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Music: A Mathematical Offering

Music: A Mathematical Offering

$156.00 (P)

  • Date Published: December 2006
  • availability: In stock
  • format: Hardback
  • isbn: 9780521853873

$ 156.00 (P)
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About the Authors
  • 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
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    Reviews & endorsements

    "Perhaps our children will one day remark on the group symmetries in their favorite music in the way that we now simply note a beautiful tune. They, no less than we, will have much to learn from this delightful book, which sets a new standard of excellence and inclusiveness. Anyone who knows some college-level mathematics and is curious about how it can illuminate music will be richly rewarded by reading Benson's outstanding book."
    Peter Pesic, Tutor and Musician-in-Residence at St. John's College, Santa Fe

    "... A precise selection of solutions..."
    Luigi Carlo Berselli, Mathematical Reviews

    "… an excellent introduction to the interdisciplinary subject of music and mathematics (which also involves physics, biology, psycho-acoustics, and the history of science and digital technology). The book can easily be used as the text for undergraduate courses."
    The Mathematical Intelligencer

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    Product details

    • Date Published: December 2006
    • format: Hardback
    • isbn: 9780521853873
    • length: 426 pages
    • dimensions: 253 x 178 x 25 mm
    • weight: 1.002kg
    • contains: 263 b/w illus. 17 colour illus.
    • availability: In stock
  • Table of Contents

    Preface
    Introduction
    Acknowledgements
    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 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
    Bibliography
    Index.

  • Instructors have used or reviewed this title for the following courses

    • Computer Music 3
    • Mathematics and Music
    • Music Composition
    • Music and Mathematics
    • Temperament and Tuning in Western Music
    • The Physics of Music and Sound
    • The Science of Music
  • Author

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

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