~ harmony that results from the upper neighbor motion of the bass (E-F-E), the maintenance of the Al in the middle voice (which moves on to

Example 13. "Die Trauer-Gondel I": voice leading of first section of design, mm. 1-38

16 19 23 mm. 12 27 32 34 36 37




the passing tone Gt in m. 34 with the return of the E~ in the bass), and the introduction of this passing Bt in the upper voice. The apparent E minor harmony of m. 34 is also illusory. It functions as a passing harmony and results entirely from the maintenance of the Et in the bass while the upper voices descend through the chromatic passing tones (B[t and Gb ). Simi- larly, the B major harmony of m. 36 is a passing harmony, but on an even more foreground level, resulting from the combina- tion of a chromatically passing D# with an anticipation of the F# of the concluding augmented chord. The appearances of these apparent triadic harmonies are much like situations found in the introduction to the Faust Symphony (what Morgan refers to as Scheinharmonien). Here, as there, local and large-scale con- texts and familiar voice-leading patterns, rather than conventions of harmonic function, determine the structural relationships among the harmonies.

The second section (mm. 39-76) begins on the same augmented harmony with which the first section ends and presents a virtually literal transposition of the first section at the major second below. This results in the arrival at another augmented harmony, built on C, in m. 75. This third augmented chord, however, gains additional significance because it is also an inversion of the harmony with which the first section begins. On a larger scale, therefore, the D-F# -Bb, augmented chord, which ends the first section and begins the second, may be seen as a middleground passing harmony between two inversions of the same tonic augmented chord. This large-scale passing motion results in a 76-measure prolongation of that referential harmony. Example 14 illustrates the voice leading that forms the basis of these 76 measures.

The structural procedures employed in these first two sections of design produce an equal division of the E-C major third that employs the transposition operation. Although the third section of design (mm. 77-120) does not continue this pattern of exact transposition, it does complete the equal division of the E-E octave by successive major thirds that forms

Example 14. "Die Trauer-Gondel I": middleground voice

leading, mm. 1-77

38 39 76 77

0d---- ~ --zz

the basis of tonal structure in the piece. In the context of this underlying structure, the descent of the first major third (from E to C) is only the first step in the larger process. Example 15

presents the voice leading of the entire piece. In the closing section, the unfolding of the tonic harmony is

accelerated in such a way that the balance of its arpeggiation takes place within a section of design no longer than each of the two preceding ones. The descent of the second major third (C-Al ) takes part in a voice exchange with the top voice. This major third, like the one which precedes it, is divided symmet- rically into two major seconds by a passing augmented harmony, here with Bb as its bass. With the arrival of AN in the bass (m. 95), the only complete return of the main melodic




Example 15. "Die Trauer-Gondel I": voice leading of entire piece

mm. 39

A A I I I I

77 87

B

idea in this section occurs. During the course of this melodic statement the bass drops to E (m. 101), thereby completing the

equal division of the octave and the unfolding of the tonic sonority. This lack of coordination between elements of design and tonal structure is entirely consistent with the way these elements are handled throughout the piece. Here, as in the introduction to the Faust Symphony, the conflict between tonal structure and design helps to avoid monotony, while the accel-

eration of tonal motion towards the end of the piece contributes to the achievement of closure.

The harmonic-contrapuntal structure that is produced in conjunction with this equal division of the octave is not based upon the transposition operation, but it does bear striking and significant similarities to a structure that would be so produced. Example 16 presents a comparison between an equal division of the octave that employs the transposition operation, in

95 101 11.2




Example 16. Comparison between equal division of the octave employing transposition operation and middleground of "Die Trauer-Gondel I"

a.

b.

- - -

# - +f r--- -I

which each step of the arpeggiation is subdivided into two major seconds (Example 16a), and the middleground structure of "Die Trauer-Gondel I" (Example 16b).

In the equal division of the octave that employs the transposition operation (Example 16a), the consistency in each step of the procedure produces a series of seven transpositionally equivalent augmented harmonies. While each of these harmonies has a different bass tone, the successive transpositions at the interval of a major second result in the occurrence of only two different harmonies, E-C-ANl and D-F#-A# (assuming enharmonic equivalence), each of which appears in three different inversions. These two harmonies combine to make up a

single whole-tone collection (E, F#, G#, A,, C, D) a collection from which all the middleground harmonic material is drawn.

Because there is no inherent hierarchic relationship between these two harmonies, any establishment of a tonal hierarchy within such an equal division would be almost entirely dependent upon voice leading. In a situation based on the exact duplication of voice-leading procedures at each step in the equal division, hierarchic differentiation would be quite difficult. Equal division of the octave by successive major thirds that both unfolds an augmented chord and strictly employs the transposition operation would be, therefore, impractical as the basis of a piece of substantial length.

The underlying voice leading of "Die Trauer-Gondel I" (Example 16b) exhibits striking similarity to the equal division of the octave that employs the transposition operation, but it also exhibits significant differences. These differences contribute importantly to the effectiveness of this procedure as a background structure. While it employs the same harmonies in the same roles (save the omission of the passing harmony that would have filled in the last of the descending thirds), only the first segment of this structure (mm. 1-76) is based on the transposition operation, and there the transposition operation appears on a relatively foreground level. The balance of the piece employs voice leading that emphasizes independence of the voices, the voice exchange of measures 77-95, and the oblique motion of the bass at measure 101, thereby making the establishment of a tonal hierarchy much easier. In other words, the harmonic material that would be produced under the transposition operation is employed within voice leading not employing that operation in order to exploit the potential for the genera- tion of a tonal hierarchy available within the latter procedure.

This adaptation of an equal division of the octave that employs the transposition operation combines with the disparity between design and tonal structure to give the piece a vitality and musical flow that otherwise would not be present. The three segments of the tonal structure could easily have been dis-




tributed evenly among the three sections of design so that each would correspond to one of the major-third descents. The transposition operation also could have been maintained as the basis of tonal organization throughout the piece. The harmonic-contrapuntal structure that would have resulted, however, would be static, undifferentiated, and uninteresting, and a sat-

isfying sense of closure would have been very difficult to achieve. In adapting, modifying, and combining these design and tonal elements, Liszt demonstrates a skill in handling these materials that attests to a career of experimentation with similar procedures.

While it is valid to note the role of whole-tone materials on the deep middleground level in this piece, it is essential to realize that the achievement of these whole-tone materials is not the primary goal of the structural procedures employed here. In the context of the maintenance of the augmented chord as a stable and referential harmony and its arpeggiation, such whole-tone materials result as a by-product of the equal division and subdivision of the octave and its constituent segments.

Admittedly the view of this piece offered here may be con- troversial. The very idea that a harmonic entity that is viewed as

inherently unstable within the conventional tonal system (the augmented chord) might serve as the tonic of a piece like this one, or even undergo prolongation in a way derived from conventional tonal practices, seems somewhat contradictory to many traditional views of tonality. For this reason analysts have often tried to explain the problematic late works of Liszt in terms of more conventional tonal practices, often seizing upon harmonies like the apparently more normative and 5 chords found in this piece as the basis of their analyses. Such readings are common within the analytical literature on the late piano pieces and contribute significantly to the confusion surrounding these pieces.14 They betray a commonly held fundamental bias

'4See, for example, the analysis of this piece that appears in Bernard Charles Lemoine, "Tonal Organization in Selected Late Piano Works of Franz

towards apparently more normative triadic sonorities, which insists on finding such a sonority as the basis of this music even when context indicates that some other interpretation is more justified.

For other theorists quite the contrary is true. Some analysts have promoted the idea of examining Liszt's late piano works and other highly chormatic nineteenth-century works from the perspective of theories of small set relations that have been applied primarily to twentieth-century music.15 This approach sees these pieces as precursors of twentieth-century syntax and de-emphasizes their association with, and derivation from, earlier and more conventional tonal practices. Such an approach to this piece would, almost certainly, attribute a great deal of significance to the augmented sonority as an abstract pitch-class set and would likely try to demonstrate a hierarchy of relationships within which this set and other prominent sets that appear in the piece would be seen to function. While this viewpoint might be justifiable on the basis of the prominence of this set on the surface of the piece, the full significance of the augmented harmony can not be appreciated without acknowledging its role on deeper levels of structure and the relationship of the procedures applied to this sonority to the conventions of earlier practice.

Certainly, this piece and others of the late piano pieces can serve important functions in illustrating portions of the evolution from the tonal practices of the conventional tonal system to those of twentieth-century music. But this evolution can never

Liszt," (Ph.D. dissertation, The Catholic University of America, 1976; Ann Arbor: University Microfilms International), 30-36, reprinted in Liszt- Studien: Refera Des 2. Europiischen Liszt-Symposium Einstadt 1978, he-

rausgegeben von Serge Gut, (Munchen-Salzburg: Musikverlag Enid Katzbich-

ler, 1981), 123-131, especially 124-125. 15The reader will probably recognize this approach as that developed by

Allen Forte in The Structure of Atonal Music (New Haven and London: Yale

University Press, 1973) and elsewhere.




be clearly understood if analysts insist on adhering too closely to analytical assumptions based on the conventions of either style. This could lead (and up to now often has led) to a failure to perceive fundamental features that both styles have in common.

Both the introduction to the Faust Symphony and "Die Trauer-Gondel I" illustrate structural procedures that may be directly related to those observed in the pieces from the Annees de Pelerinage and the middleground of the first movement of the Faust Symphony. Significant differences between structural procedures in these pieces should be emphasized, however. In the pieces from the Annees and in the larger portion of the Faust Symphony movement, the prolonged harmonies are conventional (i.e., major or minor) triads. When a true equal division of the octave occurs, as in the middleground of the Faust Symphony, it results in a dichotomy between the harmonic and linear dimensions. In the introduction to the Faust Symphony and "Die Trauer-Gondel I," though, there are correlations between the augmented harmonies that are prolonged and the successions of major thirds that prolong them. The equal divisions found in these two pieces may thus be said to unfold the prolonged augmented harmonies in a way analogous to that whereby a I-III-V progression arpeggiates the major or minor triad that it prolongs.

The evolutionary process, whose completion is illustrated by these two works, resolves the dichotomy between the harmonic and linear dimensions in favor of the apparent arpeggiation and results in a systematically consistent means by which unconventional harmonies, like augmented or diminished- seventh chords can be prolonged. Structures like those found in the two pieces are, thus, reasonable extensions of procedures found in Liszt's earlier music and not the radical departures from his earlier style they are often said to be. The evolutionary progression from correlation, to dichotomy, to correlation between the harmonic and linear dimensions, is illustrated in Ex-

ample 17. Like any other evolution, this one is not strictly chronological nor is it continuous. This evolution is, however, a general tendency which is strongly evident in much of Liszt's music and may also be observed in the music of many other nineteenth-century composers.

Two pertinent points regarding equal divisions of the octave that also unfold a prolonged harmony should be made before closing. First, though this procedure bears significant similarities to tonic-arpeggiating I-III(# )-V-I progressions, it is also significantly different. The harmonies in a I-III(# )-V-I progression, while analogous to one another-they are all major or minor triads-are nonetheless different harmonies; they are not merely different inversions of the same harmony. In an equal division of the octave that unfolds an augmented chord, however, the harmony produced at each step in the arpeggiation is also an inversion of each of the others. The distinctions between III,, , VI, and inversions of I no longer exist. (It is for this reason that Roman-numeral analyses have been omitted from the last stage of Example 17 and from the analyses of the introduction to the Faust Symphony and "Die Trauer-Gondel I.") This fact severely limits the harmonic variety available within a systematically consistent tonal organization produced in this manner.

Second, though both augmented and diminished-seventh sonorities can be unfolded in this way, the unfolding of an augmented chord offers a greater potential for further equal subdivision. (While the diminished-seventh chord can be equally subdivided into a succession of minor seconds, it would be difficult to distinguish the resulting structure from an undifferentiated chromatic succession.) For this reason, the more advanced stages of this evolution tend to employ equal divisions of the octave by successive major rather than minor thirds. Further- more, since equal subdivision of this unfolding tends to result in a harmonic structure drawn entirely from one whole-tone collection, these whole-tone structures may be seen to result directly as a by-product of this evolution.




Example 17. Evolutionary progression of prolongation procedures

() jNIL- I A 1,_ L- I 1 I

e *w1 'I - e

. _ rd ^ -- " -- I^. + ^ L\- _ I\ s

LI- 9-.-

- -II) - - v- -I

(tonic arpeg.)

or

I- -11 I(t)-- bVI- i --I

(incipient equal div.)

correlation between - -- > dimensions

I-- -ii- - v- ---I

(equal div. of octave by thirds)

dichotomy between --- -> dimensions

(arpeg. of aug. chord)

correlation between dimensions

* The parallel fifths and octaves, shown in this abstraction, would certainly be avoided on the foreground, probably through an approach to the dominant through a cadential 6 or through some intervening voice-leading chords (e.g., an augmented-sixth chord) or contrapuntal motion.

Both the introduction to the Faust Symphony and "Die Trauer-Gondel I" contain extended prolongations of harmonies that would be relatively unstable in the conventional tonal system. The fact that these unconventional prolongations are achieved by means derived from conventional tonal practices and can develop sophisticated systems of hierarchic relationships in the process suggests significant ramifications of our understanding of music from both earlier and later periods. In both these pieces, context, generated by the consistency of relationships on and among the levels of structure, determines the tonal hierarchy, not an arbitrarily determined system of primacy. Each piece sets up its own hierarchic universe of tonal relationships that is, in some ways, an alternative to the con-

ventional tonal system and employs that system of relationships consistently.

The fact that this can be achieved to the satisfaction of most listeners, and that these systems can be effectively employed as the basis of tonal organization within pieces of significant length, has implications for the further investigation of much twentieth-century music that is outwardly similar to these pieces, wherein similar structural procedures may be in use. The effectiveness of these contextually generated systems also has implications for the understanding of the conventional tonal system and should motivate questions as to the roles of context and consistency of procedures across structural levels within that system of hierarchic relationships as well.

o ____j ag 17. - -1" -_ -11 1- _,"

iy

'A. -01 -0-

i



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