310edo
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Prime factorization
2 × 5 × 31
Step size
3.87097¢
Fifth
181\310 (700.645¢)
Semitones (A1:m2)
27:25 (104.5¢ : 96.77¢)
Dual sharp fifth
182\310 (704.516¢) (→91\155)
Dual flat fifth
181\310 (700.645¢)
Dual major 2nd
53\310 (205.161¢)
Consistency limit
3
Distinct consistency limit
3
| ← 309edo | 310edo | 311edo → |
310 equal divisions of the octave (abbreviated 310edo or 310ed2), also called 310-tone equal temperament (310tet) or 310 equal temperament (310et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 310 equal parts of about 3.87 ¢ each. Each step represents a frequency ratio of 21/310, or the 310th root of 2.
It is part of the optimal ET sequence for the 31-5-commatic, fantastic, quadrasruta and wizard temperaments.
As a multiple of 10 and 31, it supports many 10th-octave temperaments and 31st-octave temperaments.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.31 | +0.78 | -1.08 | +1.25 | -1.64 | -0.53 | -0.53 | -0.44 | +0.55 | +1.48 | -1.18 |
| Relative (%) | -33.8 | +20.2 | -28.0 | +32.3 | -42.4 | -13.6 | -13.6 | -11.3 | +14.2 | +38.2 | -30.4 | |
| Steps (reduced) |
491 (181) |
720 (100) |
870 (250) |
983 (53) |
1072 (142) |
1147 (217) |
1211 (281) |
1267 (27) |
1317 (77) |
1362 (122) |
1402 (162) | |