> 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.
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.
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:
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.
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...
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.
https://jimishol.github.io/post/tonality/
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...