1308edo
| ← 1307edo | 1308edo | 1309edo → |
1308 equal divisions of the octave (abbreviated 1308edo or 1308ed2), also called 1308-tone equal temperament (1308tet) or 1308 equal temperament (1308et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1308 equal parts of about 0.917 ¢ each. Each step represents a frequency ratio of 21/1308, or the 1308th root of 2.
1308edo is distinctly consistent to the 21-odd-limit, and is the 15th zeta gap edo. With 23/17 barely missing the line, it has reasonable approximations up to the 37-limit.
The equal temperament tempers out [37 25 -33⟩ (whoosh comma) and [-46 51 -15⟩ (171 & 1137 comma) in the 5-limit; 250047/250000, 2460375/2458624, and [47 4 0 -19⟩ in the 7-limit; 9801/9800, 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; 4225/4224, 6656/6655, 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; 2601/2600, 5832/5831, 11016/11011, 11271/11264, 12376/12375, and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.120 | -0.075 | -0.019 | +0.058 | -0.161 | -0.368 | -0.265 | +0.166 | -0.219 | -0.081 | +0.032 |
| Relative (%) | +0.0 | -13.1 | -8.2 | -2.0 | +6.3 | -17.5 | -40.1 | -28.9 | +18.1 | -23.9 | -8.9 | +3.5 | |
| Steps (reduced) |
1308 (0) |
2073 (765) |
3037 (421) |
3672 (1056) |
4525 (601) |
4840 (916) |
5346 (114) |
5556 (324) |
5917 (685) |
6354 (1122) |
6480 (1248) |
6814 (274) | |
Subsets and supersets
Since 1308 factors into 22 × 3 × 109, 1308edo has subset edos 2, 3, 4, 6, 12, 109, 218, 327, 436, and 654.