312edo

← 311edo

312edo

313edo →

Prime factorization	23 × 3 × 13
Step size	3.84615 ¢
Fifth	183\312 (703.846 ¢) (→ 61\104)
Semitones (A1:m2)	33:21 (126.9 ¢ : 80.77 ¢)
Dual sharp fifth	183\312 (703.846 ¢) (→ 61\104)
Dual flat fifth	182\312 (700 ¢) (→ 7\12)
Dual major 2nd	53\312 (203.846 ¢)
Consistency limit	3
Distinct consistency limit	3

This edo is the first multiple of 12 to have a patent val fifth that does not correspond to the 12edo fifth of 700 cents. It is strong in the 2.9.15.7 subgroup. Beyond that, it is harmonic quality is quite poor for its size.

Odd harmonics

Approximation of odd harmonics in 312edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23	25
Error	Absolute (¢)	+1.89	-1.70	+0.40	-0.06	-1.32	+1.78	+0.19	-1.11	-1.36	-1.55	-1.35	+0.45
	Relative (%)	+49.2	-44.2	+10.5	-1.7	-34.3	+46.3	+5.0	-28.8	-35.3	-40.3	-35.1	+11.7
Steps (reduced)		495 (183)	724 (100)	876 (252)	989 (53)	1079 (143)	1155 (219)	1219 (283)	1275 (27)	1325 (77)	1370 (122)	1411 (163)	1449 (201)

Subsets and supersets

Since 312 factors into 2³ × 3 × 13, 312edo has subset edos 2, 3, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, and 156. 624edo, which doubles it, provides the much needed correction to many of the lower harmonics.