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, and it tempers out the smallest superparticular intervals with all primes up to 7, all primes up to 11, all primes up to 13, all primes up to 17, and all primes up to 19 (known as SPIFEs). 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.