# 777edo

 ← 776edo 777edo 778edo →
Prime factorization 3 × 7 × 37
Step size 1.5444¢
Fifth 455\777 (702.703¢) (→65\111)
Semitones (A1:m2) 77:56 (118.9¢ : 86.49¢)
Dual sharp fifth 455\777 (702.703¢) (→65\111)
Dual flat fifth 454\777 (701.158¢)
Dual major 2nd 132\777 (203.861¢) (→44\259)
Consistency limit 3
Distinct consistency limit 3

777 equal divisions of the octave (abbreviated 777edo or 777ed2), also called 777-tone equal temperament (777tet) or 777 equal temperament (777et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 777 equal parts of about 1.54 ¢ each. Each step represents a frequency ratio of 21/777, or the 777th root of 2.

777edo is inconsistent to 5-odd-limit and harmonic 3 is about halfway between its steps. Otherwise it is excellent in approximating harmonics 5, 7, 9, 11, 13, and 17, making it suitable for a 2.9.5.7.11.13.17 subgroup interpretation. A comma basis for the 2.9.5.7.11.13 subgroup is {4459/4455, 41503/41472, 496125/495616, 105644/105625, 123201/123200}. In addition, it tempers out the landscape comma in the 2.9.5.7 subgroup.

### Odd harmonics

Approximation of odd harmonics in 777edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.748 -0.213 -0.486 -0.049 +0.033 -0.373 +0.534 +0.064 +0.556 +0.262 +0.297
Relative (%) +48.4 -13.8 -31.5 -3.2 +2.2 -24.2 +34.6 +4.1 +36.0 +16.9 +19.2
Steps
(reduced)
1232
(455)
1804
(250)
2181
(627)
2463
(132)
2688
(357)
2875
(544)
3036
(705)
3176
(68)
3301
(193)
3413
(305)
3515
(407)

### Subsets and supersets

Since 777 factors into 3 × 7 × 37, 777edo has subset edos 3, 7, 21, 37, 111, and 333.