Music: A Mathematical Offering

Front Cover
Cambridge University Press, 2007 - Mathematics - 411 pages
5 Reviews
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.
  

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||||||||||||||||||||| Excelent Text, could perhaps do with more about larger and more complex issues in Mathematics of Music

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下载地址: http://www.maths.abdn.ac.uk/~bensondj/html/music.pdf

Contents

Introduction
1
A mathematicians guide to the orchestra
91
Consonance and dissonance
144
the fivefold way
161
More scales and temperaments
210
Digital music
245
Synthesis
265
Symmetry in music
312
Appendix A Bessel functions 361
xiii
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About the author (2007)

David J. Benson is a 6th Century Professor in the Department of Mathematical Sciences at the University of Aberdeen.

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