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

jimishol Friday, February 20, 2026

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?

Summary
This article provides a case study of Chopin's Prelude Op. 28 No. 4, analyzing its harmonic structure and exploring the concept of Cholidean harmony, which combines elements of the Lydian and Dorian modes to create a unique and expressive musical language.
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