A Compendium of Musical Mathematics

Description

The purpose of this book is to provide a concise introduction to the mathematical theory of music, opening each chapter to the most recent research. Despite the complexity of some sections, the book can be read by a large audience. Many examples illustrate the concepts introduced. The book is divided into 9 chapters. In the first chapter, we tackle the question of the classification of chords and scales. Chapter 2 is a mathematical presentation of David Lewin's Generalized Interval Systems. Chapter 3 offers a new theory of diatonicity in equal-tempered universes. Chapter 4 presents the Neo-Riemannian theories based on the work of David Lewin, Richard Cohn and Henry Klumpenhouwer. Chapter 5 is devoted to the application of word combinatorics to music. Chapter 6 studies the rhythmic canons and the tessellation of the line. Chapter 7 is devoted to serial knots. Chapter 8 presents combinatorial designs and their applications to music. The last chapter, chapter 9, is dedicated to the study of tuning systems. Franck Jedrzejewski is a researcher in mathematical physics at INSTN/CEA (Paris-Saclay University). He has also a PhD in music and musicology and in philosophy. In 2013, he was elected Director of Program at College International de Philosophie (CIPh), an institute founded in 1983 by Jacques Derrida, François Châtelet and Dominique Lecourt. He has pub lished more than 20 books, most of them in French: Dictionnaire des musiques microtonales (Dictionary of Microtonal Music), Hétérotopies musicales (Modèles mathématiques de la musique), La musique dodécaphonique et sérielle: une nouvelle histoire, or in English Looking at Numbers with the composer Tom Johnson. His research is highly transdisciplinary (music, philosophy, mathematics and Polish and Russian avantgardes). He currently teaches at Paris-Saclay University and the National Institute for Nuclear Science and Technology (INSTN).