Describing global musical structures by integer programming on musical patterns

Tsubasa Tanaka

Koichi Fujii

pp. 52-63

in: Tom Collins, David Mérédith, Anja Volk (eds), Mathematics and computation in music, Berlin, Springer, 2015

Abstract

Music can be regarded as sequences of localized patterns, such as chords, rhythmic patterns, and melodic patterns. In the study of music generation, how to generate sequences that are musically adequate is an important issue. In particular, generating sequences by controlling the relationships between local patterns and global structures is a difficult and open problem. Whereas grammatical approaches, which examine global structures, can be used to analyze how a piece is constructed, they are not necessarily designed to generate new pieces by controlling the characteristics of global structures, such as the redundancy of a sequence or the statistical distribution of specific patterns. To achieve this, we must overcome the difficulty of solving computationally complex problems. To deal with this problem, we take an integer-programming-based approach and show that some important characteristics of global structures can be described only by linear equalities and inequalities, which are suitable for integer programming.