Above is a diagram for mode 1. As with the diagrams in the post from a couple days ago for diatonic modes, the green arrows represent perfect fifths, the blue arrows are major thirds, and the red arrows are minor thirds.
This is a diagram for mode 7.
This is a diagram for mode 5. If you remove all the black keys, you can see that it corresponds to the 5th diatonic mode that I posted two days ago. There are seven diatonic modes and twelve dodecatonic modes, so they don't line up exactly. But each diatonic mode will appear as a sort of spine inside at least one of the dodecatonic modes, and their orderings are consistent with each other.
There are many ways to use just intonation to tune the twelve notes on a piano, and to step along a path through these options. I chose this particular approach because it is consistent with the diatonic modes I described.
Yesterday I posted algorithmic examples for modes 1 and 7. Here is an example for mode 5. I've been tweaking my code to work better with these examples. Usually I am experimenting with temperament, working to traverse commas that a tuning tempers out. Temperament creates a non-trivial topology for the interval networks. This topology combines with the non-trivial topology of the rhythmic structure to create knots, so the order that emerges from the thermodynamic simulation doesn't collapse into triviality. These just tuned interval graphs have a trivial topology, i.e. there are no cycles, which means there are no knots that prevent collapse. My approach with these tunings is mostly just to keep the temperature higher. With this piece, I gradually lowered the temperature, watching for some pitch class to start to dominate. So this piece is more about order just starting to emerge, which will happen before the phase transition, i.e. at a higher temperature than most of what I post. Anyway, it still sounds fun enough for me!
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