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Mathematics and Music

A Diderot Mathematical Forum

  • Book
  • © 2002

Overview

Editors:
  1. Gerard Assayag

    1. UMR 9912, IRCAM - CNRS, Paris, France

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  2. Hans Georg Feichtinger

    1. Dept. of Mathematics, University of Vienna, Vienna, Austria

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    You can also search for this editor in PubMed   Google Scholar

  3. Jose Francisco Rodrigues

    1. CMAF, University of Lisboa, Lisboa, Portugal

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    You can also search for this editor in PubMed   Google Scholar

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XVIII
    Download chapter PDF

  2. Proportions in Ancient and Medieval Music

    • Manuel Pedro Ferreira
    Pages 1-25

  3. The Sounding Algebra: Relations Between Combinatorics and Music from Mersenne to Euler

    • Eberhard Knobloch
    Pages 27-48

  4. The Use of Mechanical Devices and Numerical Algorithms in the 18th Century for the Equal Temperament of the Musical Scale

    • Benedetto Scimemi
    Pages 49-63

  5. Lagrange, “Working Mathematician” on Music Considered as a Source for Science

    • Jean Dhombres
    Pages 65-78

  6. Musical Patterns

    • Wilfrid Hodges, Robin J. Wilson
    Pages 79-87

  7. Questions of Logic: Writing, Dialectics and Musical Strategies

    • F. Nicolas
    Pages 89-111

  8. The Formalization of Logic and the Issue of Meaning

    • Marie-José Durand-Richard
    Pages 113-137

  9. Musical Analysis Using Mathematical Proceedings in the XXth Century

    • Laurent Fichet
    Pages 139-145

  10. Universal Prediction Applied to Stylistic Music Generation

    • Shlomo Dubnov, Gérard Assayag
    Pages 147-159

  11. Ethnomusicology, Ethnomathematics. The Logic Underlying Orally Transmitted Artistic Practices

    • Marc Chemillier
    Pages 161-183

  12. Expressing Coherence of Musical Perception in Formal Logic

    • Marc Leman
    Pages 185-198

  13. The Topos Geometry of Musical Logic

    • Guerino Mazzola
    Pages 199-213

  14. Computing Musical Sound

    • Jean-Claude Risset
    Pages 215-231

  15. The Mathematics of Tuning Musical Instruments — a Simple Toolkit for Experiments

    • Erich Neuwirth
    Pages 233-241

  16. The Musical Communication Chain and its Modeling

    • Xavier Serra
    Pages 243-255

  17. Computational Models for Musical Sound Sources

    • Giovanni De Poli, Davide Rocchesso
    Pages 257-288
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Keywords

About this book

In Western Civilization Mathematics and Music have a long and interesting history in common, with several interactions, traditionally associated with the name of Pythagoras but also with a significant number of other mathematicians, like Leibniz, for instance. Mathematical models can be found for almost all levels of musical activities from composition to sound production by traditional instruments or by digital means. Modern music theory has been incorporating more and more mathematical content during the last decades. This book offers a journey into recent work relating music and mathematics. It contains a large variety of articles, covering the historical aspects, the influence of logic and mathematical thought in composition, perception and understanding of music and the computational aspects of musical sound processing. The authors illustrate the rich and deep interactions that exist between Mathematics and Music.

Reviews

From the reviews:

"Springer has just released a couple of very interesting and off-beat books. Mathematics and Music, edited by Assayag, Feichtinger and Rodrigues, is a collection of articles on math and music. … Even the title is fascinating reading!" (Bulletin of Mathematics Books, November, 2002)

"It is a kaleidoscope of various interactions between mathematics and music. … This is the books strength and attraction. The interaction and impact of mathematics on music is illustrated … . It is a book for the mathematician who already knows about some key aspects of music … and wishes to learn about their historical development … . It is a book for the musician who has an interest in musical theory and wishes to learn … how it is connected to mathematics." (Bob Anderssen and Wayne Stuart, The Australian Mathematical Society Gazette, Vol. 30 (3), 2003)

"The Fourth Diderot Mathematical Forum took place simultaneously in Lisbon, Paris and Vienna … in 1999. Relationships between Mathematics and Music were presented at this conference … . The present book collects the sixteen written contributions to this Forum, illustrating with its large variety of articles the rich and deep interactions that exists between Mathematics and Music … . this rare collection of papers presents a comprehensive list of topics relating fundamental mathematics, applications of mathematics and the relation of both to society." (Zentralblatt für Didaktik der Mathematik, June, 2002)

"Composers and early music buffs will be fascinated by this collection of 16 essays constituting part of the proceedings of the 1999 Diderot Mathematical Forum. … Not a light read but thoroughly recommended." (William Mcvicker, Classical Music, January, 2003)

Editors and Affiliations

  • UMR 9912, IRCAM - CNRS, Paris, France

    Gerard Assayag

  • Dept. of Mathematics, University of Vienna, Vienna, Austria

    Hans Georg Feichtinger

  • CMAF, University of Lisboa, Lisboa, Portugal

    Jose Francisco Rodrigues

Bibliographic Information

  • Book Title: Mathematics and Music

  • Book Subtitle: A Diderot Mathematical Forum

  • Editors: Gerard Assayag, Hans Georg Feichtinger, Jose Francisco Rodrigues

  • DOI: https://doi.org/10.1007/978-3-662-04927-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Hardcover ISBN: 978-3-540-43727-7Published: 10 July 2002

  • Softcover ISBN: 978-3-642-07836-1Published: 08 October 2011

  • eBook ISBN: 978-3-662-04927-3Published: 29 June 2013

  • Edition Number: 1

  • Number of Pages: XVIII, 288

  • Topics: Mathematics, general, Music, History of Mathematical Sciences

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