This book constitutes the refereed proceedings of the 9th International Conference on Mathematics and Computation in Music, MCM 2024, held in Coimbra, Portugal, during June 18–21, 2024. The 30 full papers and 9 short papers included in this book were carefully reviewed and selected from 45 submissions. They were organized in topical sections as follows: mathematical scale theory and tuning; rhythm analysis and rhythm generation; categorical and algebraic approaches to music; quantum music; theory and algorithms for melodic- harmonic analysis and generation; geometric approaches to musical algorithms and microtonality; fourier analysis for music; similarity and distance measures for music; short papers; communication-performances; and tribute to Yves Hellegouarch.