Integer Programming Formulation of the Problem of Generating Milton Babbitt's All-partition Arrays

Tsubasa Tanaka, Brian Bemman, David Meredith

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5 Citationer (Scopus)

Abstrakt

Milton Babbitt (1916–2011) was a composer of twelve-tone serial music noted for creating the all-partition array. The problem of generating an all-partition array involves finding a rectangular array of pitch-class integers that can be partitioned into regions, each of which represents a distinct integer partition of 12. Integer programming (IP) has proven to be effective for solving such combinatorial prob- lems, however, it has never before been applied to the problem addressed in this paper. We introduce a new way of viewing this problem as one in which restricted overlaps between integer partition regions are allowed. This permits us to describe the problem using a set of linear constraints necessary for IP. In particular, we show that this problem can be defined as a special case of the well-known problem of set-covering (SCP), modified with additional constraints. Due to the difficulty of the problem, we have yet to discover a solution. However, we assess the potential practicality of our method by running it on smaller similar problems.
OriginalsprogEngelsk
TitelProceedings of the 17th International Conference on Music Information Retrieval
UdgivelsesstedNew York, NY
ForlagInternational Society for Music Information Retrieval
Publikationsdato2016
Sider171-177
ISBN (Trykt)978-84-606-8853-2
StatusUdgivet - 2016
BegivenhedInternational Society for Music Information Retrieval Conference - New York, USA
Varighed: 7 aug. 201616 aug. 2016
Konferencens nummer: 17
https://wp.nyu.edu/ismir2016/

Konference

KonferenceInternational Society for Music Information Retrieval Conference
Nummer17
LandUSA
ByNew York
Periode07/08/201616/08/2016
Internetadresse

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