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."
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.
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.