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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 musically adequate sequences 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 the grammatical approaches that represent global structures are suitable to analyze how the pieces are constructed, they are not necessarily designed to generate new pieces with controlling their characteristics of global structures such as the redundancy of the sequence and the statistical distribution of specific patterns. To achieve this, we must overcome the difficulty of solving computationally complex problems. In this paper, 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 the integer programming.

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In polyphonic music, melodic patterns (motifs) are frequently imitated or repeated, and transformed versions of motifs such as inversion, retrograde, augmentations, diminutions often appear. Assuming that economical efficiency of reusing motifs is a fundamental principle of polyphonic music, we propose a new method of analyzing a polyphonic piece that economically divides it into a small number of types of motif. To realize this, we take an integer programming-based approach and formalize this problem as a set partitioning problem, a well-known optimization problem. This analysis is helpful for understanding the roles of motifs and the global structure of a polyphonic piece.