777edo

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← 776edo777edo778edo →
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.