John Cage's Number Pieces as Stochastic Processes: a Large-Scale Analysis

TL;DR

This paper models John Cage's Number Pieces as stochastic processes, enabling a comprehensive statistical analysis of their potential sonic content and performance variability.

Contribution

It introduces a novel statistical framework to analyze the Number Pieces as stochastic processes, capturing all possible outcomes during performances.

Findings

Provides a probabilistic description of pitch-class set distributions over time.

Enables static and dynamic analysis of the score considering all possible sonic outcomes.

Applies the approach to specific works 'Four' and 'Five' for detailed study.

Abstract

The Number Pieces are a corpus of works by composer John Cage, which rely on a particular time-structure used for determining the temporal location of sounds, named the "time-bracket". The time-bracket system is an inherently stochastic process, which complicates the analysis of the Number Pieces as it leads to a large number of possibilities in terms of sonic content instead of one particular fixed performance. The purpose of this paper is to propose a statistical approach of the Number Pieces by assimilating them to stochastic processes. Two Number Pieces, "Four" and "Five", are studied here in terms of pitch-class set content: the stochastic processes at hand lead to a collection of random variables indexed over time giving the distribution of the possible pitch-class sets. This approach allows for a static and dynamic analysis of the score encompassing all the possible outcomes during the performance of these works.