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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.
Original language | English |
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Title of host publication | Principles and Practice of Constraint Programming : 22nd International Conference, CP2016, Toulouse, France, Spetember 5-9, 2016, Proceedings |
Place of Publication | Toulouse, France |
Publisher | Springer |
Publication date | 2016 |
Pages | 802-810 |
ISBN (Print) | 978-3-319-44952-4 |
ISBN (Electronic) | 978-3-319-44953-1 |
DOIs | |
Publication status | Published - 2016 |
Event | International Conference on Principles and Practice of Constraint Programming - Toulouse Business School, Toulouse, France Duration: 5 Sept 2016 → 9 Sept 2016 Conference number: 22 http://cp2016.a4cp.org |
Conference
Conference | International Conference on Principles and Practice of Constraint Programming |
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Number | 22 |
Location | Toulouse Business School |
Country/Territory | France |
City | Toulouse |
Period | 05/09/2016 → 09/09/2016 |
Internet address |
Series | Lecture Notes in Computer Science |
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Volume | 9892 |
ISSN | 0302-9743 |
Keywords
- music analysis
- constraint programming
- Milton Babbitt
- all-partition array
- 12-tone music
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- 1 Finished
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Lrn2Cre8: Learning to Create
Meredith, D. & Bemman, B.
EU Seventh Framework Programme (FP7)
01/10/2013 → 30/09/2016
Project: Research