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date: 30 September 2020

Abstract and Keywords

Pure mathematics provides principles, procedures, and ways of thinking that can be fruitful starting points for music composition, performance, and algorithmic generation. In this chapter, a number of mathematical methods are suggested as useful ways to define and transform underlying musical structures such as metres and scales, and to realize these structures as finished pieces of music. The mathematical methods include the discrete Fourier transform, geometry, algebraic word theory, and tiling, and the chapter explains how these relate to musical features such as periodicity (or lack of periodicity), well-formedness, microtonality, canons, rhythmic hierarchies, and polyrhythms. The chapter closes with a detailed examination of a musical piece derived from the described processes.

Keywords: music, algorithmic music, math and music, perfect balance, well-formedness, Christoffel words, discrete Fourier transform, canons, Lindenmayer systems

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