Indeterminate Music and Probability Spaces: The Case of John Cage’s Number Pieces

Abstract

Indeterminate music is characterized by the use of random outputs, either during the compositional process or during its performance. John Cage's Number Pieces are works indeterminate in their realization in which the performer, through a framework of time-brackets, has control over the temporal limits of fixed sounds. In this paper we analyze John Cage's temporal system of time-brackets using a statistical approach. It is shown that for a single time-bracket a probability space can be defined concerning the choice of the temporal limits of a sound. The performer's attitude toward choice is modelled through different probability distributions over the sample space and the audible quantities (in particular, length) of the sound contained within a time-bracket are calculated. We show how time-brackets can be considered as flexible structures ensuring complex outputs from simple assumptions. The limits of our statistical model as compared to real human behavior are discussed, and perspectives are given concerning the study of complete sets of time-brackets.