812edo
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Prime factorization
22 × 7 × 29
Step size
1.47783¢
Fifth
475\812 (701.97¢)
Semitones (A1:m2)
77:61 (113.8¢ : 90.15¢)
Consistency limit
5
Distinct consistency limit
5
| ← 811edo | 812edo | 813edo → |
812 equal divisions of the octave (abbreviated 812edo or 812ed2), also called 812-tone equal temperament (812tet) or 812 equal temperament (812et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 812 equal parts of about 1.48 ¢ each. Each step represents a frequency ratio of 21/812, or the 812th root of 2.
812edo is a tuning for the copper temperament in the 5-limit, although it has a high error on the 5th harmonic. It is much better considered as a 2.3.11.17 subgroup tuning, where it is strong, with errors of 6% or less.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.015 | -0.599 | +0.632 | -0.086 | +0.359 | -0.029 | -0.469 | -0.196 | +0.472 | +0.285 |
| Relative (%) | +0.0 | +1.0 | -40.6 | +42.8 | -5.8 | +24.3 | -2.0 | -31.7 | -13.2 | +31.9 | +19.3 | |
| Steps (reduced) |
812 (0) |
1287 (475) |
1885 (261) |
2280 (656) |
2809 (373) |
3005 (569) |
3319 (71) |
3449 (201) |
3673 (425) |
3945 (697) |
4023 (775) | |