The Arithmetic of Listening

What Hacker News says

1. iainctduncanNov 2022
   The best current resource is the Kyle Gann book, "The Arithmetic of Listening". It's fantastic, by a world authority on the topic. https://www.kylegann.com/Gannbooks.html

   Also for anyone interested in just intonation based microtonality, I did a video demo of a tool I made using my open source Scheme for Max extension to Max here:

   https://www.youtube.com/watch?v=2L7edwef-5k&t=2s&ab_channel=...

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2. yoctonautMar 2026
   Kyle Gann's Arithmetic of Listening goes deeply into this. Given an infinite number of ways of dividing the range from f to 2f, some other equal-division temperaments (31 or 53, for example) get closer than 12TET to maintaining low-integer ratios across key centers, but each additional pitch adds complexity. I'd recommend that book in particular. https://www.kylegann.com/Gannbooks.html
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