Music: A Mathematical Offering

David J. Benson

420 pages, parution le 23/11/2006

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Résumé

Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres or digital music and many things in between.

The only modern account that is comprehensive and thorough
Lots of musical examples that make the mathematical ideas concrete; lots of illustrations
Self-contained for the enthusiast but also usable as a course text in mathematics, physics and engineering departments

L'auteur - David J. Benson

Dave Benson : University of Aberdeen

Sommaire

Introduction
Waves and harmonics
Fourier theory
A mathematician's guide to the orchestra
Consonance and dissonance
Scales and temperaments: the fivefold way
More scales and temperaments
Digital music
Synthesis
Symmetry in music

Appendix A. Bessel functions
Appendix B. Equal tempered scales
Appendix C. Frequency and MIDI chart
Appendix D. Intervals
Appendix E. Just, equal and meantone scales compared
Appendix F. Music theory
Appendix G. Recordings;

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	David J. Benson
Parution	23/11/2006
Nb. de pages	420
Format	18 x 25
Couverture	Broché
Poids	860g
Intérieur	Noir et Blanc
EAN13	9780521619998
ISBN13	978-0-521-61999-8