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The Mathematics of Music and Art

  • Textbook
  • © 2023

Overview

Authors:
  1. Arturo Portnoy

    1. Mayaguez, Puerto Rico

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  • Discuses the relationships between the arts, sciences, and mathematics in the realm of music
  • Explores the language of music as deciphered through the language of mathematics
  • Shows readers how apparently unrelated areas of knowledge complement each other and propel each other’s advancement

Part of the book series: Synthesis Lectures on Mathematics & Statistics (SLMS)

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About this book

This book explores the relationships between music, the sciences, and mathematics, both ancient and modern, with a focus on the big picture for a general audience as opposed to delving into very technical details. The language of music is deciphered through the language of mathematics. Readers are shown how apparently unrelated areas of knowledge complement each other and in fact propel each other’s advancement. The presentation as well as the collection of topics covered throughout is unique and serves to encourage exploration and also, very concretely, illustrates the cross- and multidisciplinary nature of knowledge. Inspired by an introductory, multidisciplinary course, the author explores the relationships between the arts, sciences, and mathematics in the realm of music. The book has no prerequisites; rather it aims to give a broad overview and achieve the integration of the three presented themes. Mathematical tools are introduced and used to explain various aspects of music theory, and the author illustrates how, without mathematics, music could not have been developed.

Keywords

Table of contents (10 chapters)

  1. Front Matter

    Pages i-xxiv
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  2. Preliminaries

    • Arturo Portnoy
    Pages 1-17

  3. The Pigeonhole Principle

    • Arturo Portnoy
    Pages 19-26

  4. Continued Fractions

    • Arturo Portnoy
    Pages 27-34

  5. Pythagoras and Music

    • Arturo Portnoy
    Pages 35-47

  6. Temperaments of the Scale

    • Arturo Portnoy
    Pages 49-60

  7. Patterns in Music

    • Arturo Portnoy
    Pages 61-82

  8. Analysis and Synthesis of Music

    • Arturo Portnoy
    Pages 83-95

  9. Beats, Resonance, and Tuning

    • Arturo Portnoy
    Pages 97-100

  10. Digital Music and Information

    • Arturo Portnoy
    Pages 101-109

  11. Last Thoughts

    • Arturo Portnoy
    Pages 111-114

  12. Back Matter

    Pages 115-129
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Authors and Affiliations

  • Mayaguez, Puerto Rico

    Arturo Portnoy

About the author

Arturo Portnoy, Ph.D., is a Professor of Mathematical Sciences at the University of Puerto Rico at Mayaguez. He is also Co-Director of the Puerto Rico Mathematical Olympiads. He received his B.Sc. in Applied Mathematics at the Instituto Tecnológico Autónomo de México (1992) and his M.Sc. (1994) and Ph.D. (1997) at Rensselaer Polytechnic Institute. His areas of interest include inverse problems, mathematical modeling, optimization, regularization, math education, and math Olympiads. He also explores the use of technology to increase efficiency, transparency, and consistency in teaching mathematics.

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