5 ms·

Holly cow, the torus is topologically the product of two circles S1*S1 so he must have been thinking of something cycling in two dimensions, not just one as the

Holly cow, the torus is topologically the product of two circles S1*S1 so he must have been thinking of something cycling in two dimensions, not just one as the circle of fifhts or chord-scale theory.

lucasgonze 10y ago
The actual shape in this diagram contains five octaves. That's 60 semitones. The 60 semitones correspond to minutes on a clock, of course. The correspondence between music theory and time is not accidental. Both came out of Babylonian numerology, which had a thing with the integers that pop out of trigonometry - 12, 60, 360. Thanks for pointing out the "two circles" way of factoring a torus. I hadn't thought of that.
- qiuwob 10y ago
  could you elaborate on the toroidal structure for people like me who don't know music theory please ? what are the two fundamental cycles that make ZxZ ? I see semitones going around the main circle - but how are they connected back to themselves the other way ?
  - lucasgonze 10y ago
    Here is a cross-section drawing I did of the toroidal structure. This is for minor thirds instead of whole tones, meaning that there are three semitones per winding instead of two. https://goo.gl/photos/U6gKHvRTUtM3p49z7 https://goo.gl/photos/U6gKHvRTUtM3p49z7
theoh 10y ago
I'm not a music theory guy, but Dmitri Tymoczko's work comes to mind here. That uses moebius bands rather than torii: https://www.simonsfoundation.org/multimedia/mathematical-impressions-making-music-with-a-mobius-strip/ https://www.simonsfoundation.org/multimedia/mathematical-imp...
- jesuslop 10y ago
  Oh my, a scribbled diagram of Coltrane as an application of Tymoczko. That would be a nice motivation to study him. Sweet video, I think in the end they show the moebius strip obtained by glueing opposite points, opposite meaning the two points pinned by a needle perpendicular to the donut.

5 ms·

Holly cow, the torus is topologically the product of two circles S1*S1 so he must have been thinking of something cycling in two dimensions, not just one as the

by jesuslop 10y ago

lucasgonze 10y ago
The actual shape in this diagram contains five octaves. That's 60 semitones. The 60 semitones correspond to minutes on a clock, of course. The correspondence between music theory and time is not accidental. Both came out of Babylonian numerology, which had a thing with the integers that pop out of trigonometry - 12, 60, 360. Thanks for pointing out the "two circles" way of factoring a torus. I hadn't thought of that.
- qiuwob 10y ago
  could you elaborate on the toroidal structure for people like me who don't know music theory please ? what are the two fundamental cycles that make ZxZ ? I see semitones going around the main circle - but how are they connected back to themselves the other way ?
  - lucasgonze 10y ago
    Here is a cross-section drawing I did of the toroidal structure. This is for minor thirds instead of whole tones, meaning that there are three semitones per winding instead of two. https://goo.gl/photos/U6gKHvRTUtM3p49z7 https://goo.gl/photos/U6gKHvRTUtM3p49z7
theoh 10y ago
I'm not a music theory guy, but Dmitri Tymoczko's work comes to mind here. That uses moebius bands rather than torii: https://www.simonsfoundation.org/multimedia/mathematical-impressions-making-music-with-a-mobius-strip/ https://www.simonsfoundation.org/multimedia/mathematical-imp...
- jesuslop 10y ago
  Oh my, a scribbled diagram of Coltrane as an application of Tymoczko. That would be a nice motivation to study him. Sweet video, I think in the end they show the moebius strip obtained by glueing opposite points, opposite meaning the two points pinned by a needle perpendicular to the donut.