Music: A Mathematical Offering – Dave Benson – 1st Edition

Description

Since the time of the Ancient Greeks; much has been written about the relation between 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; ; psycho acoustics; the history of ; and digital as well as; of course; mathematics and music. Starting with the structure of the human ear and its relationship with ; 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 if you want to know about the music of the spheres or digital music and many things in between.

Table of Contents

Frontmatter

Contents

Preface
Acknowledgements
Introduction
1 Waves and harmonics
2 Fourier theory
3 A mathematician´s guide to the orchestra
4 Consonance and dissonance
5 Scales and temperaments: the fivefold way
6 More scales and temperaments
7 Digital music
8 Synthesis
9 Symmetry in music
Appendix A- Bessel fuctions
Appendix B Equal tempered scales
Appendix C Frequency and MIDI chart
Apendix D Intervals
Appendix E Just, equal and meantone scales compared
Appendix F Music theory
Appendix G Recordings
References
Bibliography
Index
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