This is a graphical score for the piece. The horizontal axis is time, in seconds. The vertical axis is pitch classes, from 0 to 269. All the octaves have been folded into a single octave.
The score shows the scale I used for this piece. This scale is an example of what Olivier Messiaen called a "mode of limited transposition" - I am calling it a symmetric scale. A nice feature of 270edo is that 270 factors very nicely: 270 = 2 x 5 x 27. These factors create opportunities for symmetries: a pattern of notes in or out of the scale can be repeated within an octave. In the scale here, the pattern is 27 pitch classes long, and repeats 10 times in an octave, to cover the full 270 pitch classes. From the 27 pitch classes in the pattern, 9 are in the scale and the other 18 are excluded. The 9 included are a simple sequence of every other pitch class in the scale, every other pitch class out of the scale.
So the complete scale starts with pitch classes 0, 2, 4, 6, 8, 10, 12, 14, 16, 27, 29, 31, 33, 35, etc.
My goal with this scale was to support traversal of the comma 2080:2079. This comma is not too complicated but it includes all the primes involved in the notion of consonance I imposed for this piece: 2080 = 32 x 5 x 13; 2079 = 27 x 7 x 11. I figured that if a scale could allow traversal of this comma, it could support a rich harmonic language.
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