THREE APPROACHES TO MODULARITY IN CONTEMPORARY MUSIC1 CHRISTOPHER GAINEY MODULAR ANALYSIS,” ACCORDING TO a recent study by Peter Schubert and Marcelle Lessoil-Daelman, “provides a high degree of descriptive precision . . . by showing which . . . ideas the composer thought worthy of repetition and how those repetitions are disposed.”2 Since these scholars focus on Renaissance music, they define a module as “two welldefined melodies in a specific relationship to one another.”3 However, modules may also be conceived more generally as musical elements that gain structural significance—from the perspective of both listeners and performers—through some form of repetition. Such a broad approach to modular analysis can “provide clues to unique aspects of . . . compositional process”4 across a broader stylistic range that includes recent post-tonal music. In this study, I adapt Schubert’s and LessoilDaelman ’s analytical method in order to develop “a narrative of compositional process based on the deployment of modules”5 in Figment No. 2 by Elliott Carter, the second of Thomas Adès’s Mazurkas Op. 27, and “Papillon II” from Sept Papillons by Kaija Saariaho. Prior to discussing these works, it is useful to consider the fundamental concepts of modular analysis and the challenges of applying this analytical perspective to stylistically diverse repertoire. The structural “ 132 Perspectives of New Music significance of modules is rooted in the formative processes of repetition. “All musical structure,” writes John Rahn, “derives from repetition . . . if structure, then repetition, and if no repetition, no structure.”6 Rahn qualifies these rather axiomatic statements by characterizing the most musically satisfying type of repetition as a germinal stage in the formation of a final cause (telos) that points “beyond the thing repeated to the thing being formed.”7 This cognitive framework applies even in the absence of exact repetitions. If a listener relates a series of musical events in some way to a single archetypal module, then there remains a sense that the overall structure of the passage results from repetition. Gretchen Horlacher has applied an analytical perspective to the music of Stravinsky that demonstrates this principle at work. She asserts that words like “block” (i.e., module) and “superimposition” do not necessarily imply interruptions to continuity, as “the contingency of a series of repetitions is paramount: how the series is set forth and plays out ‘shapes’ the quality of the time it inhabits.”8 Thus, by understanding the ways in which modules are deployed, a listener or performer can more fully appreciate the dramatic character of spans of musical time that feature repeating modules. From this perspective, the goal of a modular analytical approach is to highlight and describe a “process of continual transcendence”9 at the heart of the relationship between module, “the thing repeated,” and structure, “the thing being formed.” The fewer discrete modules, the more concise and efficient the analysis as each module contributes relatively more to the structure of the piece. This consideration is moot when comparing, as in Schubert and Lessoil-Daelman’s study, works that are part of an inherently modular and relatively well-defined stylistic tradition.10 When comparing works that are stylistically distinct from one another, however, their relative modularity is an essential factor in the comparison. For example, the structure of the well-known C Major Prelude from Book I of the Well-Tempered Clavier results from the interaction of fewer discrete modules than Terry Riley’s In C, and thus it can be said to be more highly modular—a quality separate from considerations of style. There is by necessity a retrospective element to parsing a continuous musical experience into structurally significant modules. Christopher Hasty, writing of the challenges inherent in identifying analytically significant pitch structures in post-tonal music, warns that “highly abstracted analytic objects,”11 such as pitch-class sets, are not necessarily important to a listener’s or performer’s experience of the music. Segmentation is the most basic level of structural formation and identifying perceptually salient structures in a piece of music is the first Three Approaches to Modularity in Contemporary Music 133 step toward an appreciation of the network of interactions that shape the music and produce significant formal articulations. “Segmentation,” writes Hasty, “can be understood not...