Bug or Feature?

Here is a new piece in 53edo. My intent was for this to be a traversal of the kleisma comma, repeated 32 times with variations. I'm not too sure what I actually got!

The idea behind the thermodynamic approach I use in my software is that order can emerge spontaneously. I use unusual tunings; my hope is that this kind of spontaneous order can reveal some of the potential of these tunings. There is one significant challenge though: is the order that can be discovered in the output something that I introduced accidentally, or is is truly spontaneous?

I often do introduce a simple structure into the system I am simulating, and try to preserve that order. In these cases, I just hope that the variations will reveal additional order around that structure. In the piece here, I initialized the system with a traversal of the kleisma comma along one axis of the system. The variations can then emerge in the other dimensions.

I use various types of graphs or scores in trying to see what sort of order might be present in the output. The graph above is a simple score for the piece. Time is on the horizontal axis, in seconds. Pitch class is on the vertical axis: the pitches in the piece are all folded into a single octave, so the vertical axis runs from 0 to 52. The graph looks a bit like a coarsely woven fabric. Since the topology of the system is 32 repetitions of an 80 second measure, folding all the repetitions together might make the order more clear:

It's clear that the measures share some sort of structure, but it's not so clear what the order is. There is a vague sort of staircase structure, so it looks a bit like a comma traversal. It's pretty surprising that almost all the pitch classes are present. A simple comma traversal doesn't need so many pitch classes!

The kleisma comma is dominated by minor thirds. Six minor thirds is very close to a perfect fifth, and in 53edo they are exactly the same (modulo octaves). So I had the idea of shuffling the pitch classes. This graph has the same rows as the previous graph, but instead of ordering the pitch classes in a sort of chromatic way, just climbing microstep by microstep, in these graph each row is a pitch class a minor third above the pitch class below it. Horizontal stripes appear in this graph, with a period of about 6 rows. These are the perfect fifths. But if this was a kleisma traversal, there should just be a few stripes that angle very slightly so they change height by 6 rows from one side to the other; the right side of this graph wraps over to the left side, so the traversal should look like a helix. This graph has a strongly helical shape, but it is very steep. I don't think I ended up with a kleisma traversal! But all those stripes of a perfect fifth...

Here the rows are ordered so each row is a perfect fifth above the row immediately below it. There are about six stripes that gradually rise from left to right, wrapping to the next stripe to form a helix. Ah, this looks like a traversal of the schisma. With a schisma, eight perfect fifths plus a major third bring one back to the starting point (again, modulo octaves).

My intent was to produce a traversal of the kleisma, but I got instead a traversal of the schisma. I need to go back to my code... did I bungle the initialization? Or maybe I jostled too much, the initialization got erased, and the schisma traversal emerged spontaneously. Either way, when I listen to the piece, it sounds pretty good to my ears!