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

https://github.com/jimishol/cholidean-harmony-structure/blob/main/docs/03-case-study-chopin-prelude04.md
2•jimishol•2d ago
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?

Comments

jimishol•2d ago
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...

madcaptenor•2d ago
Would be nice to have a link to the music itself, both recording and sheet music.

This is the E minor prelude - I happened to recognize it by key but not by number.

See e.g. the Wikipedia article (https://en.wikipedia.org/wiki/Prelude,_Op._28,_No._4_(Chopin...) which has a recording embedded, although there are surely better ones.

Sheet music from IMSLP: https://s9.imslp.org/files/imglnks/usimg/3/3c/IMSLP319636-PM...

jimishol•2d ago
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.

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