771edo

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← 770edo771edo772edo →
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.