Tiling problems in music composition: Theory and Implementation

This paper aims at presenting an application of algebraic methods in computer assisted composition. We show how a musical problem of construction of rhythmic canons can be formalized algebraically in two equivalent ways: factorization of cyclic groups and products of polynomials. These methods lead to the classification of some musical canons having the property of tiling the time axis (tiling rhythmic canons). They generalize a compositional model originally proposed by the French composer Olivier Messiaen. The implementation of a large family of tiling rhythmic canons in the visual programming language OpenMusic offers to the composer a wide spectrum of new compositional applications.