Copyright © Institute of Stuff. All rights reserved.


Enumerations of Musical Scales formed from the conventional set of Twelve Pitch Classes

All possible 2048 scales are represented by 1 to 12 sided polygons (unigons to dodecagons)  embedded in a clock face numbered from 0 to 11 starting with the tonic note of the scale (always at 0) at the top and with a vertex visit for each note present in the scale.

Polygonal rotations of otherwise identical (congruent) polygons - which may be perceived as modes of the same scale - reduce the set 0f 2048 to 351.

Left-right (bilateral) reflections - in the vertical axis - reduce these 351 congruences further to 223 similarities.

Finally, autocorrelations (distributions of intervals between every pair of notes in a scale) reduce these from 223 to 200 consonances.