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Mathematics and music

a Diderot mathematical forum

edited byGerard AssayagHans Georg FeichtingerJose Francisco Rodrigues

Abstract

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.

Details | Table of Contents

Proportions in ancient and medieval music Manuel Pedro Ferreira

pp.1-25

https://doi.org/10.1007/978-3-662-04927-3_1
The sounding algebra

relations between combinatorics and music from Mersenne to Euler

Eberhard Knobloch

pp.27-48

https://doi.org/10.1007/978-3-662-04927-3_2
The use of mechanical devices and numerical algorithms in the 18th century for the equal temperament of the musical scale Benedetto Scimemi

pp.49-63

https://doi.org/10.1007/978-3-662-04927-3_3
Lagrange, "working mathematician" on music considered as a source for science Jean Dhombres

pp.65-78

https://doi.org/10.1007/978-3-662-04927-3_4
Musical patterns Wilfrid Hodges Robin J Wilson

pp.79-87

https://doi.org/10.1007/978-3-662-04927-3_5
Questions of logic

writing, dialectics and musical strategies

F. Nicolas

pp.89-111

https://doi.org/10.1007/978-3-662-04927-3_6
The formalization of logic and the issue of meaning Marie-José Durand-Richard

pp.113-137

https://doi.org/10.1007/978-3-662-04927-3_7
Musical analysis using mathematical proceedings in the XXth century Laurent Fichet

pp.139-145

https://doi.org/10.1007/978-3-662-04927-3_8
Universal prediction applied to stylistic music generation Shlomo Dubnov Gerard Assayag

pp.147-159

https://doi.org/10.1007/978-3-662-04927-3_9
Ethnomusicology, ethnomathematics

the logic underlying orally transmitted artistic practices

Marc Chemillier

pp.161-183

https://doi.org/10.1007/978-3-662-04927-3_10
Expressing coherence of musical perception in formal logic Marc Leman

pp.185-198

https://doi.org/10.1007/978-3-662-04927-3_11
The topos geometry of musical logic Guerino Mazzola

pp.199-213

https://doi.org/10.1007/978-3-662-04927-3_12
Computing musical sound Jean-Claude Risset

pp.215-231

https://doi.org/10.1007/978-3-662-04927-3_13
The mathematics of tuning musical instruments

a simple toolkit for experiments

Erich Neuwirth

pp.233-241

https://doi.org/10.1007/978-3-662-04927-3_14
The musical communication chain and its modeling Xavier Serra

pp.243-255

https://doi.org/10.1007/978-3-662-04927-3_15
Computational models for musical sound sources Giovanni De Poli Davide Rocchesso

pp.257-288

https://doi.org/10.1007/978-3-662-04927-3_16

Publication details

Publisher: Springer

Place: Dordrecht

Year: 2002

Pages: 288

ISBN (hardback): 978-3-642-07836-1

ISBN (digital): 978-3-662-04927-3

Full citation:

Assayag Gerard, Feichtinger Hans Georg, Rodrigues Jose Francisco (2002) Mathematics and music: a Diderot mathematical forum. Dordrecht, Springer.