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Page 00000337 Segmentation and Interpretation in Atonal Music. John F. Doerksen University of Western Ontario London, Ontario, Canada Email: firstname.lastname@example.org Abstract This paper argues that, in the analysis of atonal music, segmentation and interpretation are two sides of the same coin. While it has been long recognized that segments determine interpretation, the impact of interpretive goals upon segmentation strategies has been less examined. This paper describes two essentially different approaches to atonal music-the structuralist versus the contextualist stance-and examines how their various assumptions inform segmentation strategies. It then goes on to outline a contextualist approach to the segmentation of atonal music, attempting to render explicit the influence of the interpretive goal on the process of segmentation. 1. Introduction You might well ask of the statement in my Abstract whether or not it is reasonable to polarize the two terms structural and contextual: the distinction, you may argue, is not so clear as that. And that point you must be granted. The structuralist approach to atonal analysis often engages the contextuality of the music, and at some level the contextualist approach makes assumptions about how the music defines significant structures. To some extent my polarization of the two terms is indeed4 artificial. Nevertheless, the specific ways in which the two approaches engage structuralism and contextualism differ, they find their points of departure in rather different underlying assumptions, and they will most likely produce contrasting analytical outcomes. By treating them as opposites I attempt to clarify the general characteristics of each analytical approach. In this paper I touch upon salient aspects of the two analytical approaches, and explore their impact on segmentation strategies. Before proceeding to the details, however, let me name what I believe are the defining characteristics of the two approaches. By the structuralist approach to atonal music I mean analysis that privileges collections of pitches for reasons that lie outside of the individual piece. In this view it is reasonable to defend a particular segment, for instance, with reference to the role of a particular collection of pitches in the composer's cevre as a whole. By the contextualist approach, on the other hand, I mean analysis that aims to derive the significance of materials by engaging the surface motives and gestures of the individual piece. In a contextualist analysis a segment is defended principally on the basis of its gestural identity in the music. As the discussion and selected examples in the following pages show, the structuralist approach is well represented in the literature.' The contextualist approach, however, has been less explored, particularly when it comes to the interpretation of contextually-defined segments. For this reason I include in this essay the results of a contextualist analysis of the first of Anton Webern's Zwei Lieder, Op. 8: it serves to demonstrate the benefits and limitations of contextualism. 2. The Structuralist Approach Of the various external sources of support to which analysts turn to justify structuralist segments, one can identify at least three main categories: (1) extramusical significance; (2) compositional intent; and (3) analytical experience. Allen Forte's analysis of the first ofSchoenberg's Three Piano Pieces, Op. 11, provides an example of the role of extra-musical significance. In his article "Pitch-Class Set Analysis Today," Forte returns to this piece-one which he has analysed in considerable detail elsewhere (see Forte 1972 and 1981)-to demonstrate how a collection of pitches derived from Schoenberg's name plays an important compositional role. Reproduced in example 1 is the segment he identifies.2 Forte writes this about the segment:...in this opening music of Op. 11, No. 1, we find, as we do in all the music after the 1905 songs of Op. 6, Schoenberg's signature, Es-C-H-B-E-G, here transposed up six 'Given space limitations, this paper focuses primarily on the analytical practice of Allen Forte as representative of the structuralist approach. Forte is, of course, a pioneer in the analysis of atonal music, and his work continues to wield great influence. His formulation of pitch-class set theory in The Structure of Atonal Music (1973) still serves as a standard reference in the field. 2Forte presents this set-class, 6-Z44, in a lettername diagram in his Example 4 (1985, 44). ICMC Proceedings 1999 -337 -
Page 00000338 semitones, for Schoenberg almost never presented the hexachord in its literal form (Forte 1985, 45-46). Consider the assumptions about atonal analysis that this segment reveals. As we see in example 1, Forte's segment interrupts the opening gesture of the melody and it excludes the B t in the inner voice of the accompaniment, even though this note is not particularly set apart in the texture. At first glance the segment would seem the result of an ad hoc procedure. Certainly the boundaries at the musical surface would not invite this grouping; indeed, the segment crosses significant boundaries. Nevertheless, the segment is not without basis: it flows logically from Forte's assumption that Schoenberg took a truly intervallic approach to composition-the pitches are unordered and transposed, thus retaining only an intervallic relationship to the signature that Forte invokes as justification for the grouping-and that he would usually conceal his signature.' Example 1. Schoenberg's Op. 11, No. 1: Set-Class 6-Z44 6-4............., i,; h*d, l ',-t,-,t L The knotty problem of compositional intent occasionally finds its way into the question of segmentation. Whereas some analysts discount its usefulness,4 others find in compositional intent a key to interpretation. Ethan Haimo (1996), for example, applies Schoenberg's concept of "developing variation" in his analysis of the composer's Op. 11, No. 1, the work in which Forte finds the signatures. 'In an article entitled, "Schoenberg's Creative Evolution," Forte shows how the signature appears in many of Schoenberg's pieces and in various contexts, but he has also come under criticism for his segmentation strategies. Ethan Haimo, for instance, disputes Forte's claims, concluding that "there is not a single case that shows that Schoenberg ever consciously used his musical signature" (Haimo 1996, 190). 4Forte, for instance, expresses his view clearly when he writes, "From the practical standpoint, a presumed knowledge of'what the composer thought he was about' is not adequate for the development of analytical tools that lead to an understanding of his music" (Forte 1986, 336). Haimo purports to reveal a series of underlying motivic relationships in the piece. In example 2 I Example 2. An Abstract Motive in Schoenberg's Op. 11, No. 1 Motive b beam the notes in the opening phrase of the piece that Haimo identifies as general motive type b. He writes: Taken by itself, it might seem capricious to isolate b as a discrete motivic identity. After all, this figure is extracted from the middle of the phrase, and there are no rhythmic, phrasing, or other features that seem to isolate it as a distinct, apprehensible unit. What might justify the consideration of b as a significant motive is not its initial appearance, which is moderately veiled, but the many different ways in which this motive returns (Haimo 1996, 194). In the course of his interpretation, Haimo identifies three such abstract motives, and shows how Schoenberg develops them in the course of the work. Like the signature in Forte's analysis, the three notes of this motive also seem drawn out of context. What is the likelihood that two analysts working independently on this passage would identify this segment? Haimo openly recognizes the apparent capriciousness of his segmentation, but he is prepared to justify it by reaching outside of the particular composition, by invoking Schoenberg's practice of developing variation, and by demonstrating that one can understand the entire piece as a working out of a few general motives. The final category listed above as a source of support for segments-analytical experience-is rather less defined than the others, and it is often invoked indirectly. We find an example in Forte's description of pitch materials in Schoenberg's work: Some of these hexachords were special favourites of the composer's. For example, 6-Z10/39 occur in Op. 23/4. The hexachordal pair 6-Z13/42 is fundamental to Die Jakobsleiter, while 6-Z 19/6-Z44 occur in every atonal and 12-tone work. And 6-21 is the first hexachord of Pierrot lunaire, Op. 21" (Forte 1981, 133). While knowledge of a repertoire is without a doubt invaluable, the experienced analyst who's segmentation strategy is too strongly focussed by assumptions of what constitutes the preferred pitch materials of a given composer runs the risk of overlooking other materials that might also be - 338 - ICMC Proceedings 1999
Page 00000339 representative. This is especially pertinent in the situation where contextual clues in the music itself are disregarded in favour of segments that reinforce the initial assumptions. There is one additional aspect of structuralist approach that falls outside the three categories just described but that merits comment. It is simply this: structuralism tends to be theory-centred rather than music-centred. It tends to assume that significant theoretical relationships-complement or similarity relations, for instance-also constitute significant musical relationships.5 This is not to say that the structuralist approach is entirely theory-driven, but rather that, in the reciprocal relationship between theory and object, the theory may be given greater weight than the music. This assumption is evident in a list of informal guides to segmentation Forte offers: (1) the set occurs consistently throughout... (2) the complement of the set occurs consistently throughout; (3) if the set is a member of a Zpair, the other member also occurs; (4) the set is an "atonal" set, not a set that would occur in a tonal work (1972, 45). Suggestions (2) and (3) in particular supply theoretical rather than musical constraints to segmentation. The types of segmentation strategies one usually finds in structuralist analyses of atonal music, then, favour external criteria as a source of justification. The approach offers various benefits. Perhaps most importantly, pc set theory sets out clear definitions and categories of relationships, and thus supplies a basis for assigning significance to segments. Furthermore, the interpretive basis is systematic: an Rp relation involving actual pitch-classes, for instance, is more significant than one involving only interval-classes. What is not systematic, however, is the segmentation process, which is all the more reason for analysts to engage the issues directly. Analysts, however, tend to treat this aspect of analysis as self-evident. 3. The Contextualist Approach Whereas the structuralist approach tends to identify segments based on external criteria, the contextualist approach identifies segments based on their viability as musical gestures. What drives the contextualist segmentation strategy above all else is the assumption that gestural boundaries in the music are crucial determinants of the analytical unit. Christopher Hasty (1981) offers a lucid discussion of 'Various scholars have hinted at this aspect of atonal analysis. Fred Lerdahl sets the criticism in the context of perception, writing, "The question is whether these particular abstractions reflect and illuminate our hearing" (1989, 66). contextual factors that contribute to the cohesiveness of a segment. He argues that discontinuities within a musical domain-a rest in a melodic line, for example-form boundaries. In a given context, discontinuities in different domains may not all correlate with each other, but their grouping function is nonetheless of central importance. Hasty's notion focuses the segmentation strategy on the musical context and diminishes the role of external factors. The segments that appear in example 3, for instance, are decided primarily on the basis of gestural discontinuities. Presented are the last two measures Example 3. Webern, Op. 8, No. 1, mm. 13-14. r---.-----.-----.----.---- 9-5 r 4-2 of Webern's Op. 8, No. 1. The rest after the G 0 (m. 13), slurs, and text all set apart the first part of the passage from the second. One can also understand the entire passage, however, as possessing a unity that sets it apart from material that precedes it. For this reason a compound segment is included in the voice. The gesture in the harp is distinguished from the vocal segments on timbral grounds, and because it does not correlate rhythmically with vocal gestures, it is not included in a compound segment. This example gives an indication of the contextualist strategy: its main goal is to identify as analytic units all gestures that have a distinct musical identity. The benefit of such an approach to segmentation is that the process can be systematized to a relatively high degree. The difficulty that ensues, however, is that the richness of the atonal musical surface will tend to yield a plethora of set-classes, and traditional means of constructing analytic meaning are not as effective with such results as they are in analyses where the analytic results are more tightly controlled during the segmentation process. One way to deal with the range of set-classes that result from a gesturally-based segmentation, however, is to rank results on the basis of their connectedness within the composition. The analytic results of Webem's Lied presented in table I are based on connections derived largely from classical pc set theory. The matrix in table I evaluates the range of contextual connections of a given musical event, and then ranks the event accordingly. In short, it represents a network of relationships and supplies a basis for interpretive statements about the work.6 6See Doerksen (1998) for matrix details. ICMC Proceedings 1999 - 339 -
Page 00000340 Table 1. Matrix: Webern's Op. 8, No. 1 3-3 4-2 3-5 4-8 5-7 5-z12 7-1 7-28 5-9 3-1 4-1 5-6 5-2 3-7 8-4 4-6 6-z3 7-4 6-1 6-15 3-4 3-2 4-3 4-9 3-8 5-3 5-15 4-11 6-2 6-z24 5-z37 4-7 6-9 4-16 PCSC PCS PS 3 2 1 2 LR PCX INC OVL LC EMB FS 30 16 27 18 6 5 11 8 2 5 5 7 3 7 11 4 8 7 PHR SEC WHL BV 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SSI.8000.7900.6133.5533.3733.3500.3400.3200.3133.3000.3000.2967.2867.2800.2733.2600.2533.2467.2333.2333.2333.2267.2267.2267.2200.2200.2200.2200.2200.2133.2133.2133.2067.2067 PCSC = Pitch-Class Set-Class PCX = Pitch-Class Exchange EMB = Embedded Complement WHL = Boundary: Whole Piece PCS = Pitch-Class Set INC = Literal Inclusion FS = Formally Significant U = Usage PS = Pitch Set OVL = Overlapping Complement PHR = Phrase Boundary SSI = Set-Class Salience Index LR = Literal Repetition LC = Literal Complement SEC = Section Boundary - I I I-r 4. Conclusion Having gone to some effort to distinguish between structuralist and contextualist approaches, I would not be representing atonal analytical practice fairly if I failed to underscore the fact that concepts from each approach inform the other; the distinction is not always clear-cut. What is clear, however, is that each approach takes a distinctive position on the process of segmentation. 5. References Doerksen, J. (1998) Set-Class Salience and Forte's Theory of Genera. Music Analysis 17/2: 195 -205. Forte, A. (1972) Sets and Nonsets in Schoenberg's Atonal Music. Perspectives of New Music 11/1: 43-65. Forte, A. (1973) The Structure ofA tonal Music. New Haven: Yale University Press. Forte, A. (1978) Schoenberg's Creative Evolution: the Path to Atonality. Musical Quarterly 64: 133-76. Forte, A. (1981) The Magical Kaleidoscope: Schoenberg's First Atonal Masterwork, Opus 11, No. 1. Journal of the Arnold Schoenberg Institute 5: 127-68. Forte, A. (1985) Pitch-Class Set Analysis Today. Music Analysis 4: 29-58. Forte, A. (1986) Letter to the Editor in Reply to Richard Taruskin from Allen Forte. Music Analysis 5: 321-337. Haimo, E. (1996) Atonality, Analysis, and the Intentional Fallacy. Music Theory Spectrum 18/2: 167-99. Hasty, C. (1981) Segmentation and Process in Atonal Music. Music Theory Spectrum 3: 54 -73. Lerdahl, F. (1989) Atonal Prolongational Structure. Contemporary Music Review 4: 65-87. -340 - ICMC Proceedings 1999