Surface Elaboration of Pitch-Class Sets Using Nonpitched Musical Dimensions

Abstract

surface elaboration of pltch Class Sets Using Nonpitched musical dimensions IE_7fa 1 Jason Eckardt For listeners, music is not an undifferentiated stream of perceptual stimuli, but rather a rich interaction of elements, which are grouped together into segments, compared, and retroactively assessed to infer a formal structure.While composers may begin their creative process by defining motivic material, considering the timbrai constraints dictated by a particular instrumentation, devising harmonic plans, or by using some other compositional strategy, considering how these compositional ideas will influence segmentation isparamount. The generating compositional material may itselfeven suggest possible approaches for articulating these segments, but the composer may also need to shape the material in vari ous musical dimensions to provide the listenerwith events that encour age segmentation. Surface Elaboration of Pitch-Class Sets 121 My attraction to pitch-class sets as fundamental units of harmonic organization inposttonal music stems frommy early interest in the reper toire towhich set-theory analysis is often applied. This music of the Sec ond Viennese School and postwar composers Milton Babbitt, Elliott Carter, Donald Martino, Mel Powell, and others with similar technical and aesthetic concerns formed the core ofmy early compositional iden tity. Their works, and the compositional techniques introduced inor sug gested by thewritings of Babbitt, Martino, and Robert Morris, present formidable organizational strategies that remain amajor influence on my compositional thinking. In my mid-twenties, I was concerned that the pitch-class sets that I was so carefully constructing a priori were getting farther and farther away from a perceptible interaction on themusical surface.My segmentation of pitch-class sets did not reflecthow I had deployed them locally in the flow ofmusical events. This problem found its solution in a flexible sys tem of subset and superset derivations of pitch-class sets that are com posed out using nonpitch musical dimensions. My preoccupation with harmonic continuity stemming from pitch class set-type similarity led me to derive pitch-class set types thatwere either subsets or supersets of some "generating" pitch-class set type. Ech oes^ White Veil, for piano solo, features generating set type [0,1,2,3,6,7], a hexachord chosen for both itsparticular intervallic profile and its com binatorial properties. From this hexachord type, unordered subsets and supersets are derived to supply the pitch material for local gestures. Using T and Imatrices (Morris 1987, 70-3), the degree of pitch-class intersec tion is controlled by transpositional and inversional operators as deter mined by thematrices. While aggregate formation isnot a prerequisite of my harmony, I often seek an environment of chromatic saturation. How these pitch-class sets are articulated on the musical surface is cru cial to the elaboration of the harmonic materials inmy music. I conceive the musical surface as the succession of the local, moment-to-moment events which constitute themusical flow. While I seek to establish conti nuity through my harmony, I also try to encourage perceptual segmenta tion, the mental chunking of this flow into smaller parts, using nonpitched musical dimensions. The harmonic motion of the musical surface, for example, may be characterized by distinct harmonies that change at various rates; as subset- and superset-related pitch-class sets are used to define harmonic segments, the beginning and ending of these segments are defined by nonpitched changes in other dimensions on the musical surface. By differentiating segments this way, I articulate the aforementioned pitch-class sets as perceptually discrete, independent local structures. I intend that the listener infer patterns and invariances 22 Perspectives of New Music among these segments, ultimately leading to the inference of middle ground and large-scale formal structures. Research inmusic theory and cognitive psychology supports my intui tions regarding how various musical dimensions, in collaboration, encourage perceptual segmentation. In theirwritings on the contempo rary repertoire, JamesTenney and Larry Polansky,Wallace Berry,Marilyn Nonken, and Fred Lerdahl and Ray Jackendoff concur that changes in individual musical dimensions on themusical surface contribute to per ceptual segmentation (Lerdahl and Jackendoff 1983, 297-8; Tenney 1988; Tenney and Polansky 1980; Berry 1976, 37; Nonken 1999). These scholars agree that the strongest factors for segmentation are prox imity (in time) and similarity (in all other musical dimensions). If the determination of...