Exact Cover Problem in Milton Babbitt's All-partition Array

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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 exclu- sively 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.
Original languageEnglish
Title of host publicationMathematics and Computation in Music : 5th International Conference, MCM 2015, London, UK, June 22-25, 2015, Proceedings
EditorsTom Collins, David Meredith, Anja Volk
Number of pages6
Place of PublicationCham, Switzerland
PublisherSpringer
Publication date2015
Pages237-242
ISBN (Print) 978-3-319-20602-8
ISBN (Electronic)978-3-319-20603-5
DOIs
Publication statusPublished - 2015
EventFifth Biennial International Conference on Mathematics and Computation in Music - Queen Mary University of London, London, United Kingdom
Duration: 22 Jun 201525 Jun 2015
Conference number: 5

Conference

ConferenceFifth Biennial International Conference on Mathematics and Computation in Music
Number5
LocationQueen Mary University of London
CountryUnited Kingdom
CityLondon
Period22/06/201525/06/2015
SeriesLecture Notes in Computer Science
Volume9110
ISSN0302-9743

Keywords

  • Exact cover
  • Milton Babbitt
  • music theory
  • music analysis
  • serial music
  • 12-tone music
  • all-partition array

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