[hmaoauxw] All possible musical scales

Enumerate all possible scales: subsets of the 12 chromatic scale degrees.

Add the constraint that cyclic transformations are in the same equivalence class.   So the major scale, the natural minor scale, and all 7 major modes are equivalent.

Organize by the largest gap between scale notes. Of particular interest are scales whose largest gap is at most a whole tone (e.g., major scale, ascending melodic minor scale, whole tone scale, octotonic scale, chromatic scale), or at most an augmented 2nd (harmonic minor scale, blues scale, pentatonic scale).

Also organize by the number of notes in the scale. Of particular interest are heptatonic scales.  Heptatonia prima, secunda, and tertia (and their modes) are the heptatonic scales whose largest gap is a whole tone.