Mathematical and Computational Modeling of Tonality

Theory and Applications

  • Elaine Chew

Part of the International Series in Operations Research & Management Science book series (ISOR, volume 204)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Elaine Chew
      Pages 3-18
    3. Elaine Chew
      Pages 19-37
  3. The Model

    1. Front Matter
      Pages 39-39
    2. Elaine Chew
      Pages 41-60
  4. Key Finding

    1. Front Matter
      Pages 61-61
    2. Elaine Chew
      Pages 63-71
    3. Elaine Chew
      Pages 73-91
  5. Segmentation

    1. Front Matter
      Pages 93-93
    2. Elaine Chew
      Pages 95-107
    3. Elaine Chew
      Pages 109-130
  6. Pitch Spelling

    1. Front Matter
      Pages 131-131
    2. Elaine Chew
      Pages 133-156
  7. Visualization

    1. Front Matter
      Pages 157-157
    2. Elaine Chew
      Pages 159-178
    3. Elaine Chew
      Pages 179-190
  8. Extensions

    1. Front Matter
      Pages 191-191
    2. Elaine Chew
      Pages 193-222
  9. Back Matter
    Pages 223-305

About this book


From the Preface:

Blending ideas from operations research, music psychology, music theory, and cognitive science, this book aims to tell a coherent story of how tonality pervades our experience, and hence our models, of music.

The story is told through the developmental stages of the Spiral Array model for tonality, a geometric model designed to incorporate and represent principles of tonal cognition, thereby lending itself to practical applications of tonal recognition, segmentation, and visualization. Mathematically speaking, the coils that make up the Spiral Array model are in effect helices, a spiral referring to a curve emanating from a central point. The use of “spiral” here is inspired by spiral staircases, intertwined spiral staircases: nested double helices within an outer spiral.

The book serves as a compilation of knowledge about the Spiral Array model and its applications, and is written for a broad audience, ranging from the layperson interested in music, mathematics, and computing to the music scientist-engineer interested in computational approaches to music representation and analysis, from the music-mathematical and computational sciences student interested in learning about tonality from a formal modeling standpoint to the computer musician interested in applying these technologies in interactive composition and performance. Some chapters assume no musical or technical knowledge, and some are more musically or computationally involved.


cognitive science computational models mathematical programming music information retrieval music theory operations research tonality

Authors and affiliations

  • Elaine Chew
    • 1
  1. 1.Centre for Digital MusicQueen Mary University of LondonLondonUnited Kingdom

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media New York 2014
  • Publisher Name Springer, Boston, MA
  • eBook Packages Business and Economics
  • Print ISBN 978-1-4614-9474-4
  • Online ISBN 978-1-4614-9475-1
  • Series Print ISSN 0884-8289
  • Series Online ISSN 2214-7934
  • Buy this book on publisher's site
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