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Cool Math for Hot Music

A First Introduction to Mathematics for Music Theorists

  • Textbook
  • © 2016

Overview

  • Based on authors' experience teaching mathematics to music theorists
  • Presents ideas in a critical manner, highlighting problems with earlier teaching approaches
  • Includes many illustrations and exercises with solutions
  • Includes supplementary material: sn.pub/extras

Part of the book series: Computational Music Science (CMS)

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About this book

This textbook is a first introduction to mathematics for music theorists, covering basic topics such as sets and functions, universal properties, numbers and recursion, graphs, groups, rings, matrices and modules, continuity, calculus, and gestures. It approaches these abstract themes in a new way: Every concept or theorem is motivated and illustrated by examples from music theory (such as harmony, counterpoint, tuning), composition (e.g., classical combinatorics, dodecaphonic composition), and gestural performance. The book includes many illustrations, and exercises with solutions.

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Table of contents (34 chapters)

  1. Introduction and Short History

  2. Sets and Functions

  3. Numbers

  4. Graphs and Nerves

Reviews

“The authors try to develop a discourse full of pleasure and fun that in every moment motivates concepts, methods, and results by their musical significance-a narrative that inspires the reader to create musical thoughts and actions. … The book contains many interesting musical and mathematical examples and exercises, and the last part of the book is devoted to the solutions of exercises. The book has also an interesting list of references for further studies in this field.” (Peyman Nasehpour, Mathematical Reviews, September, 2017)



“This textbook in mathematics for music theorists introduces topics such as sets and functions, algebraic structures including groups, rings, matrices and modules, and more. The book includes many illustrations, online sample music files, and exercises with solutions. … Concepts are motivated and supported by examples from composition music theory.” (Tom Schulte, MAA Reviews, maa.org, February, 2017)

Authors and Affiliations

  • School of Music , University of Minnesota, Minneapolis, USA

    Guerino Mazzola, Yan Pang

  • School of Music, University of Minnesota, Minneapolis, USA

    Maria Mannone

About the authors

Prof. Dr. Guerino Mazzola earned his Ph.D. in Mathematics from Zurich University. He wrote the groundbreaking book The Topos of Music in 2002, its formal language and models are used by leading researchers in Europe, India, Japan, and North America and have become a foundation of music software design. Prof. Mazzola has an appointment as professor in the School of Music at the College of Liberal Arts, University of Minnesota.

Maria Caterina Mannone is completing her Ph.D. in the School of Music of the University of Minnesota.

Yan Pang Clark is completing her Ph.D. in the School of Music of the University of Minnesota.

Bibliographic Information

  • Book Title: Cool Math for Hot Music

  • Book Subtitle: A First Introduction to Mathematics for Music Theorists

  • Authors: Guerino Mazzola, Maria Mannone, Yan Pang

  • Series Title: Computational Music Science

  • DOI: https://doi.org/10.1007/978-3-319-42937-3

  • Publisher: Springer Cham

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-42935-9Published: 08 November 2016

  • Softcover ISBN: 978-3-319-82698-1Published: 22 April 2018

  • eBook ISBN: 978-3-319-42937-3Published: 26 October 2016

  • Series ISSN: 1868-0305

  • Series E-ISSN: 1868-0313

  • Edition Number: 1

  • Number of Pages: XV, 323

  • Number of Illustrations: 67 b/w illustrations, 112 illustrations in colour

  • Topics: Computer Appl. in Arts and Humanities, Music, Mathematics in Music, Mathematics of Computing, Artificial Intelligence

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