Edges and curves - Modulation (Developer's personal view)

[jimishol]

Edges and curves are the only structural directed elements of the construction, consisting a graph. (The whole story, of how the idea for this structure came about, is recorded in my article in pdf format on tonality).

Since chords is out of picture, the 12 edges and 12 curve segments must correspond to scales. We have to differentiate graph directed branches that start from notes (joints) So their names must correspond to the different targets and not to the same source. I assume that a joint (note) refer to his "major" back space. So, curve segment that arrive at note, say G->C, correspond to major scale that has this note as tonic, in our example GC corresponds to C. Since the 12 curve segments correspond to major scales, the 12 edges must correspond to minor scales. Lets examine EC. Since C is the "major" target joint, then EC correspond to a minor scale, relative to C major. Lets examine CAb. Since Ab is the "major" target joint, then CAb correspond to f minor scale, relative to Ab major. The same logic that translate the major targets of directed edges to relative minors, constructs the following table that may apply in modulations.

Start	Chord 1	Chord 2	Chord 3	End
↑	c (Eb)	f (Ab)	bb (Db)	↑
↑	G	C	F	↑
↑	e (G) from B	a (C) from E	d (F) from A	↑

[jimishol]

🎨 Choice of Harmonic Flow: "Projection" vs. "Attraction"

To clarify the visual logic behind how lights activate in this project: the current behavior is a specific design choice rooted in the idea of Generative Harmony.

As noted in the README:

"The outgoing edges emit light discreetly to activate their destination."

1. The "Projection" Model (Default)

In the current code, an active note (the source) acts as a generator. If you play an E, it "powers" the paths leading toward its natural companions (like C and A). This makes the note feel like a creator projecting energy outward.

• Feel: Active and generative.
• Logic: Lights up when the starting joint is active.

2. The "Attraction" Model (Alternative)

For those who prefer a more "reactive" feel, you can change the logic so that the geometry glows only when it points toward an active note. This makes the structure look like it is "falling into" or "resolving" toward the notes you play.

• Feel: Magnetic and resolving.
• Logic: Lights up when the destination joint is active.

How to switch:
If you want to experiment with the "Attraction" style, you can find the -- Apply emission block in the source code (src/utils/materials.lua) and change the activation check from the current note to the shiftedNote (the destination):

-- Change this:
local factor = note.active and levels.active or levels.inactive

-- To this:
local shiftedNote = notes[useIndex] 
local factor = shiftedNote.active and levels.active or levels.inactive

I’m keeping the Projection style as the default because it best represents the core philosophy of the Cholidean structure "creating" harmonic space, but this simple swap is a great way for anyone to customize the "gravitational pull" of the visualization!