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William Sethares, creator of "xenotality" and "exotonality," wrote a book called Tuning, Timbre, Spectrum, Scale. According to Dave Benson in Music: A Mathematical Offering p. 490: The basic thesis of this book is the idea, first put forward by John Pierce, that the harmonic spectrum or timbre of an instrument determines the most appropriate scales ...


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Anything can inspire creation of mathematical systems expressed in music. However, whether the connection is actually less tenuous than any kind of voodoo is a different question. In the manner you pose the question, I don't think that it can be answered positively with an approach reasonably called justifiable. One obvious problem here is that Fourier ...



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