Mathematics and Music, Softcover reprint of the original 1st ed. 2002
A Diderot Mathematical Forum

In Western Civilization Mathematics and Music have a long and interesting history in common, with several interactions, traditionally associated with the name of Pythagoras but also with a significant number of other mathematicians, like Leibniz, for instance. Mathematical models can be found for almost all levels of musical activities from composition to sound production by traditional instruments or by digital means. Modern music theory has been incorporating more and more mathematical content during the last decades. This book offers a journey into recent work relating music and mathematics. It contains a large variety of articles, covering the historical aspects, the influence of logic and mathematical thought in composition, perception and understanding of music and the computational aspects of musical sound processing. The authors illustrate the rich and deep interactions that exist between Mathematics and Music.

1 Proportions in Ancient and Medieval Music.- 2 The Sounding Algebra: Relations Between Combinatorics and Music from Mersenne to Euler.- 3 The Use of Mechanical Devices and Numerical Algorithms in the 18th Century for the Equal Temperament of the Musical Scale.- 4 Lagrange, “Working Mathematician” on Music Considered as a Source for Science.- 5 Musical Patterns.- 6 Questions of Logic: Writing, Dialectics and Musical Strategies.- 7 The Formalization of Logic and the Issue of Meaning.- 8 Musical Analysis Using Mathematical Proceedings in the XXth Century.- 9 Universal Prediction Applied to Stylistic Music Generation.- 10 Ethnomusicology, Ethnomathematics. The Logic Underlying Orally Transmitted Artistic Practices.- 11 Expressing Coherence of Musical Perception in Formal Logic.- 12 The Topos Geometry of Musical Logic.- 13 Computing Musical Sound.- 14 The Mathematics of Tuning Musical Instruments — a Simple Toolkit for Experiments.- 15 The Musical Communication Chain and its Modeling.- 16 Computational Models for Musical Sound Sources.