A statistical approach to the global structure of John Cage's number piece $${five}^5$$

Alexandre Popoff

pp. 231-236

in: Tom Collins, David Mérédith, Anja Volk (eds), Mathematics and computation in music, Berlin, Springer, 2015

Abstract

The Number Pieces are a body of late works composed by John Cage using particular temporal structures called time-brackets. In a Number Piece with multiple performers, the superposition of the various parts, each containing time-brackets, creates an everchanging polyphonic work whose structure cannot be determined in advance. We provide here a statistical study of the global structure of the Number Piece (Five^5) in terms of probabilities of occurence of the various possible set classes, completed by the use of various measures from information theory.

Cited authors

Cage John