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International Studies in Phenomenology and Philosophy

Series | Book | Chapter

226957

Exact cover problem in Milton Babbitt's all-partition array

Brian BemmanDavid Meredith

pp. 237-242

Abstract

One aspect of analyzing Milton Babbitt's (1916–2011) all-partition arrays requires finding a sequence of distinct, non-overlapping aggregate regions that completely and exactly covers an irregular matrix of pitch class integers. This is an example of the so-called exact cover problem. Given a set, A, and a collection of distinct subsets of this set, S, then a subset of S is an exact cover of A if it exhaustively and exclusively partitions A. We provide a backtracking algorithm for solving this problem in an all-partition array and compare the output of this algorithm with an analysis produced manually.

Publication details

Published in:

Collins Tom, Meredith David, Volk Anja (2015) Mathematics and computation in music: 5th international conference, MCM 2015, London, UK, June 22-25, 2015. Dordrecht, Springer.

Pages: 237-242

DOI: 10.1007/978-3-319-20603-5_25

Full citation:

Bemman Brian, Meredith David (2015) „Exact cover problem in Milton Babbitt's all-partition array“, In: T. Collins, D. Meredith & A. Volk (eds.), Mathematics and computation in music, Dordrecht, Springer, 237–242.