[jancsika]

> 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.

[jimishol]

You are absolutely right about the voice leading. Acoustically, it is the definition of smoothness.

When I wrote 'tension,' I was describing the Geometric Re-contextualization visible in the visualizer. The note (A) stays put, but the 'world' (the Surface) rotates underneath it.

To be clear: The Grammar is simply my attempt to describe the movements I observed in the 3D structure. I am not a theorist; I am a builder. I see the Structure itself (the lattice) as the real contribution.

My hope is that theorists will see this structure and develop their own grammars for it. I would love to see a 'Baroque Grammar' or a 'Jazz Grammar' that maps these geometric paths according to their specific stylistic rules. The geometry is neutral; the grammar is just the lens I used to read it.