jimishol

Please do! I would love to hear how the lattice interprets original compositions.

For the only piece I have ever composed ( https://jimishol.github.io/post/young_and_confused/ )—a harmony exercise written before I built this tool—I find the visualization acts primarily as a mnemonic device.

However, for pieces like Satie's Gnossienne No. 1, the geometry makes profound sense, while others like Flight of the Bumblebee are just beautiful to watch purely for the motion.

I actually just pushed a new update (v2.5.2-2) that attempts a topological estimation of keys based on the active surface. Give it a try and let me know what you find.

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.

Apologies for the delay! You don't need to run the code to see the theory in action.

I have included a visualization GIF in the main README. While the demos in the installation section are short, they do contain audio-visual examples.

Direct link to the README: https://github.com/jimishol/cholidean-harmony-structure/blob...

You are absolutely right about the voice leading. Acoustically, it is the definition of smoothness.

When I wrote 'tension,' I was describing the Geometric Re-contextualization visible in the visualizer. The note (A) stays put, but the 'world' (the Surface) rotates underneath it.

To be clear: The Grammar is simply my attempt to describe the movements I observed in the 3D structure. I am not a theorist; I am a builder. I see the Structure itself (the lattice) as the real contribution.

My hope is that theorists will see this structure and develop their own grammars for it. I would love to see a 'Baroque Grammar' or a 'Jazz Grammar' that maps these geometric paths according to their specific stylistic rules. The geometry is neutral; the grammar is just the lens I used to read it.

### HN reply

Thanks — the main repo page includes demos, screenshots, and *installation instructions in `README.md`*.

Thank you! That is a crucial omission.

I avoided including the MIDI/Score files in the repo to avoid licensing issues, but I have updated the analysis document immediately with the Wikipedia and IMSLP links.

The ideal experience (as shown in the README gif) is actually running the visualizer alongside a score editor like MuseScore via MIDI port sniffing, so you can see the geometric cursor sync with the sheet music cursor. But for reading the text, the recording is essential context. Thanks for the links.

OP here.

Note on Terminology: This analysis uses specific geometric terms (like 'Station Shift' and 'P-Rotation') defined in the Grammar Specification. If the logic seems opaque, the definitions are here:

1. The Grammar Spec: https://github.com/jimishol/cholidean-harmony-structure/blob...

2. The Topological Basis: https://github.com/jimishol/cholidean-harmony-structure/blob...

Α projection of 12-tone Equal Temperament (12ET) music systems into 3D space.

I find it ideal for students or teachers of musical harmony, as it enriches discussions about musical harmonic relationships with spatial representations.