indeterminate—incomputable

by Lucie Nezri

Indeterminacy is one of the most important notions for science and contemporary music from the XXth century. Its scientific emergence can be traced back to the expansion of the mechanical computation of probability distribution functions and randomness. In music, the early 'indeterminate' experiments found in the works of Iannis Xenakis and John Cage are exemplary of the development of different compositional strategies—along with, sometimes, radical and polarized philosophies, resulting from their respective understandings of indeterminacy. With time, this notion has revealed its paradoxical multifacetedness and nuances both in science and music, to the point where it seems to evoke an elusive, all-encompassing ideal. 

This research questions the significance of the concept of indeterminacy in the context of stochastic musical compositions, specifically in the face of the recent evolutions of computability theory.

An element of the answer is presented thanks to the analysis of advanced probabilistic compositional techniques, often associated with 'indeterminate' pieces of music. Computability theory helps revealing how these pieces are primarily rooted in a set of finite, determinate compositional decisions, i.e. computational limits, from and within which their stochastic procedures unfold. Hence, computational limits are considered in this research as interstices of a particular, compositional indeterminacy. Different loci of indeterminacy, imbued with various degrees of uncertainty or determinancy, are explored in this theoretical aspect of the research, as well as the compositions it brings along. The first compositions resulting from this research consist in a cycle of pieces written for solo acoustic instrument and computer.