Augmentation

Here is a new piece in 53edo, using the scale in the diagram above, with 12 notes per octave out of the 53 made available in the tuning system.

My idea here was to make a small scale that both circulates and supports traversal of the kleisma comma. A scale with 11 notes per octave, generated by the minor third of 14 steps of 53edo, has these properties. But my algorithmic composition software does not like that scale! The problem is that traversing that comma with triads includes an augmented triad, with pitch classes 0, 17, and 34 in the diagram. This corresponds to a just tuned triad 16:20:25. This is too dissonant. The jostling process used in my software was consistently breaking the traversal at that point, and the whole piece would degenerate to just a small number of notes repeated. By extending the scale from 11 to 12 notes per octave, adding the pitch class 48 in the diagram, then the whole traversal can be built from major and minor triads. The jostling process did not destroy the traversal with this added pitch class.

This 12 note scale does not circulate. It's like extending a C major diatonic scale to eight notes by adding F#. Now, to move to the key of G, one would remove the F and add C#. The removed note and the added note are far apart: it's not just flattening or sharpening a single note.