Debussy, Wolpe and Dialectical Form

Matthew Greenbaum

It is hard to imagine music more dissimilar than that of Claude Debussy and Stefan Wolpe. And yet Wolpe's approach to form owes a great deal to Debussy, who - as I will try to show - first elaborated the dialectical scheme so common in Wolpe. By examining the historical evolution of this hitherto unlabelled form we can better understand Wolpe's indebtedness. We shall use as illustrations a preliminary example from Don Giovanni, then Debussy's "Des pas sur la neige" and finally Wolpe's Form for piano.

In the most rudimentary dialectical form a musical idea progressively generates its antithesis: a gradually emerging contradictory idea. ⁽¹⁾ Conflict, contrast, and opposition: all are types of antithesis. Just as other aspects of music, antithesis also had a historical development, which culminated in new form-generating structures in late-19th century music, as I will try to demonstrate below. This was a result of the increasingly subjective musical aesthetic that was to find its full flowering in Symbolism and which required a new vehicle of representation once it had transcended the structural and representational confines of common practice tonality.

While a work like "Des pas sur le neige" can be analyzed in many ways - the most inviting being, perhaps, a modified strophic structure or rounded binary form - these descriptions do not account for its evolutionary dynamic. I maintain that its underlying dialectical process is powerful enough to reduce details of formal repetition to epiphenomena; or rather, that the dialectical process appears to produce form as it moves through time. Even though one may bridle at the use of the word 'form' to describe what at first might appear to be only a process, the totalizing effects of this process are impossible to ignore.

You may have assumed that Hegelian logic is the source of this dialectical thinking; but it is difficult to determine the direction of influence as far as Hegel and his musical contemporaries were concerned. Beethoven owned a few of Hegel's works although it is unclear to what extent he made use of them. ⁽²⁾ In fact, Beethoven and Hegel both drew upon conventions of musical rhetoric which themselves originated in the classical tropes. ⁽³⁾

The Enlightenment organicism of Kant and Goethe valued artworks that developed from a motivic kernel, and which seemed to be driven by an inner necessity comparable to a biological process. No detail should be extraneous to the cellular growth of the whole. Beethoven is heir to this aesthetic. It would seem, then, that the organicist model left no room at all for self-contradiction. But contradiction had already entered music with the classical rhetorical figures, which had permeated the logic of Baroque music as oratorical tropes and which persisted through the Classical Period.

The Baroque fully embraced Aristotle's definition of rhetoric as a counterpart of dialectic (disputation). The enthymeme, or rhetorical demonstration, ⁽⁴⁾ underlay the Affekten; contradiction in music was meant to exert the same oratorical force as rebuttal in debate, but whose object now was the listener's submission to an Affekt rather than to an argument.

This is borne out in Baroque music theory. According to Mattheson, the main idea (Propositio) is to be succeeded by one or more counter-statements (Propositio variate) at last opposed by the Confutatio, or resolution of objections "expressed by ... the citation and refutation of apparently foreign passages. ... Everything that goes against the proposition is resolved and settled." ⁽⁵⁾

Affirming this redendes Prinzip - the "speaking" or "oratorical" principle in music - Riepel writes, in analogy to the rhetoric of exegesis: "A preacher cannot constantly repeat the Gospel and read it over and over; instead, he must interpret it. ... In addition to the thesis [Satz], he has at the very least an antithesis [Gegensatz]." ⁽⁶⁾ These terms were given to the themes of the sonata movement a generation later by Forkel (1788), who calls the main theme the Hauptsatz [thesis] and the contrasting theme the Gegensatz [antithesis]. ⁽⁷⁾

All this antedates Hegel, who, in the Vorlesungen über die Äesthetik (1820 - 1829) uses similar language to describe musical contrast. ⁽⁸⁾ Borrowing Riepel's terms, Hegel sees thematic contrast as a contradiction (Gegensatz). Most comprehensively Hegel describes the antithesis (Gegensatz) of consonance and dissonance as a conflict between imaginative freedom and the necessity of an underlying harmonic logic. ⁽⁹⁾ It is in the Äesthetik that Hegel links the principal of rhetorical conflict with an overarching metaphysics of time and consciousness.

The naturalism of the Enlightenment had streamlined the relationship between form and content: the "public" nature of the late-18th century sonata required that the affective intention must be grasped immediately along with the form. (Indeed, the dialectic of tonic and dominant - a closed circle of distance and return - is a rhetorical figure in itself.) Themes were character types, essentially interchangeable with operatic figures. The aim was the depiction of human nature; or, rather, nature in its human dimension. The Kantian sublime was new to this schema, although the harbinger of things to come.

The representation of the sublime, which includes everything terrifying and otherworldly, required the employment of contemporary outer limits of tonality: sequences of diminished seventh chords, functional chromaticism and modulatory sequences. In Don Giovanni Mozart begins to press beyond these conventions. Consider the following curious moment, where the ghostly statue of the Commandatore is about to drag the Don to Hell:

Example 1: From Mozart: Don Giovanni

The distinctiveness of this passage is the result of rather startling chromatic and whole-tone implications, brought into relief by octaves with no explanatory harmonies to support them. Note the:

- 0148 tetrachord (at A).

- chromatic accumulation in the voice part at B

- subsequent orchestral scalar figure at A', which completes the 12-tone aggregate, as does the chromatic bass movement A'').

- the implied descending whole-tone sequence at C, which also includes a C#/F dyad at D whose harmonic logic is nearly impossible to grasp by ear.

In the dialectic of Don Giovanni, the carnal world of the earthly characters emerges from a supernatural world first enunciated in the overture and concluding in the spirit-ridden scene where the Don meets his perdition. (The work originally ended here, nicely resolving the metaphysical conflict, but this solution was considered insufficiently moralistic, impelling Mozart to add a final sextet). As a result of a new arsenal of compositional innovations, music vastly expanded its capacity to represent the subjective. Modulation to heretofore inaccessible key areas (thanks to equal temperament), Lisztian octatonicism, whole-tone scale expansions of the French sixth chord, extended chromaticism; all permitted the depiction of novel psychological worlds. Coinciding with - and indeed linked with - the Symbolist movement, this panoply of devices allowed the pictorialization of transcendent, infinitely subtle psychological states. The character contrast of sonata form was subsumed into metaphysical opposition. The extension, or even abolition, of tonal conventions offered the possibility of a form based entirely on the generation of contradiction. The replacement of tonality by other scalar forms and extended chromaticism, as in Liszt and Debussy, demanded a dialectical logic to avoid a discontinuous, "inorganic" partitioning of unrelated materials. But this form required a rhetoric of imagery to make it comprehensible: the imagery of Symbolism.

Hegel had already made a connection between musical logic and the symbolic. He describes the logic of instrumental music as a representation (Vorstellung) of abstract feelings (abstraktere Empfindungen) ⁽¹⁰⁾; but also as ready to represent the most varied meanings; a correspondence with the inner self of the listener who must quickly decode (entziffern) and grasp its symbolic (symbolisch) meaning. ⁽¹¹⁾

Given our limitations of space it must be pointed out only in passing that it was Wagner who first made music out of this new rhetoric of symbols. Baudelaire, whose sonnet "Correspondances" was the exemplar of Symbolism, was a passionate Wagnerite. ⁽¹²⁾ The Ring can be understood as a vast dialectic in which the world of the gods and men emerges from Nature, i.e., the Rhine, only to plunge back in a final cataclysm. ⁽¹³⁾ This grand metaphysic is reflected in the basic level of character conflict and its musical analog, the Leitmotif.

It was Debussy, however, who perfected a dialectical form without words. Here, he followed Liszt, whose Nuages gris is a daring - if rather modular - example of the form. The music of Debussy is less a discourse, in the 18th century sense, than a sounding correspondence with the natural world. ⁽¹⁴⁾ Here, the redendes Prinzip - music as discourse - has been overshadowed by a new sense of music as object, as a process resonating with the natural world: organicism enriched by Symbolism.

A "symbolic" music must stand in opposition to developing variation and other conventional techniques of development since symbols, sound-symbols included - must be taken in as a sensuous whole at the moment of their occurrence. Conventional development would destroy their meaning; they can only emerge and disappear.

"Des pas sur la neige..." (Préludes I #6) is a completely realized dialectical form. ⁽¹⁵⁾ It evolves from the interpenetration of disparate pitch materials (diatonic, octatonic, whole-tone and chromatic). Its brief apotheosis, an "organum" in the G diatonic pitch collection, emerges from this matrix and stands in dramatic opposition to the prelude's initial D modal minor tonality. ⁽¹⁶⁾

Example 2 illustrates the emergent process in "Des pas sur la neige". Pitches in the D minor collection are represented by diamond-shaped noteheads while normal noteheads represent the emergent G major collection (overlapping pitches E - enharmonic F, and B diamond-shaped). The whole-tone and octatonic collections, which mediate between the D and G collections, are indicated by dotted shapes; the former by dotted circles and the latter by rectangles.

The point of emergence in "Des pas sur la neige" is signaled by a brief halt in the D E F ostinato figure that runs through the rest of the prelude. The pitches of this ostinato are shared by the D minor, whole tone and octatonic collections. This permits a constant reinterpretation of the figure, as if it were moving through a gradually changing physical space. ⁽¹⁷⁾

Example 2: Debussy; Des pas sur la neige, Pitch Collection Analysis

Diamond noteheads indicate D minor collection. Normal noteheads indicate G major collection.

Whole-tone collections are indicated by dotted curves and octatonic collections by dotted rectangles.

The whole-tone set shares three pitches each with the D minor and G major collections, allowing it to function as a pivot-an extended French sixth (F# C B D and then E) in mm. 8 to 10 - in relation to the preceding D minor region as well as the succeeding (enharmonically-spelled) D dominant seventh chord. This harmony recurs in measures 14 and 15 and again in m. 23, finally to be resolved in the emergence of the G area in measures 29 through 31.

Example 2 shows the gradual submersion of the D collection and the reciprocal emergence of the G collection. ⁽¹⁸⁾ The intervals of the ostinato comprise the basic cell of the octatonic collection [013], and it is therefore not surprising that octatonicism plays an integrative role in the prelude, where it aids the transformation of the D into the G ⁽¹⁹⁾

Figure 1: Overlapping sets in "Des pas sur la neige"

An additional aspect of organization in the prelude, one that enhances the ambiguity of the pitch collections, is the reordering of repeated material. This technique plays a similar role in Wolpe's Form for Piano, as shown in Martin Brody's "Sensibility Defined: Set Projection in Stefan Wolpe's Form for piano" ⁽²⁰⁾, where Brody describes the migration of what Wolpe calls "autonomous fragments." Although these fragments are sometimes no larger than a single interval, their irregular patterns of repetition have a mnemonic function similar to reordered measures in Debussy.

Mm. 3 and 19 in "Des pas sur la neige" are nearly identical, and mm. 5 and 20 are completely so. But the logic of source measures 3 to 5 is broken by the omission of the intermediary m. 4: there is no duplicate m. 4 separating m. 19 from m. 20. Such telescoping makes it difficult to recall the original order of materials. This stands in stark contrast to conventional tonal forms, which depend on strict succession and literal repetition to support recollection and comparison. The technique of fugitive retrospection in "Des pas sur la neige" is suggestive of the Symbolist aesthetic of transcendence that sought trans-temporal "recollections" of prior existences throughout painting and poetry.

Dialectical form pervades 20th century music. Elliott Carter speaks of his own 'epiphanic form' and articulates a lineage with Debussy and Schoenberg. In Carter's 'epiphanic form,'

... the relations between musical ideas are revealed non-linearly across a piece rather than in the

form of theme and variation or development. The term 'epiphany' was adopted by James Joyce

to mean the sudden revelation of meaning; ... Carter points to Schoenberg's Erwartung and to

Debussy's Jeux as musical precedents for this technique. ⁽²¹⁾

Carter might have added Stravinsky to his list; examples abound: Symphonies of Wind Instruments (1920, rev. 1947) is a case in point. It originated as a chorale for piano in memory of Debussy. Stravinsky made the chorale serve as the conclusion to the wind piece and composed the rest of the work to lead up to it. The chorale is foreshadowed a number of times before its emergence.

A dialectic of emergence is at work in much of Schoenberg's music. The Serenade op. 24 - a direct predecessor of 12-tone composition - is a case in point. The motif of the parodistic first section of the Tanzscene movement is a hexachord whose symmetrical complement is the thematic basis of the movement's more lyrical trio sections. ⁽²²⁾ Hexachordal opposition produces a polarity in the fabric of the work. Schoenberg was to make use of this polarity - to a greater or lesser degree - in all subsequent hexachordal compositions. Here, the emergent moment is replaced by an oscillation between complementary hexachords. Wolpe extended this idea to include an oscillation between two unequal or asymmetrical pitch collections, as in the second movement of Piece in Two Parts for flute and piano and Form for piano.

Stefan Wolpe's long friendship with Varèse reinforced his early predilection for dialectical thinking. Many of Wolpe's works - particularly the late music - must be understood in this perspective. ⁽²³⁾ Both Wolpe and Varèse posited a musical space that acts as a field for pitch structure. ⁽²⁴⁾ Varèse's works (and Wolpe's from Form for piano and after) are made up of assemblings and dispersals of pitch symmetries that underlie and motivate such structures, generating a total form that Varèse describes as analogous to the growth of crystals. ⁽²⁵⁾ Here, the dialectical opposition is a series of contradictions, the totality of which is the form of the work.

Austin Clarkson, speaking of Wolpe's notion of fantasy, quotes Karl Jung's distinction between 'symbol' and 'sign', where a sign stands for a "known thing" while a symbol "formulates an essential unconscious factor." ⁽²⁶⁾ Wolpe not only drew upon Debussy's formal innovations, but also, surprisingly, his art of fashioning symbol-laden musical ideas as well.

Clarkson describes Form for piano as a series of "forty or so images." He goes on to say that

The forces needed to make so many different items cohere are generated not from

familiar rhetorical strategies of exposition, complication, crisis, and release, but from the ten-

sions generated from the juxtaposition of strongly contrasted images. ⁽²⁷⁾

Wolpe suggests this in his notes to Form for piano, as well as verifying its dialectical basis, when he writes:

Since opposites become adjacencies, the modes of opposite expression as hard and soft, wild

and tame, flowing and hesitant, etc., all these modes become self-inclusive. The piece feeds its

own totality and brings everything into its focus. ⁽²⁸⁾

The "thesis" of Wolpe's Form for piano is self-evident; it is the hexachordal monody that begins the piece (see Example 3). Its antithesis is the complementary hexachord in m. 4. The dialectical unfolding and interpenetration of these two hexachords eventually generates their transpositions, which emerge at just before the midpoint of the piece at m. 30 and then dominate it until m. 58, as shown in Figure 2. The emergence of the transpositions is the dialectical core of the work.

I shall borrow Brody's nomenclature and call hexachord I, "P"; its transposition is T5P. Hexachord II is called Q and its transposition is T5Q. In Figure 2 P is indicated with black noteheads and Q with white. Transpositions are indicated with small noteheads. This makes clear the interpenetration of the hexachords and the emergence of the transpositions. Pushing Debussy's principle of non-repetition even farther, no measures - or even symmetries - are repeated literally.

Although P and Q are equally well-represented in Form, P is granted special status; it makes up the opening monody and its two successive variants, and is repeated just before the end in MM. 59 to 61; an octave lower and with varied attack patterns, but still recognizable as a thematic idea. Q, however, functions as the "Other"; the antithetical content into which P continually dissolves. Clarkson, paraphrasing Wolpe, describes each hexachord with a compound image: the first as "inward, centering, compressing, and contracting" while the second "expands, rarifies, unfocuses, and releases."

Two principles govern the structure of Form. The first is the interpenetration of hexachords; the second is the disposition of symmetrical relations between them. Where these groups appear alone there tend to be fewer symmetries and very little polyphony (as in MM. 1-3, 5,  the first half of 6, 11-12 or 60-64.) When they interpenetrate, a web of symmetries appears, often spanning the entire range of the passage from the highest to the lowest pitch, as in MM. 28 and 51.

Example 3 : Wolpe Form, opening page

© Tonos Editions, distr. Seesaw Music 2067 Broadway Ave, NYC

Figure 2: Wolpe: Form, Hexachodal Analysis: Boxes and brackets mark symmetries. Dotted boxes show dotted symmetries. Intervals of symmetry is sometimes indicated for clarity. Whlte noteheads: Hexachord P. Black noteheads: Hexachord Q. Small noteheads: transpositions.

These symmetrical progressions are dynamic; they result from the projection of intervals from register to register. Such interval likenesses create the spatial dimensionality so characteristic of Wolpe's music. The projected intervals operate in the manner of rhymes which link together dissimilar ideas and project a poem forward in time. Figure 2 shows symmetries as boxed pitch groups or as bracketed pitches connected by dotted lines. Dotted boxes show additional symmetries. Hexachord mixtures tend to present the greatest symmetrical content, as in mm. 14-15, 27, and particularly 28.

The interaction of symmetries is the dialectic of Form for piano. As Example 3 shows, there is very little music that escapes these symmetrical relationships, which must have been sketched out first in what Wolpe called "precompositional selectivity." Pitches that do not sound in vertical symmetries are nearly always part of a horizontal symmetry, as the G and A in m. 4, which, together with the E F#, are in symmetrical opposition to the D C in the same measure. More than simply reiterating an interval, the G and A from hexachord P are projected onto kindred intervals in the suddenly emerging hexachord Q in dialectical forward motion.

There are four basic dialectical tropes in Form::

Emergence: of hexachord T5P and T5Q

Interpenetration: here, the hexachordal process

Transformation: the recomposition of hexachords, as in the reworkings of P in mm.1-4

Symmetry

As we have seen, the first three are also characteristic of "Des pas sur la neige". It is here that that the kinship between Wolpe and Debussy visibly emerges. While symmetry plays no obvious role in Debussy, it is worth noting that the whole tone, octatonic and pentatonic collections are symmetrical, as are many of their subsets, and this colors the pitch language of "Des pas sur la neige". The above categories are not meant to be exhaustive - many others are possible - but are offered as a first step in the creation of a new analytic instrument.

The notion of dialectical form permits us to think about post-tonal music in an active mode. Viewed from this perspective, each event in a work so constructed bears a meaningful and dynamic relationship to the process of emergence that governs it, rather than simply manifesting a series of "one thing after another" that Wolpe parodies in "Thinking Twice" ⁽²⁹⁾ and often dismissed as a "mittler Zustand Extase" (average-state ecstasy).

Wolpe delighted in teaching "Des pas sur la neige". It must be admitted that no Wolpe sound surface resembles it, Form for piano least of all. That composers as dissimilar as Wolpe and Debussy could have shared a common understanding of musical form- as well as a kinship relation as far as musical imagery is concerned - is evidence of a broader historical process that embraced them both.

1. There are also extended types of dialectical form: a rondo-like succession of syntheses (as in the emergent moments of Debussy's "La Cathedrale engloutie"; or a continuous series of momentary syntheses, as in works of Edgard Varèse and Stefan Wolpe. See Greenbaum, "The Proportions of Density 21.5: Wolpean Symmetries in the Music of Edgard Varèse" in On the Music of Stefan Wolpe, Austin Clarkson, ed., Pendragon (Hillsdale, New York: 2003) 207-219.

2. David B. Dennis, "Beethoven at large: reception in literature, the arts, philosophy, and politics" in The Cambridge Companion to Beethoven, Glenn Stanley, ed., Cambridge U Press (Cambridge: 2000) 300. Beethoven's motivic unity over multiple-movement compositions, as well as his use of cyclical forms, are suggestive of dialectical thinking.

3. The Frankfort School post-Hegelian Theodor Adorno understood the Beethoven's late-period style as a dialectic between the subjective and objective which embodied a fatalistic reaction to the failure of political ideals. More to the point, he understood exposition/development/ recapitulation in Beethoven's middle period style as embodying the thesis/antithesis and integration of the dialectic. See Rose Rosengard Subotnik, "Adorno's Diagnosis of Beethoven's Late Style: Early Symptoms of a Fatal Condition," JAMS 29, 1976 242-275. A rather simplistic dialectical-materialist approach to Beethoven and Hegel can be found in Ballantine C., "Beethoven, Hegel and Marx" in Music Review 33, 1972, pp. 34-7.

Philip T. Barford ("Beethoven and Hegel," Musica 1953, 437-440) has pointed out that the tension between subjectivity and objectivity in Beethoven's sonata forms is precisely that of Hegel's understanding of music in the Aesthetik.

4. The Art of Rhetoric, trans. H. C. Lawson-Tancred. Penguin (London: 1991) 68.

5. Hans Lenneberg, "Johann Mattheson on Affect and Rhetoric in Music (II)," Journal of Music Theory 119-236. 195.

6. Hans Lenneberg, "Johann Mattheson on Affect and Rhetoric in Music (II)," Journal of Music Theory 119-236. 195.

7. Riepel, Anfangsgründe zur musikalischen Setzkunst 1752; quoted in Mark Evan Bonds, Wordless Rhetoric: Musical Form and the Metaphor of the Oration Harvard University Press (Cambridge and London: 1991) 99.

8. Bonds 124.

9. E.g., " ... such progressions and modulations ... which require none too violent antitheses [Gegensätzen] ... Rather, a satisfactory unity [Einheit] is produced." Georg Wilhelm Friedrich Hegel, Vorlesungen über die Äesthetik III: Works: 15. Surhrkamp (Frankfurt am Main: 1970) Hegel 187.

10. Hegel 188-189.

11. Hegel 217.

12. "Correspondances [in Les Fleurs du Mal] ... became the gospel of the new poetic movement. The language of Baudelaire appeals as much to the intellect of the reader as to his physical sensibilities. It does not directly represent things and feelings; it offers a choice of the most suggestive correspondences among analogies which exist between words, and sounds and their atmosphere-a choice which tends to create a harmonious poetic substance which acts upon the imagination, not only through its meaning, but also through its sound." Stefan Jarocinski, Debussy: Impressionism and Symbolism, Rollo Myers trans. Eulenberg Books (London: 1976) 65.

13. Wagner speaks of Hegel only in connection with his metaphysics; Hegel was replaced, first by Feuerbach and then Schopenhauer, in his philosophical development. See Bryan Magee, The Tristan Chord, Metropolitan Books (NY: 2000) 134 and passim.

14. It is no longer "confined to reproducing, more or less exactly, Nature, but the mysterious correspondences which link Nature with Imagination."Jarocinski 96.

15. An attempt to diagram its form as AB A/B (A/B = combination) appears in Richard S. Parks, The Music of Claude Debussy. Yale University Press (New Haven and London 1989) 222. Parks writes, "Another ternary-derived archetype is the tripartite design ... whose last section synthesizes characteristic features of the first two." The above AB A/B schema obscures an essential quality of dialectical form: the progressive generation of B from A and their interaction, so that B gradually and organically emerges as the antithesis of A.

16. See also "Voiles" (Préludes I #2), where a whole-tone collection cedes to the emergence of a pentatonic collection).

17. Pitch-class E is a member of the whole-tone collection, pitch-class F is a member of the G major collection, and pitch-class D is shared by both. The figure is meant to have the sonic value of a sad and frozen landscape: "Ce rhythme doit avoir la valeur sonore d'un fond du paysage triste et glacé."

18. In Example 2 the D minor collection is marked by diamond-shaped noteheads, the octatonic collection by dotted rectangles and the whole-tone collection by circles. The G collection is shown in conventional noteheads. Pitch-classes F and B are shared between the D minor and G collections,

but are not indicated as such in Figure 1so as to make the emergent processes clearer.

19. Chromaticism also plays a constructive role. A half-step source is immediately established in the ostinato's E F. The half-step idea is further extended in measure 8 and the near-duplicate 9, accompanied by parallel chromatic minor sevenths B/C to B/C# in half notes. These are in turn connected by the chromatic trichord F# G G# in quarter-note motion. Measure 10 - an altered repetition of measure 8 - presents a chromatic trichord in contrary motion BA A. All this produces an eleven-member chro-matic set A A B C# D E F F# G G# . The aggregate is completed by the prelude's first E, in measure 12. (The trichord connection reappears as C B B in measure 15.) The chromatic process continues in measures 23 to 24. Here, a tetrachord D D E E supports a series of altered dominants. This leads to a culmination of the chromatic process at measure 26 to 27 where the trichord G G F supports a series of minor triads as well as a tetrachord D D C B. These triads, along with the accompanying ostinato form the 11-member collection E F G G G# A B B C D D. Again, the missing pitch is E, which had just been heard in the bass motion in measure 24.

20. Perspectives of New Music Spring-Summer 1977.

21. The Music of Elliott Carter, David Schiff, Cornell University Press (Ithaca: 1998) 39-40.

22. George Perle, Serial Composition and Atonality. Fourth Edition (U Cal Press: 1977) 94-5.

23. Greenbaum, "Stefan Wolpe's Dialectical Logic."

24. Varèse - the revolutionary sound surface of his works notwithstanding - was profoundly influenced by Debussy; this influence is manifest in his brief Un grand sommeil noir (1906).

25. Matthew Greenbaum, "The Proportions of Density 21.5."

26. "'The Fantasy Can be Critically Examined': Composition and theory in the thought of Stefan Wolpe," in Music Theory and the Exploration of the Past, D. Bernstein & C. Hatch eds., (U Chicago 1993), 505-524.

27. Clarkson 507.

28. Clarkson 520.

29. in Elliott Schwartz and Barney Childs, eds., Contemporary Composers on Contemporary Music (New York, 1967) 274.