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 is inconsistent to the 5-odd-limit and harmonic 3 is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.11 subgroup, where it notably tempers out 9801/9800.

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

Since 770 factors into 2 × 5 × 7 × 11, 770edo has 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