[jimishol]

Thanks for digging that up! That blog post covers the early "from scratch" version—essentially a mind experiment.

Interestingly, Dmitri Tymoczko arrives at a similar prism structure (Figure 14b) in his paper "The Generalized Tonnetz" ( https://read.dukeupress.edu/journal-of-music-theory/article/... ).

I reached a similar shape (Figure 11 in my pdf: https://jimishol.github.io/thoughts_on_harmony_en.pdf#page=2... ), but the specific, even arbitrary, twisting I used to realize the torus topology gives it a unique advantage: it immediately reveals the "hinge note" of a scale.

I discuss that specific geometric comparison here: https://github.com/jimishol/cholidean-harmony-structure/disc...

The new documentation in this repo ( https://github.com/jimishol/cholidean-harmony-structure ) represents the mature "Umbilic-Surface Grammar" that explains why those shapes happen.