Narrowing the Range

Here is a new piece in 53edo. This is another attempt to create a kleisma traversal. Yesterday I posted a first attempt, whose score did not look like a kleisma traversal. I looked back at the code, and it sure looks like the system had been initialized to a kleisma traversal. So the most likely thing would be that I jostled the system at too high a temperature which erased the kleisma traversal, and then as I brought the temperature down a different structure spontaneously emerged.

To test this hypothesis, I used the same rhythmic structure and the same initialization of pitch values, but just set the temperature near the phase transition and jostled the system at that relatively cool temperature.

Here is a score of the piece. The 32 varying repetitions have been folded on top of each other. The vertical axis is the pitch classes, ordered by minor thirds. I.e. each row is the pitch class one minor third above the pitch class below it. This score looks exactly like a kleisma traversal. There is a gradual ramp from the beginning of each 80 second measure, moving up 6 minor thirds, which then wraps over to the beginning of the next measure but a perfect fifth higher. There is a whole band of pitch classes that is absent: a kleisma traversal has no business visiting all the pitch classes of the tuning. It just needs to follow a path to the tempered out comma, in this case the kleisma.

This brings up another facet of the puzzle of yesterday's piece. This piece did cover all the pitch classes. It looked a bit like a schisma traversal, but that shouldn't cover all the pitch classes either. So I suspect the structure that emerged was some kind of compound comma traversal. I have code to initialize a system with a pattern like that... but how to detect it once it has emerged... I don't know quite how to do that!

Here is another score for the piece, but with the rows reordered so now each row is a perfect fifth above the row below it. There is no helical structure here at all: the dense regions don't connect to form any sort of path. This shows that the piece is not any kind of schisma traversal.