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Computational Counterpoint Worlds

Mathematical Theory, Software, and Experiments

  • Octavio Alberto Agustín-Aquino
  • Julien Junod
  • Guerino Mazzola

Part of the Computational Music Science book series (CMS)

Table of contents

  1. Front Matter
    Pages i-x
  2. Octavio Alberto Agustín-Aquino, Julien Junod, Guerino Mazzola
    Pages 1-4
  3. Octavio Alberto Agustín-Aquino, Julien Junod, Guerino Mazzola
    Pages 5-25
  4. Octavio Alberto Agustín-Aquino, Julien Junod, Guerino Mazzola
    Pages 27-40
  5. Octavio Alberto Agustín-Aquino, Julien Junod, Guerino Mazzola
    Pages 41-66
  6. Octavio Alberto Agustín-Aquino, Julien Junod, Guerino Mazzola
    Pages 67-99
  7. Octavio Alberto Agustín-Aquino, Julien Junod, Guerino Mazzola
    Pages 101-125
  8. Octavio Alberto Agustín-Aquino, Julien Junod, Guerino Mazzola
    Pages 127-133
  9. Octavio Alberto Agustín-Aquino, Julien Junod, Guerino Mazzola
    Pages 135-148
  10. Octavio Alberto Agustín-Aquino, Julien Junod, Guerino Mazzola
    Pages 149-159
  11. Octavio Alberto Agustín-Aquino, Julien Junod, Guerino Mazzola
    Pages 161-178
  12. Back Matter
    Pages 179-220

About this book

Introduction

The mathematical theory of counterpoint was originally aimed at simulating the composition rules described in Johann Joseph Fux’s Gradus ad Parnassum. It soon became apparent that the algebraic apparatus used in this model could also serve to define entirely new systems of rules for composition, generated by new choices of consonances and dissonances, which in turn lead to new restrictions governing the succession of intervals.

 

This is the first book bringing together recent developments and perspectives on mathematical counterpoint theory in detail. The authors include recent theoretical results on counterpoint worlds, the extension of counterpoint to microtonal pitch systems, the singular homology of counterpoint models, and the software implementation of contrapuntal models.

 

The book is suitable for graduates and researchers. A good command of algebra is a prerequisite for understanding the construction of the model.

Keywords

Composition software Counterpoint Exotic interval dichotomies Homology Mathematical music theory Microtones

Authors and affiliations

  • Octavio Alberto Agustín-Aquino
    • 1
  • Julien Junod
    • 2
  • Guerino Mazzola
    • 3
  1. 1.Instituto de MatemáticaLa Universidad de la CañadaTeotitlan de Flores MagónMexico
  2. 2.IUMSPUniversité de LausanneEpalingesSwitzerland
  3. 3.School of MusicUniversity of MinnesotaMinneapolisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-11236-7
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-11235-0
  • Online ISBN 978-3-319-11236-7
  • Series Print ISSN 1868-0305
  • Series Online ISSN 1868-0313
  • Buy this book on publisher's site
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