Lecture-Concert "Iannis Xenakis: Random Walks in Sound and Music"

In mathematics, a random walk is a process that describes a path that consists of a succession of random steps on some mathematical space (e.g., 2-dimensional space: amplitude-time, or pitch-time). It was first introduced by Karl Pearson in 1905. Iannis Xenakis became interested in random walks in the 1960s, while working on a new approach to digital sound synthesis. Prior, he had applied stochastic processes to the creation of discrete events (notes, durations, etc.). The research he carried out at Indiana University (1967-72) finally bore fruit back in Paris at CEMAMu (his computer music centre) in 1972 with stochastic waveforms used for his multimedia work, Polytope de Cluny.  

Around the same time, it seems to have occurred to Xenakis that stochastically generated waveforms could also be mapped onto higher-order time scales, pitch-time rather than sample amplitude-time. His first effort to apply random walk output to a musical work, where the waveform was used to create a melody rather than a soundwave, was in 1971. Mikka, for solo violin, consists of a single sound unfolding continuously throughout the piece, mapping randomly generated output onto bowed glissandi.  

Having accomplished his adaptation of random walk output from the micro level to the instrumental time-scale and pitch mapping, Xenakis adapted the random walk technique to a number of other compositions. With Mikka S (1976), also for violin, he combined two lines for one instrument, which necessitated careful consideration of random walk barriers for the two parts, so that it would be physically possible to play the two--that is, the random walk pitch barriers are constrained by performability issues. Theory combines with practice, giving rise to new creative avenues to explore. With other works such as Noomena (1974) for orchestra, or Épéi (1976) for six instruments, he was able to build complex linear musical structures generated by random walks, constrained in various ways. 

One of the most important innovations Xenakis explored subsequently was with music based on a grid-like approach, where the output of the random walk is applied to discrete points. He used random walks applied to a 2-dimensional grid (pitch-pulse) in a number of works, notably Evryali (1973) for solo piano. Xenakis also explored pitch grids generated by sieves, or non-uniform values. A clear example of combining constrained random walks with pitch sieves is the opening section of Jonchaies (1977) for orchestra, where a held note in the strings turns into a quasi-modal melody, proliferating into a bundle of six melodies, the overall elastic random-walk barrier producing a composite wave shape from all six lines. 

BIO:

James Harley, University of Guelph

James Harley is a Canadian composer presently based at the University of Guelph, where he teaches digital music, composition, and related courses. He obtained his doctorate in composition at McGill University in 1994, after spending six years (1982-88) composing and studying music in Europe (London, Paris, Warsaw). His music has been awarded prizes in competitions in Canada (CBC, New Music Concerts, SOCAN), USA (McKnight Foundation), UK (Holland Prize, Huddersfield Festival), France (Bourges, MC2), Poland (Lutoslawski, Serocki), Japan (Irino), and has been performed and broadcast around the world. Some of Harley's compositions are available on disc (Artifact, ATMA, Centrediscs, Kappa, McGill, Musicworks, PeP, Soundprints) and his scores are primarily available through the Canadian Music Centre and Art Music Promotion. He has been commissioned by, among others, Codes d'Accs, Continuum, Ensemble contemporain de Montral, Hammerhead Consort, Kappa, Kore, Kovalis Duo, New Music Concerts, NUMUS, Oshawa-Durham Symphony, Open Ears Festival, Polish Society for New Music, SMCQ, Transit FestivalBelgium, Trio Phoenix, Vancouver Bach Choir. He composes music for acoustic forces as well as electroacoustic media, with a particular interest in multi-channel audio. According to Marc Couroux (Musicworks 69), Harley's music "resides at the intersection of a network of influences rather than proliferating from a central ideology Harley accepts that the complexity of nature requires a more artistically imaginative interpretation than the simple extension of an Arcadian, placid contemplation Harley consequently oriented himself towards the theory of chaos, which derives its principles from a much more global study of natural mechanisms than was previously allowed due to hyperspecialization James Harley defends on the highest level the great Canadian creative tradition, rooted in the natural world, a metaphor for the irreducible complexity of Canada and, by extension, of universal humanity.