# 771edo

 ← 770edo 771edo 772edo →
Prime factorization 3 × 257
Step size 1.55642¢
Fifth 451\771 (701.946¢)
Semitones (A1:m2) 73:58 (113.6¢ : 90.27¢)
Consistency limit 21
Distinct consistency limit 21

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

Approximation of prime harmonics in 771edo
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.