Communication and Interaction in Stravinsky's Scherzo fantastique (1907-1908) Kip Wile Recent years have witnessed numerous contributions toward the "new branch of theory" which Arthur Berger prophesied for Stravinsky's music, one prepared "to deal with the nature oftwentieth­ century music that is centric (Le., organized in terms of tone center) but not tonally functional." 1 Perhaps most well known among the new approaches is that inaugurated by Berger himself and further developed by Pieter van den Toorn, in which Stravinsky's tone structures are classified according to octatonic, diatonic, and interacting octatonic­ diatonic pitch organization. 2 Berger's and van den Toorn's procedure 1Arthur Berger, "Problems of Pitch Organization in Stravinsky," Perspectives of New Music 2 (1963): 11. 2This method is set forth most comprehensively in Berger, "Problems of Pitch Organization" and in Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven: Yale University Press, 1983). See also by van den Toorn, "Some 88 Indiana Theory Review Vol. 13/1 has recently been supplemented by Richard Taruskin, who, in response to certain of its critics, has sought to "shore up" particular aspects of the approach through an increased historical perspective and with an analysis of the second tableau of Petrushka. 3 Despite its apparent shortcomings, the Berger-van den Toorn method has yielded discoveries of octatonic, diatonic, and octatonic­ diatonic pitch organization in Stravinsky that have proven so widespread that a stage appears to have been reached at which, as Taruskin has put it, "no further objection to those findings can, I think, be entertained.' '4 It is for this reason that a next logical step toward the "new branch of theory" which Berger predicted would comprise the development of principles centering not upon the isolation and classification of relevant pitch collections-this procedure would now be considered a required preliminary step - but rather upon a study of dynamic relations existing among the collections themselves. With this purpose in mind I wish to introduce principles of a well-defined Characteristics of Stravinsky's Diatonic Music," in Perspectives of New Music 14 (1975): 104-138; "Octatonic Pitch Structure in Stravinsky," in Confronting Stravinsky, ed. Jann Pasler (Berkeley: University ofCalifornia Press, 1986), 130-156; Stravinsky and the Rite of Spring: The Beginnings of a Musical Language (Berkeley: University of California Press, 1988). 3Richard Taruskin, "Chernormor to Katschei: Harmonic Sorcery; or, Stravinsky's Angle," Journal of the American Musicological Society 38 (1985): 72-142; "Chez Petrouchka: Harmony and Tonality chez Stravinsky," Nineteenth-Century Music 10 (1987): 265-86. A principal critic of Berger and van den Toorn (to whom Taruskin specifically responds) has been Joseph Straus; see his Review of Pieter C. van den Toorn, The Music ofIgor Stravinsky in Journal ofMusic Theory 28 (1984): 129-134. Taruskin's "shoring up" of the Berger-van den 'loom approach, which can be considered a partial concession to the criticism of Straus and others, is particularly evident in his Petrushka analysis. Taruskin employs the analysis as a corrective in order to demonstrate the possibility of (1) large-scale referability ofan octatonic collection, (2) consistent distinction between referable and "chromatic" pitches with respect to given referential collections and (3) delineation of voice leading at diverse structural levels. ~aruskin, "Chernormor to Katschei": 78. Wile, Communication and Interaction 89 collection, communication, and interaction. 5 The notion of well-defined collection provides a formal basis for the isolation and classification of pitch collections that must precede a study of the relationships among such collections. Specifically it seeks to characterize the degree of consistent distinction available between pitch classes attributable to a given referential collection and those that are not. A "collection" (Le., a specific unordered grouping of pitch classes) is thus "well-defined" to the extent that it can be clearly differentiated from foreign pitch classes by means of musical context (e.g., predominance of pitch classes belonging to the collection, rhythmic or articulative stress upon such pitch classes, distinction of such pitch classes through register or texture). This might seem insignificant in light of Taruskin's work (or similarly, that ofJay Reise for the music of Scriabin), where distinction between members and non-members of a given collection is made during the process of analysis. Yet formalizing the concept ofwell-defined collection ensures recognition ofa fundamental consideration in any collectional approach: the degree and nature ofpurity (or "definition") in collections asserted to be operative. 6 Well-defined collections can relate to one another in either oftwo ways: in succession (''horizontally'') or in combination (''vertically''). Coherent transition between successive collectional domains is often achieved through techniques of voice leading or by means of a mutual pivot (as with successive keys in tonal modulation), and we say that sets bearing this relation communicate with one another. An interesting method of whole tone-diatonic communication, for example, is the treatment of part or all of a whole-tone collection as a dominant 5An earlier version of this paper was presented at the inaugural meeting of Music Theory Midwest at Northwestern University, May 1990. <Yraruskin, "Chez Petrouchka," and Jay Reise, "Late Scriabin: Some Principles Behind the Style," Nineteenth-Century Music 6 (1983): 220-31. Systematic differentiation of pitches accountable from those not accountable to a given referential collection is something that, as Taruskin states (with reference to the octatonic collection and its four remaining "chromatic" tones), "neither Berger nor van den Toorn has tried very rigorously to do" ("Chez Petrouchka": 267). 90 Indiana Theory Review Vol. 13/1 complex (Figure 1).7 The actual combination of well-defined collections is called collectional interaction. Interacting pitch complexes exhibit varying degrees of mutual integration; that is, they range from combinations of distinct collections that simultaneously inhabit disparate regions of the overall musical texture to formations that are more thoroughly fused and can be discerned only through careful attention to musical detail. Figure 1. Whole tone-diatonic communication. I 1 3 5 7 9 11 : odd whole tone collection ~ -'- )( -=l=F0 .... \ 0 -& r .• As used here, the term interaction expands a specific analytical method (that of Berger and van den Toorn) into a generalized principle. Thus the principle of interaction - as well as that of well-defined collection and communication - has the capacity to embrace not only octatonic and diatonic configurations, but whole-tone and chromatic ones as well, and indeed any means of pitch organization that is deemed germane to the music at hand. And since by definition these collections are being well-defined, it is possible to be very precise in describing the manner in which such collections communicate and interact. Well-defined collections thus provide the basis for a similarly precise definition of communication and interaction among such collections within overall musical contexts. The following essay presents examples of communication and 7For a discussion of the relationship of the whole tone collection and dominant complexes, see Arnold Schoenberg, Theory ofHarmony, ed. Roy E. Carter (Berkeley: University of California Press, 1988), 391-92. Wile, Communication and Interaction 91 interaction derived from Stravinsky's early composition for orchestra, Scherzo fantastique (1907-1908). Van den Toorn has noted that "few of Stravinsky's works exhibit a more persistent referential commitment to the octatonic collection than the early Scherzo fantastique. "8 To this I add that the Scherzo exhibits communication and interaction among well-defined octatonic, diatonic, whole-tone, and chromatic collections. In order to demonstrate the applicability ofthese principles to later works of Stravinsky and to the works of other composers, the paper concludes with an example of diatonic-octatonic whole tone interaction in Stravinsky's Les noces (1914-1917) and an example of pentatonic-whole tone-diatonic communication in Claude Debussy's Prelude a l'apres-midi d'unfaune (1894). Before beginning, some terminological notes are in order, and these will be clarified by looking at Example 1. First, measures are indicated by reference to rehearsal numbers in the score, plus or minus a number of measures. Example 1 thus ranges from 7-1 to 7+ 1. Second, integer notation denotes pitches and pitch classes (pc's), with C = 0, C-sharp or D-flat = 1, ...,B = 11. Whole-tone collections containing either even or odd integers will be referred to as "even" or "odd" whole-tone collections, respectively. Third, sets given in prime form are in parentheses, while actual pitches and pitch classes are not. Thus in Example 1, the integers in the score and in the summary at the bottom of the page represent actual pitches, while those in the six Roman numeral partitions surrounding the score are in prime form. Finally, transpositional combination, a procedure identified by Richard Cohn, 9 in which intervals and sets are combined with their transpositional products, is denoted by an asterisk. Thus in partition II of Example 1, (0 4 8) * (read "by") (0 1 2 3 4) indicates that an (0 4 8) "augmented