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by fixed_carbon 3360 days ago
I'm pretty sure both rings are normal whole-tone scales and all the places you have marked as Xn are simply Xb.

Curious though if you have a take on the boxed numbers over the C's. Perhaps calling out how the original tonic position changes in relation to everything else as you move around the circle?
1 comments
lucasgonze 3360 days ago
The boxed numbers are octaves. This graph stretches the 12 semitone octave-image that we're used to seeing out to 60 semitones.
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fixed_carbon 3359 days ago
"out to 60 semitones" -- does this mean you're interpreting the diagram as a pitch-map covering five octaves? I was interpreting it as a tone-map comprising 12 semitones grouped into five distinct tonal regions with the center web indicating specific movements from one tonal region to another.

EDIT: Just saw your other comment interpreting it as a spiral, which effectively answers my question.

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lucasgonze 3359 days ago
Yes, that's the way I interpret the diagram.

I think the importance of there being five tonal regions is that this enables the multiples of 12 to line up at 60. These numbers are significant because they connect back to the Babylonian sexagesimal ("base 60") system used in both music theory and trigonometry.

https://en.wikipedia.org/wiki/Babylonian_numerals

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