908edo
| ← 907edo | 908edo | 909edo → |
908 equal divisions of the octave (abbreviated 908edo or 908ed2), also called 908-tone equal temperament (908tet) or 908 equal temperament (908et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 908 equal parts of about 1.32 ¢ each. Each step represents a frequency ratio of 21/908, or the 908th root of 2.
908edo is consistent to the 23-odd-limit. It has a flat tendency, with all the lower harmonics tuned flat except 13. As an equal temperament, it tempers out the schisma in the 5-limit; 4375/4374 in the 7-limit; 3025/3024 and 9801/9800 in the 11-limit; 4225/4224 and 10648/10647 in the 13-limit; 1275/1274, 2500/2499, 2601/2600 and 5832/5831 in the 17-limit; 1445/1444, 3250/3249, 4200/4199 and 5985/5984 in the 19-limit; and 1863/1862 and 2025/2024 in the 23-limit. It supports pontiac and its weak extension bipont.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.193 | -0.411 | -0.103 | -0.217 | +0.001 | -0.550 | -0.156 | -0.521 | -0.062 | -0.542 |
| Relative (%) | +0.0 | -14.6 | -31.1 | -7.8 | -16.4 | +0.1 | -41.6 | -11.8 | -39.4 | -4.7 | -41.0 | |
| Steps (reduced) |
908 (0) |
1439 (531) |
2108 (292) |
2549 (733) |
3141 (417) |
3360 (636) |
3711 (79) |
3857 (225) |
4107 (475) |
4411 (779) |
4498 (866) | |
Subsets and supersets
Since 908 factors into primes as 22 × 227, 908edo has subset edos 2, 4, 227, and 454.