Time-Span and Pitch-Space Analysis as a Model of Perception in Two Works by Xenakis

Ronald Squibbs (University of Connecticut, USA)

The analysis of Xenakis’s music presents serious challenges to scholars of music. Some analyses have taken the form of attempted reconstructions of the compositional process, either by clarifying the accounts given by the composer in his published writings or by assembling compositional sketches and comparing them to the form of the work as represented in the published score. Another approach that has proven useful in analyzing some of his stochastic works is to “recompose” them by inputting new successions of pseudo-random numbers into the functions that Xenakis used to generate the works originally. While these approaches may be useful in increasing the understanding of the Xenakis’s compositional methods among students and scholars, neither of them tends to address directly the musical structures that he presents to the listener’s perception in the final versions of his works. In order to address the issue of perceived musical structure in his finished compositions, this study examines salient features of the pitch structure at various levels of temporal structure in two works from different periods in the composer’s output. The excerpts chosen for study from the two works, Herma (1960-61) and Mists (1981), both for piano, were composed according to stochastic methods, but the stochastic “clouds” in each are notably different in their structure.

The analytical approach taken in this study focuses principally on two structural features—time spans and pitch space—and secondarily on such features as dynamics and timbre. This approach, which is based on Lerdahl’s work on time spans and pitch salience (Fred Lerdahl, Tonal Pitch Space [Oxford University Press, 2001]),has previously been applied to Achorripsis (Ronald Squibbs, “The Composer’s Flair: Achorripsis as Music,” in conference proceedings of the International Symposium Iannis Xenakis [University of Athens, 2005]: 258-64.).  Pitch salience was largely dependent upon instrumentation in that work. Its temporal structure was rather simple, however, since the duration of the sections remained fixed throughout. In the present study, timbre remains fixed because each of the works is for solo piano, but the durations of the sections are variable and their pitch contents vary independently of the instrument’s total pitch range. Additionally, a more refined approach to the relationship between pitch repetition and salience is taken here than was taken in the earlier study.

The results of the analysis are presented in the form of graphs in musical notation that specify the pitches a listener is likely to hear most clearly within specified time spans as the music unfolds in time. The graphs are multi-leveled, showing changes in perceived pitch salience as increasingly longer time are taken into consideration. The graphs thus model aspects of the perception of both local and longer-range structures in each work.

This analytical approach reveals that works composed at different periods of Xenakis’s career maintain their profiles as individual works and yet reveal common structural traits that transcend the differences in their compositional methods. The relative independence of this analytical approach from specific compositional methods further suggests that comparative analyses of music by Xenakis and other composers may be undertaken with potentially fruitful results.

Ronald Squibbs is Assistant Professor of Music Theory at the University of Connecticut at Storrs. His scholarly and performance interests are focused on the music of the twentieth and twenty-first centuries. He has presented his research on the music of Xenakis, Yuasa, Rudhyar and others at conferences in the United States and Europe. He has published articles in Perspectives of New Music, Contemporary Music Review, and in edited collections of articles on the music of Xenakis. His activities as a performer include a recent CD of the piano music of Joji Yuasa and a forthcoming CD of piano music by Dane Rudhyar, both on Aucourant Records.