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?

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.

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...

> 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.

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...

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.