Constraint Programming Approach to the Problem of Generating Milton Babbitt's All-partition Arrays

Tsubasa Tanaka, Brian Bemman, David Meredith

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Resumé

Milton Babbitt (1916–2011) was a composer of twelve-tone serial music noted for creating the all-partition array. One part of the problem in generating an all-partition array requires finding a covering of a pitch-class matrix by a collection of sets, each forming a region containing 12 distinct elements and corresponding to a distinct integer partition of 12. Constraint programming (CP) is a tool for solving such combinatorial and constraint satisfaction problems. In this paper, we use CP for the first time to formalize this problem in generating an all-partition array. Solving the whole of this problem is difficult and few known solutions exist. Therefore, we propose solving two sub-problems and joining these to form a complete solution. We conclude by presenting a solution found using this method. Our solution is the first we are aware of to be discovered automatically using a computer and differs from those found by composers.
OriginalsprogEngelsk
TitelPrinciples and Practice of Constraint Programming : 22nd International Conference, CP2016, Toulouse, France, Spetember 5-9, 2016, Proceedings
Udgivelses stedToulouse, France
ForlagSpringer
Publikationsdato2016
Sider802-810
ISBN (Trykt)978-3-319-44952-4
ISBN (Elektronisk)978-3-319-44953-1
DOI
StatusUdgivet - 2016
BegivenhedInternational Conference on Principles and Practice of Constraint Programming - Toulouse Business School, Toulouse, Frankrig
Varighed: 5 sep. 20169 sep. 2016
Konferencens nummer: 22
http://cp2016.a4cp.org

Konference

KonferenceInternational Conference on Principles and Practice of Constraint Programming
Nummer22
LokationToulouse Business School
LandFrankrig
ByToulouse
Periode05/09/201609/09/2016
Internetadresse
NavnLecture Notes in Computer Science
Vol/bind9892
ISSN0302-9743

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Tanaka, T., Bemman, B., & Meredith, D. (2016). Constraint Programming Approach to the Problem of Generating Milton Babbitt's All-partition Arrays. I Principles and Practice of Constraint Programming: 22nd International Conference, CP2016, Toulouse, France, Spetember 5-9, 2016, Proceedings (s. 802-810). Toulouse, France: Springer. Lecture Notes in Computer Science, Bind. 9892 https://doi.org/10.1007/978-3-319-44953-1_50
Tanaka, Tsubasa ; Bemman, Brian ; Meredith, David. / Constraint Programming Approach to the Problem of Generating Milton Babbitt's All-partition Arrays. Principles and Practice of Constraint Programming: 22nd International Conference, CP2016, Toulouse, France, Spetember 5-9, 2016, Proceedings. Toulouse, France : Springer, 2016. s. 802-810 (Lecture Notes in Computer Science, Bind 9892).
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abstract = "Milton Babbitt (1916–2011) was a composer of twelve-tone serial music noted for creating the all-partition array. One part of the problem in generating an all-partition array requires finding a covering of a pitch-class matrix by a collection of sets, each forming a region containing 12 distinct elements and corresponding to a distinct integer partition of 12. Constraint programming (CP) is a tool for solving such combinatorial and constraint satisfaction problems. In this paper, we use CP for the first time to formalize this problem in generating an all-partition array. Solving the whole of this problem is difficult and few known solutions exist. Therefore, we propose solving two sub-problems and joining these to form a complete solution. We conclude by presenting a solution found using this method. Our solution is the first we are aware of to be discovered automatically using a computer and differs from those found by composers.",
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Tanaka, T, Bemman, B & Meredith, D 2016, Constraint Programming Approach to the Problem of Generating Milton Babbitt's All-partition Arrays. i Principles and Practice of Constraint Programming: 22nd International Conference, CP2016, Toulouse, France, Spetember 5-9, 2016, Proceedings. Springer, Toulouse, France, Lecture Notes in Computer Science, bind 9892, s. 802-810, International Conference on Principles and Practice of Constraint Programming, Toulouse, Frankrig, 05/09/2016. https://doi.org/10.1007/978-3-319-44953-1_50

Constraint Programming Approach to the Problem of Generating Milton Babbitt's All-partition Arrays. / Tanaka, Tsubasa; Bemman, Brian; Meredith, David.

Principles and Practice of Constraint Programming: 22nd International Conference, CP2016, Toulouse, France, Spetember 5-9, 2016, Proceedings. Toulouse, France : Springer, 2016. s. 802-810 (Lecture Notes in Computer Science, Bind 9892).

Publikation: Bidrag til bog/antologi/rapport/konference proceedingKonferenceartikel i proceedingForskningpeer review

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Tanaka T, Bemman B, Meredith D. Constraint Programming Approach to the Problem of Generating Milton Babbitt's All-partition Arrays. I Principles and Practice of Constraint Programming: 22nd International Conference, CP2016, Toulouse, France, Spetember 5-9, 2016, Proceedings. Toulouse, France: Springer. 2016. s. 802-810. (Lecture Notes in Computer Science, Bind 9892). https://doi.org/10.1007/978-3-319-44953-1_50