Bücher von Franck Jedrzejewski

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.

Les problèmes d'accord et de tempérament sont depuis toujours une des préoccupations majeures des théoriciens de la musique. Si Pythagore est le premier à établir une correspondance entre les nombres et les sons, des événements comme la découverte des logarithmes renouvellent en profondeur le calcul des intervalles musicaux. Pour mesurer l'enjeu des questions d'accord, percevoir leur structure et faciliter la comparaison des synthèses entre eux, il fallait une théorie mathématique unifiée capable de rendre compte des anciens systèmes comme des nouveaux.

Galileo Galilei said he was "e;reading the book of nature"e; as he observed pendulums swinging, but he might also simply have tried to draw the numbers themselves as they fall into networks of permutations or form loops that synchronize at different speeds, or attach themselves to balls passing in and out of the hands of good jugglers. Numbers are, after all, a part of nature. As such, looking at and thinking about them is a way of understanding our relationship to nature. But when we do so in a technical, professional way, we tend to overlook their basic attributes, the things we can understand by simply "e;looking at numbers."e; Tom Johnson is a composer who uses logic and mathematical models, such as combinatorics of numbers, in his music. The patterns he finds while "e;looking at numbers"e; can also be explored in drawings. This book focuses on such drawings, their beauty and their mathematical meaning. The accompanying comments were written in collaboration with the mathematician Franck Jedrzejewski.