Review of Emmanuel Amiot, Music through Fourier Space: Discrete Fourier Transform in Music Theory (Springer, 2016)

[2] Amiot’s book amply demonstrates that the DFT is relevant to a wide variety of musical questions—about rhythm, about pitch-class sets and interval content, and about tonality and nontonality—so many theorists will find something in the book relevant to questions in their own research. Within each of these topics, Amiot’s discourse varies between questions of primarily mathematical interest and those of more direct musical interest. Yet for a book that generally proceeds in the manner of mathematical writing, from definition to proposition and lemma to theorem, it laudably never strays far from immediately appreciable musical relevance.