INTEGER PROGRAMMING FORMULATION OF THE PROBLEM OF GENERATING MILTON BABBITT'S ALL-PARTITION ARRAYS

Tsubasa Tanaka (1) , Brian Bemman (2) , David Meredith (2)

1 Repmus - Représentations musicales
2 AAU - Aalborg University [Denmark]

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 problems , 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.

Mots clés: Milton Babbitt; Integer programming; Computational musicology; All-partition allay

Domaines: Informatique [cs]

Tsubasa Tanaka, Brian Bemman, David Meredith. INTEGER PROGRAMMING FORMULATION OF THE PROBLEM OF GENERATING MILTON BABBITT'S ALL-PARTITION ARRAYS. The 17th International Society for Music Information Retrieval Conference, Aug 2016, New York, United States. ⟨hal-01467883⟩