7-32, (0134689), Harmonic Minor
Set Class
The harmonic minor scale is a fairly even heptatonic (seven-note) scale consisting of mostly semitone and whole-tone intervals, and one minor third (three-semitone) gap. It is involution-related to the harmonic major scale. More
In both cases, the presence of the minor third makes these scales less regular and more uneven or ungainly, which may partially explain why they are less common in jazz theory. Overall they are fairly even and interesting harmonically, so their modes are still worth exploring.
These two scales can be thought of as slightly-modified, more-uneven versions of the acoustic or melodic minor scale, when treated as OPTIC-equivalent objects. The harmonic minor scale is traditionally thought of as a natural minor scale modified by one sharp (on the seventh scale degree), or a melodic minor scale with an extra flat on the sixth scale degree (when thought of as an OTC-equivalent object). However, in Harmonious we refer to the harmonic major or minor scales as OPTC-equivalent objects, unordered collections of notes, with seven possible playable modes, not just the actual harmonic major or minor modes themselves.
See also Harmonic Minor, and Beyond Diatonic for more about the set class behind the harmonic minor scale.
the minimum Euclidean distance from this set to any transposition of the perfectly even 7 note chord, in semitones