User:Tristanbay/My favorite EDOs

My favorite EDOs greater than 12edo are 19, 22, 31, 41, 46, 53, 72, and 270.

Why?

19edo: Good potential for more complex tonal modulation that doesn't sound too harsh without needing too many more notes than 12edo, diatonic semitone is just sharp enough to provide a bit of a zing without going overboard (in the right context), and has a surprisingly usable 4:5:6:7:8 chord given that 7/4 is about 21 cents flat.

22edo: Super simplistic and warped yet rather consistent representation of undecimal harmony provides tonality that feels novel and exaggerated compared to 12edo.

31edo: Great system for those who still want a relatively standard diatonic scale but want the added benefit of septimal and neutral intervals (despite 81/64 being inconsistent); it makes working with them quite easy and manageable.

41edo: Highlights the distinction between Pythagorean, syntonic, and septimal intervals by exaggerating both 81/80 and 64/63. It also works quite well (skip-fretted) on guitar and is consistent in the 15-odd-limit.

46edo: Good, although simplistic, representation of the 13-limit. The only interval in the entire 15-odd-limit it represents inconsistently is 15/13, and only by a little bit. It works great for 13-limit neogothic tunings.

53edo: Takes advantage of the fact that the intervals found just beyond a traditional Pythagorean pentatonic scale are very close to common syntonic intervals by tempering out 32805/32768 (41edo also does this, but 53edo really focuses in on the 5-limit). Generally a good stand-in for syntonic just intonation and also approximates the 13th harmonic well.

72edo: Very simplistic tonal structure for the density of notes it has, yet it's very accurate, and is a usable full 13-limit JI stand-in. It can be used more easily with virtual instruments that aren't officially microtonal in a DAW by making 5 copies and tuning those to -33, -17, +17, +33, and +50 cents from the original and using 6 MIDI channels, one for each instrument. The FL Studio piano roll can display multiple MIDI channels in one window with differently-colored notes.

270edo: The ultimate 13-limit (tridecimal) tuning that one could potentially make a keyboard for and still be able to play relatively well. Also supports meantone and likely a number of other simpler rank-2 temperaments.