May

17

Arnold SchoenbergI have often tried to figure this out. Using harmony means there are lots of cycles of fifths that often intersect each other, and pivot chords with dual harmonic contexts, so it is hard to make a geometric picture. Schoenberg had his "regions" but these shift like mirages if one goes through different keys. But I have not found mathematical structures like groups or rings sufficient. Perhaps this explorer has found something that works? Given time I will try out the software.

Usually such things (which crop up from time to time) are Procrustean beds; but I always review them.


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