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Show HN: A geometric analysis of Chopin's Prelude No. 4 using 3D topology (github.com)

50 points by jimishol ↗ HN
OP here.

    This is a geometric decoding of Chopin's Prelude No. 4.

    I built a 3D music midi visualizer ( https://github.com/jimishol/cholidean-harmony-structure ) and realized that standard music theory couldn't explain the shapes I was seeing. So, I developed the Umbilic-Surface Grammar to map the topology of the harmony.

    This document demonstrates that the prelude's tension isn't random, but a rigorous conflict between 'Gravity' (Station Shifts) and 'Will' (Pivots).

    I am looking for feedback on the logic—specifically from anyone with a background in topology or music theory. Does this geometric proof hold up?

11 comments

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efitz
I would love to see this but don’t want to run the code. Could you link a video? I understand if you have to omit or mangle sound to avoid strikes.
jancsika
> The tension arises because the "Seventh" (A) is not a new addition, but a residue of the previous geometric state.

That residue in m.2 is common-tone voice leading. It's a technique that was used throughout the common-practice period to avoid tension, not introduce it. I'd bet the progression in m. 1-2 could be found in the figured bass at the beginning of a slow movement by Telemann or another Baroque composer.

Speaking of Baroque composers-- in the Coda of the 4th Ballade, Chopin has an exquisite passage of basso continuo plus accompaniment that would be right at home in a minor key aria by Handel. Except that:

1. There's no melody being accompanied.

2. It moves about 4x faster than it would have in the Baroque era.

I'd love to see a pianist play that passage by suddenly looking up and frantically nodding cues to an invisible, demonic singer.

jimishol
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.

anigbrowl
You would be better off posting the Github landing page with pictures and video links, since the number of music theorists on HN is probably in the single digits: https://github.com/jimishol/cholidean-harmony-structure/tree...

Honestly, I don't think the observation of accidentals as a way of creating tension with an established harmony is especially novel, but I do like the 3d visualization despite its limitations.

jimishol
### HN reply

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

kavalg
This is very interesting! I can't wait to run it on some of my own compositions...
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.