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

36 points • by jimishol • last Friday at 1:48 PM • 9 comments • view on 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?

Comments

madcaptenor • last Friday at 2:40 PM

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...

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anigbrowl • today at 3:47 AM

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 • last Friday at 2:04 PM

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...

jancsika • today at 2:39 AM

> 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.

efitz • today at 2:28 AM

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.

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kavalg • today at 7:42 AM

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