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 2^1/777, 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.