User:TromboneBoi9/EDO Impressions

5edo: Extremely simple, barely cares about diatonic structure, barely cares about approximating any harmonic besides the seventh, and yet phyiscally cannot sound bad. True gigachad.

7edo: Very dry 5edo wannabe; doesn't approximate any other useful harmonic better than it does 3/2. Perhaps useful for mixing diatonic structures with maqamic flavors, but not much else.

8edo: Interesting 24edo subset, although better treated freely, with intervals and chords chosen by ear, since it doesn't systemize in any useful way. Useful, but strictly experimental.

9edo: Interesting 36edo subset which is best treated freely like 8edo. Can be vaguely systemized since it fits antidiatonic structure, which produces very enigmatic scales.

10edo: Could be treated as doubled-up 5edo, except it has some tricks up its sleeves to separate it from 5edo, including a nice 13/8, a perfect half-octave, and a half-assed 5/4.

11edo: "Phases out" from 12edo, which produces seconds and sevenths close to 12edo and quartertonal intervals in the fourth-fifth range; for instance, a reasonable 9/8 and a great 11/8. Very interesting system when taken seriously. Technically a 22edo subset, but not particularly useful as such. Also fits antidiatonic structure, producing very useful blues-like scales.

12edo: Usually given flack for its approximation of 5/4, but if it works fine in 15edo, it works here too. Along with it's stellar 3/2, it proves itself well for Western hegemony. A very composite number, so interesting symmetries inevitably come up.

13edo: Alike to 11edo, but without antidiatonicism and a 10/9 rather than a 9/8. Sometimes treated as a 26edo subset. Notoriously awkward to notate: best notated as either a 26edo subset or with an archaeotonic (6L1s) nominal system (E-F becomes a whole step).

14edo: Grown-up, half-decent 7edo, although it really only features supermajor, neutral, and subminor intervals and no minor or major. The smallest to feature a distinguishable syntonic comma, although it's negative.

15edo: A very versatile system for its size, by far my favorite. A superset of 5edo, along with a usable 5/4. 12edo from an alternate universe. The smallest system to feature a positive syntonic comma.

17edo: A version of 15edo that can't stand on its feet. Only approximates the 3/2 well, completely ignores 5/4, and yet fits diatonic structure reasonably.

19edo: Audibly identical to 1/3-comma meantone. Quite competent prime harmonic approximations, even beyond the 7th. A very nice system for the beginner in xenharmony.

20edo: 10edo, but naturally granted better approximations due to it being twice the density. Alright 11th and 13th harmonics, but the 9th is quite off.

22edo: A very interesting system, almost identical to 15edo but without the third-fourth collapse. 5/4 is even better, and while 7/4 is worse, it's still usable.

23edo: This system makes me go mad. Virtually no useful harmonic is approximated decently in 23edo, and yet people (especially Blackwood!) manage to make it sound so good. Apparently Blackwood did it by approximating Gamelan scales... I'll see about that.

24edo: Quarter tone harmony, the most practical of the >12edos to realistically play. A great "dive in" system for the beginner microtonal experimentalist. Despite its flat 7/4, its mere contrast with 12edo's minor seventh makes it usable as such, at least as a separate identity from 16/9.

31edo: Audibly identical to 1/4-comma meantone. A very competent system, although it can be considered boring for that exact reason. Does, however, get interesting with its quartertone-like steps. Historically used for Fokker genera; much juicy history in both the far and recent pasts.

36edo: A great 7/4, perhaps a better 13/8, and not much else. Can be used to great effect if you're into "phase-shifting" techniques like Alois Hába theorized about with 24edo.

41edo: Borderline identical to just intonation, even beyond the 13-limit, to the point it's practical to notate it with HEJI or other JI notations. I personally find it odd that 81/80 and 64/63 are not only not tempered out, but are also both one step large. An innovation for instrument-makers worldwide; for computer musicians, you might as well use pure JI.

48edo: Eighth tones. Not as fruitful as 41edo since the 5/4 is quite flat.

53edo: Not that different from 41edo, although the 3/2 is dead-on.

72edo: Twelfthtones. Also borderline identical to just intonation. The best system for 12edo bootlickers who want JI. Still relatively practical, as Wyschnegradsky came to find out.