# 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

770 equal divisions of the octave (abbreviated 770edo or 770ed2), also called 770-tone equal temperament (770tet) or 770 equal temperament (770et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 770 equal parts of about 1.56 ¢ each. Each step represents a frequency ratio of 21/770, or the 770th root of 2.

## 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