- 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.
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.
Thanks for the comment. The new book by Tymoczko is interesting, but written in a more philosophical, narrative than scientific/mathematical style, why I didn't mention it. There is no mention of a programming language in the book, but he has published some examples at https://www.madmusicalscience.com. I look forward to more of his books, but I find it a little regrettable that many free spirits hinder themselves by feeling they have to justify themselves and appease with the "old curia" for their findings; as a result, a lot of material gets into these books that distracts from the actual ideas and tries to follow the traditional, authority-based style instead of one shaped by independent science.
Thanks for the feedback. The video shows my setup ten years ago; my most recent musical results are here: http://rochus-keller.ch/?p=1317.
- 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.