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?
jimishol•1h ago
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...