Name: Geometry of Musical Rhythm
ISBN: 9780815370970

Geometry of Musical Rhythm

The original edition of The Geometry of Musical Rhythm was the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explained how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly disparate fields. The book also introduced the distance approach to phylogenetic analysis and illustrated its application to the study of musical rhythm. The new edition retains all of this, while also adding 100 pages, 93 figures, 225 new references, and six new chapters covering topics such as meter and metric complexity, rhythmic grouping, expressive timbre and timing in rhythmic performance, and evolution phylogenetic analysis of ancient Greek paeonic rhythms. In addition, further context is provided to give the reader a fuller and richer insight into the historical connections between music and mathematics.

What Hacker News says

lioetersDec 2024

Great list of books on music and mathematics. It's an endlessly fascinating subject that appeals to the intellect and the heart. I remember years ago, reading Godfried Toussaint's paper, "The Euclidean Algorithm Generates Traditional Musical Rhythms". http://cgm.cs.mcgill.ca/~godfried/publications/banff-extende... (PDF)

Following the trail, I was glad to find he wrote a whole book, The Geometry of Musical Rhythm, where the article forms the basis of a chapter. It's one of my favorite books I keep returning to re-read different parts.

I hadn't seen "Exploring Musical Spaces", looking forward to reading it.

Dmitri Tymoczko's book is wonderful too, A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. Rich with ideas and insights, I like how he tells the history and development of Western music theory.

Oh I just learned from the author's website that he has a new book released.

> I have just finished a second book, Tonality: An Owner's Manual, that proposes a new, hierarchical, and geometrical model of musical stucture.

> One interesting outgrowth is the musical programming language arca. This line of thinking has also led me to contemplate a third book about category theory and music.

https://dmitri.mycpanel.princeton.edu/index.html

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This video of your live performance setup as a one-man band. Amazing.

https://www.youtube.com/shorts/S82hsEDY8Pc

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originalcopyingMar 2023

well, at least they are aware they merely discovered this. Because so could I, in fact I am well (ok, not so well) on my way to also discover those same ideas, except I'm not at Princeton nor anywhere near it.

thanks for the tip on the geometry of musical rhythm book. I was aware of the other one but not this one.

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lioetersJun 2020

Recommended:

A Geometry of Music by Dmitri Tymoczko - http://dmitri.mycpanel.princeton.edu/geometry-of-music.html

The Geometry of Musical Rhythm by Godfried Toussaint

- Original paper - http://cgm.cs.mcgill.ca/~godfried/publications/geometry-of-r... (PDF)

- Book - Review https://mtosmt.org/issues/mto.13.19.2/mto.13.19.2.gotham.php

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lioetersAug 2019

This might depend on your personal preference and approach, but I like books with high information density, with pieces that I can chew on for a long time - even if much of it is beyond my understanding at the beginning (or even at the end). Here are some of my favorites:

The Jazz Theory Book (Mark Levine)

Huge series of play-along books by Jamey Aebersold

The Geometry of Musical Rhythm (Godfried Toussaint)

Harmony (Walter Piston)

A Geometry of Music - Harmony and Counterpoint in the Extended Common Practice (Dmitri Tymoczko)

Lydian Chromatic Concept of Tonal Organization (George Russell)

Augmented Scale Theory (Javier Arau)

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_spduchampDec 2024

I too bought this book and was somewhat disappointed. Some of the algorithms seems too contrived and specific. (All the code is here: https://abrazol.com/books/rhythm1/software.html)

I guess my wish would be a companion to Geometry of Musical Rhythm with lots implementations of code to demonstrate concepts. Euclidean Rhythm implementations seem to be everywhere, but there is SO MUCH MORE to cover.

Still, I'm kind of stuck on this idea that there may be a way to map the discrete mathematics of this rhythm stuff into a continuous mathematics for more natural and fluid rhythmic expression. It's just a theory and a few experiments so far.

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RochusDec 2024

There are many with various mathematical depth:

- Fauvel et al., Music and Mathematics - From Pythagoras to Fractals, 2003, Oxford UP

- Loy, Musimatics Volume 1, 2006 MIT Press

- Tymoczko, A Geometry of Music, 2011, Oxford UP

- Walker, Mathematics and Music, 2013, CRC Press

- Toussaint, The Geometry of Musical Rhythm, 2013, CRC Press

- Chew, Mathematical and Computational Modeling of Tonality, 2014, Springer

- Hook, Exploring Musical Spaces, 2023, Oxford UP

From my point of view, all titles can be appreciated by non-musicians with mathematical background (though I'm an engineer, not a mathematician, and very much involved with non-classical music). But for your specific requirement, maybe Loy is suited, but personally I consider the later books more interesting, especially Tymoczko and Hook. Book recommendations are always very subjective.

Also note that the music theory commonly taught at high schools and universities is barely able to describe music, or only a small fraction of it. And only a fraction of this theory has a mathematical fundament. Most of it is just a heuristic projection of existing music, only useful for recognizing and classifying elements, and not for deriving new music. In recent years, however, new theories have emerged that allow for both a more formal and a more practical approach.

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