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In a similar vein, there's the Topos of Music book[0], which, according to Wikipedia, has been somewhat controversial among mathematicians and musicians alike.

[0] https://www.amazon.com/Topos-Music-Geometric-Concepts-Perfor...




Thanks for the book recommendation. I was curious about the controversy, so dug into it a bit.

From the Wikipedia page of the author:

> Dmitri Tymoczko..said of Mazzola: "If you can't learn algebraic geometry, he sometimes seems to be saying, then you have no business trying to understand Mozart."

https://en.wikipedia.org/wiki/Guerino_Mazzola

The critic, Tymoczko, is the author of A Geometry of Music. Oh, his review of Topos of Music is online.

http://dmitri.mycpanel.princeton.edu/files/publications/mazz... (PDF)

Abstract:

This paper critiques Guerino Mazzola’s derivation of traditional counterpoint rules, arguing that those rules are not well-modeled by pitch-class intervals; that Mazzola’s differential treatment of fifths and octaves is not supported musically or by traditional counterpoint texts; that Mazzola’s specific calculations are not reproducible; that there are a number of intuitive considerations weighing against Mazzola’s explanation; that the fit between theory and evidence is not good; and that Mazzola’s statistical arguments are flawed. This leads to some general methodological reflections on different approaches to mathematical music theory, as well as to an alternative model of first-species counterpoint featuring the orbifold T2/S2.




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