770edo

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← 769edo770edo771edo →
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 1.558 ¢ 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 +12 +34 +16 +24 -34 -31 -35 +10 -8 -14
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