770edo

← 769edo

770edo

771edo →

Prime factorization	2 × 5 × 7 × 11
Step size	1.55844 ¢
Fifth	450\770 (701.299 ¢) (→ 45\77)
Semitones (A1:m2)	70:60 (109.1 ¢ : 93.51 ¢)
Dual sharp fifth	451\770 (702.857 ¢) (→ 41\70)
Dual flat fifth	450\770 (701.299 ¢) (→ 45\77)
Dual major 2nd	131\770 (204.156 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

770edo tempers out 134217728/133984375, 703125/702464, 5250987/5242880 and 200120949/200000000 in the 7-limit; 56723625/56689952, 161280/161051, 234375/234256, 2097152/2096325, 496125/495616, 151263/151250, 104857600/104825259, 172032/171875, 369140625/369098752, 825000/823543, 180224/180075, 160083/160000, 766656/765625, 43923/43904, 20614528/20588575 and 781258401/781250000 in the 11-limit.

Odd harmonics

Approximation of odd harmonics in 770edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.656	+0.180	+0.525	+0.246	+0.370	-0.528	-0.477	-0.540	+0.149	-0.132	-0.222
	Relative (%)	-42.1	+11.5	+33.7	+15.8	+23.8	-33.9	-30.6	-34.6	+9.6	-8.4	-14.3
Steps (reduced)		1220 (450)	1788 (248)	2162 (622)	2441 (131)	2664 (354)	2849 (539)	3008 (698)	3147 (67)	3271 (191)	3382 (302)	3483 (403)

Subsets and supersets

770 factors into 2 × 5 × 7 × 11 with subset edos 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, and 385. 1540edo, which doubles it, gives a good correction to the harmonic 3.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[2441 -770⟩	⟨770 2441]	-0.0388	0.0388	2.49
2.9.5	[61 2 -29⟩, [40 -28 21⟩	⟨770 2441 1788]	-0.0517	0.0365	2.34
2.9.5.7	43046721/43025920, 134217728/133984375, 1220703125/1219784832	⟨770 2441 1788 2162]	-0.0855	0.0666	4.27
2.9.5.7.11	9801/9800, 820125/819896, 1296000/1294139, 1362944/1361367	⟨770 2441 1788 2162 2664]	-0.0898	0.0602	3.86

Scales

• Semidim8
• Semidim13