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Another good book in the same vein is Dave Benson's 'Music: a Mathematical Offering'. https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-music.html https

• enriquto 6y ago
  That's an incredible book! The observation that harmony depends on the timbre of instruments was mind blowing (e.g., if we used different musical instruments, the consonant and dissonant intervals would be different).
  • OscarCunningham 6y ago
    William Sethares has a good webpage about this (https://sethares.engr.wisc.edu/consemi.html https://sethares.engr.wisc.edu/consemi.html). He talks about how you can create a synthesised instrument to fit a given scale. He even has example pieces you can listen to that are written in scales that would sound terrible with our usual instruments.
    • enriquto 6y ago
      Notice that the "scalelab" tool of TFA allows you to also synthesize dissonant octaves and whatnot: https://github.com/IMAGINARY/ScaleLab https://github.com/IMAGINARY/ScaleLab