Constraint Programming Approach to the Problem of Generating Milton Babbitt’s All-Partition Arrays
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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. In: Rueher M. (eds) Principles and Practice of Constraint Programming. CP 2016. Lecture Notes in Computer Science, vol 9892. Springer, Cham
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.