WWW Ircam: Musique / Sciences Collection

Mathematical Theory of Music

Franck Jedrzejewski

This book provides a unified account of mathematical tools for music theory and analysis. After a review of the theoretical aspects well-known in systematic musicology (harmonic models, the Helmholtz approach, Costère theory, Messiaen's limited transposition modes, Allen Forte's Set Theory, and David Lewin's transformational theory), the author gives a generalization of Neo-Riemannian theory and an original method for classifying dodecaphonic séries (including all-interval series) based on the mathematical theory of knots and braids. The book also contains detailed descriptions of several musical temperaments based on continued fractions and harmonic distance theory, as well as the presentation of models for rhythmic tiling canons based on group theory and topology.