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Cool Math for Hot Music

A First Introduction to Mathematics for Music Theorists

  • Guerino Mazzola
  • Maria Mannone
  • Yan Pang

Part of the Computational Music Science book series (CMS)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Introduction and Short History

    1. Front Matter
      Pages 1-1
    2. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 1-3
    3. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 5-34
  3. Sets and Functions

    1. Front Matter
      Pages 35-35
    2. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 37-48
    3. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 49-59
    4. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 61-68
  4. Numbers

    1. Front Matter
      Pages 69-69
    2. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 71-76
    3. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 77-81
    4. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 83-84
    5. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 85-87
    6. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 89-92
    7. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 93-98
    8. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 99-105
    9. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 107-112
    10. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 113-117
  5. Graphs and Nerves

    1. Front Matter
      Pages 119-119
    2. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 121-127
    3. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 129-139
  6. Monoids and Groups

    1. Front Matter
      Pages 141-141
    2. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 143-146
    3. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 147-150
    4. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 151-162
    5. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 163-169
    6. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 171-179
    7. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 181-189
    8. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 191-202
  7. Rings and Modules

    1. Front Matter
      Pages 203-203
    2. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 205-212
    3. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 213-215
    4. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 217-224
    5. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 225-240
    6. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 241-247
    7. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 249-254
  8. Continuity and Calculus

    1. Front Matter
      Pages 255-255
    2. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 257-262
    3. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 263-265
    4. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 267-272
    5. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 273-286
  9. Solutions, References, Index

    1. Front Matter
      Pages 287-287
    2. Guerino Mazzola, Maria Mannone, Yan Pang
      Pages 289-295
  10. Back Matter
    Pages 297-323

About this book

Introduction

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.

Keywords

Counterpoint Gestures Harmony Melody Music Theory Rhythm Rubato

Authors and affiliations

  • Guerino Mazzola
    • 1
  • Maria Mannone
    • 2
  • Yan Pang
    • 3
  1. 1.School of Music University of MinnesotaMinneapolisUSA
  2. 2.School of MusicUniversity of MinnesotaMinneapolisUSA
  3. 3.School of Music University of MinnesotaMinneapolisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-42937-3
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-42935-9
  • Online ISBN 978-3-319-42937-3
  • Series Print ISSN 1868-0305
  • Series Online ISSN 1868-0313
  • Buy this book on publisher's site