312edo
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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
| ← 311edo | 312edo | 313edo → |
312 equal divisions of the octave (312edo), or 312-tone equal temperament (312tet), 312 equal temperament (312et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 312 equal parts of about 3.85 ¢ each.
Theory
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 2.7.9.15 subgroup. Beyond that, it's harmonic quality is quite poor (for its size).
| 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 | -44 | +11 | -2 | -34 | +46 | +5 | -29 | -35 | -40 | -35 | +12 | |
| 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) | |