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

Tsubasa Tanaka 1 Brian Bemman 2 David Meredith 2
1 Repmus - Représentations musicales
STMS - Sciences et Technologies de la Musique et du Son
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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Communication dans un congrès
The 22nd International Conference on Principles and Practice of Constraint Programming, Sep 2016, Toulouse, France. 2016, Principles and Practice of Constraint Programming 22nd International Conference, CP 2016, Toulouse, France, September 5-9, 2016, Proceedings. 〈10.1007/978-3-319-44953-1_50〉
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Tsubasa Tanaka, Brian Bemman, David Meredith. Constraint Programming Approach to the Problem of Generating Milton Babbitt's All-Partition Arrays. The 22nd International Conference on Principles and Practice of Constraint Programming, Sep 2016, Toulouse, France. 2016, Principles and Practice of Constraint Programming 22nd International Conference, CP 2016, Toulouse, France, September 5-9, 2016, Proceedings. 〈10.1007/978-3-319-44953-1_50〉. 〈hal-01467879〉

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