Xenakis in miniature: style and structure in a r. (Hommage a Ravel) for piano (1987).

INTRODUCTION

BETWEEN THE EARLY 1970s and the late 1990s Iannis Xenakis composed several short works for solo instruments and for small ensembles. Because of their limited duration and minimal instrumentation, these works may be thought of as miniatures in comparison to his lengthier and more numerous chamber and orchestral works. (1) Xenakis's miniatures are attractive subjects for analytical study because, in spite of their brevity and relative simplicity, they nevertheless demonstrate a masterly coordination of texture, pitch materials and temporal structure comparable to that found in the larger works. The miniature that has been chosen for analysis here is a r. (Hommage a Ravel) for piano, which was commissioned by the Radio-France International Festival at Montpellier in 1987 as part of its commemoration of the fiftieth anniversary of Ravel's death. At twenty-one measures and just over two minutes in duration, it is one of the most concentrated of Xenakis's works. While the subtitle of a r. indicates that it is a tribute to Ravel, the work contains little stylistic resemblance to the older composer's work except for a general virtuosity and brilliance of harmonic color. Stylistically it is much more closely related to Xenakis's own chamber works from the same period, works such as Jalons (1986), XAS (1987), and Waarg (1988), which are particularly notable for their exuberance and intensity of expression.

This analysis will examine the structure of a r. from three perspectives: first, texture, segmentation and formal design; second, sieve theory and pitch-class sets; and finally temporal structure. Though these three perspectives inevitably intertwine somewhat through the course of the article, each will be the principal focus of a separate section below.

TEXTURE, SEGMENTATION AND FORMAL DESIGN

In Xenakis's instrumental works, large numbers of individual sounds tend to coalesce into textures that are homogeneous with respect to rhythm, density, dynamics, articulation, and pitch collection. Relative homogeneity is maintained even when the temporal intervals between the sounds are randomized, as in the process of stochastic composition, for in such cases the average density of the resultant texture remains constant. (2) Sudden changes in any of these characteristics have the effect of setting off a given texture from other, surrounding textures, thus dividing the musical surface into clearly perceptible segments. These segments are the containers for the sound masses for which Xenakis is well known, and they serve as the primary structural units upon which the form of a work is based. As such, they are subject to hierarchical groupings that form the basis for larger structural units. (3) Segments group together to form sections and sections, in turn, group together to form parts. A small work will typically divide into no more than two or three parts.

In Xenakis's music from the 1970s and 1980s, two or three distinct types of textures are generally featured in a given work. In a r. two types of textures are used: simultaneities and random walks. Simultaneities are common to several different styles of music, and therefore do not require any particular technical explanation. Their role in Xenakis's stylistic development, however, is worth noting. As Mihu Iliescu has pointed out, the simultaneities in Xenakis's late music appear to be a transformation of the idea of sound masses--formerly manifested as collections of disconnected, individual sonic elements--into large chords, resulting in "vertical blocks" of "harmonic/timbral color." (4)

In contrast to the transformation of sound masses into simultaneities, the stylistic evolution of the random walk in Xenakis's music is not so simple, and therefore requires a more detailed explanation. A general definition of a random walk is "the movement of something in successive steps, the direction, length, or other property of each step being governed by chance independently of preceding steps." (5) Random walks are used as models of physical processes such as Brownian motion, which is "the ceaseless erratic motion of fine particles in suspension." (6) Xenakis has used both terms interchangeably to describe a type of sinuous melodic contour introduced into his instrumental music in the early 1970s. These melodies have their origin in Xenakis's first attempts to extend the principles of stochastic composition into the domain of sound synthesis through the generation of stochastic waveforms. (7) Graphic representations of stochastic waveforms consist of continuous lines that feature irregular jumps in amplitude with respect to time. When the vertical dimension of the graphs was interpreted as pitch instead of amplitude, the irregular shapes contained in the graphs resulted in a distinctive type of instrumental melody. In order to facilitate the performance of the melodies by instrumentalists, pitch-time graphs of random walks were transcribed into standard musical notation. Xenakis's first instrumental work to employ random walks is Mikka for violin (1971), in which a continuous glissando moves through pitch space with unpredictable changes of speed and direction. (8) When the notion of random walks was subsequently transferred from music for strings to music for keyboard instruments, the continuous motions that had formerly been represented by glissandi were replaced by rapid linear motions through large pitch collections, the latter lending a distinctive harmonic flavor to the random walks.