771edo
| ← 770edo | 771edo | 772edo → |
771 equal divisions of the octave (abbreviated 771edo or 771ed2), also called 771-tone equal temperament (771tet) or 771 equal temperament (771et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 771 equal parts of about 1.56 ¢ each. Each step represents a frequency ratio of 21/771, or the 771st root of 2.
771edo is distinctly consistent up to the 21-odd-limit, with all of the prime harmonics to 19 having a flat tendency.
In the 5-limit it tempers out the monzisma, [54 -37 2⟩, and the mutt comma, [-44 -3 21⟩; in the 7-limit 65625/65536 and 250047/250000; in the 11-limit 3025/3024; in the 13-limit 4225/4224 and 10648/10647; in the 17-limit 833/832, 1225/1224, 2058/2057, 2431/2430 and 2601/2600; and in the 19-limit 1445/1444, 1540/1539, 1729/1728, 2926/2925, 3250/3249, 4200/4199 and 5985/5984. It provides the optimal patent val for the rank-6 temperament tempering out 833/832 and various other temperaments tempering it out.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.009 | -0.321 | -0.733 | -0.345 | -0.061 | -0.675 | -0.237 | +0.519 | +0.773 | +0.490 |
| Relative (%) | +0.0 | -0.6 | -20.7 | -47.1 | -22.2 | -3.9 | -43.4 | -15.2 | +33.4 | +49.7 | +31.5 | |
| Steps (reduced) |
771 (0) |
1222 (451) |
1790 (248) |
2164 (622) |
2667 (354) |
2853 (540) |
3151 (67) |
3275 (191) |
3488 (404) |
3746 (662) |
3820 (736) | |
Subsets and supersets
Since 771 factors into 3 × 257, 771edo contains 3edo and 257edo as subsets.