Mathematics and Computation in Music

MCM 2015: Mathematics and Computation in Music pp 237-242 | Cite as

Exact Cover Problem in Milton Babbitt’s All-Partition Array

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9110)


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.


Babbitt Knuth All-partition array Exact cover Computational music analysis 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Architecture, Design and Media TechnologyAalborg UniversityAalborgDenmark

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