3684edo

← 3683edo

3684edo

3685edo →

Prime factorization	22 × 3 × 307
Step size	0.325733 ¢
Fifth	2155\3684 (701.954 ¢)
Semitones (A1:m2)	349:277 (113.7 ¢ : 90.23 ¢)
Consistency limit	9
Distinct consistency limit	9

3684edo is an extraordinarily strong 5-limit system, tempering out senior, [-17 62 -35⟩, gross, [144 -22 -47⟩; and the Kirnberger atom, [161 -84 -12⟩;. It is uniquely consistent through the 9 odd limit, and in the 7-limit, it tempers out the landscape comma, 250047/250000, and so supports the 7-limit atomic.

3684 = 12 * 307, and is potentially of use as a device for constructing 5-limit 12-note circulating temperaments. From that point of view, one might note that 81/80 is 66 steps, 531441/524288, the Pythagorean comma, 72 steps, and 32805/32768, the schisma, 6 steps, making it exactly 1/12 of a Pythagorean comma and 1/11 of a syntonic comma, useful approximations when dealing with this problem. Raider, [71 -99 37⟩;, pirate, [-90 -15 49⟩; and the monzisma, [54 -37 2⟩;, are all one step of 3684et.