307edo
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Prime factorization
307 (prime)
Step size
3.90879¢
Fifth
180\307 (703.583¢)
Semitones (A1:m2)
32:21 (125.1¢ : 82.08¢)
Dual sharp fifth
180\307 (703.583¢)
Dual flat fifth
179\307 (699.674¢)
Dual major 2nd
52\307 (203.257¢)
Consistency limit
7
Distinct consistency limit
7
| ← 306edo | 307edo | 308edo → |
307 equal divisions of the octave (307edo), or 307-tone equal temperament (307tet), 307 equal temperament (307et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 307 equal parts of about 3.91 ¢ each.
Theory
307et tempers out 1220703125/1219784832, 48828125/48771072, 95703125/95551488 and 2401/2400 in the 7-limit; 100663296/100656875, 939524096/935859375, 16384/16335, 226492416/226474325, 2359296/2358125, 6250/6237, 172032/171875, 42875/42768, 4302592/4296875, 15488/15435, 3388/3375, 766656/765625, 166375/165888, 391314/390625, 3294225/3294172, 43923/43904 and 102487/102400 in the 11-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +1.63 | +0.66 | +0.56 | -0.65 | -0.18 | -0.14 | -1.62 | +0.58 | -0.44 | -1.73 | +1.04 |
| relative (%) | +42 | +17 | +14 | -17 | -5 | -3 | -42 | +15 | -11 | -44 | +27 | |
| Steps (reduced) |
487 (180) |
713 (99) |
862 (248) |
973 (52) |
1062 (141) |
1136 (215) |
1199 (278) |
1255 (27) |
1304 (76) |
1348 (120) |
1389 (161) | |
Subsets and supersets
307edo is the 63rd prime edo. 614edo, which doubles it, gives a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [-973 307⟩ | ⟨307 973] | +0.1029 | 0.1030 | 2.64 |
| 2.9.5 | 32805/32768, [2 47 -65⟩ | ⟨307 973 713] | -0.0257 | 0.2004 | 5.13 |
| 2.9.5.7 | 32805/32768, 118098/117649, 589824/588245 | ⟨307 973 713 862] | -0.0687 | 0.1889 | 4.87 |
| 2.9.5.7.11 | 5632/5625, 8019/8000, 32805/32768, 46656/46585 | ⟨307 973 713 862 1062] | -0.0447 | 0.1756 | 4.49 |
| 2.9.5.7.11.13 | 729/728, 1001/1000, 4096/4095, 6656/6655, 10648/10647 | ⟨307 973 713 862 1062 1136] | -0.0311 | 0.1632 | 4.18 |
| 2.9.5.7.11.13.17 | 729/728, 936/935, 1001/1000, 1377/1375, 2025/2023, 7744/7735 | ⟨307 973 713 862 1062 1136 1255] | -0.0470 | 0.1560 | 3.99 |