770edo
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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
| ← 769edo | 770edo | 771edo → |
770 equal divisions of the octave (770edo), or 770-tone equal temperament (770tet), 770 equal temperament (770et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 770 equal parts of about 1.56 ¢ each.
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
| 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 |