1125edo
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Prime factorization
32 × 53
Step size
1.06667¢
Fifth
658\1125 (701.867¢)
Semitones (A1:m2)
106:85 (113.1¢ : 90.67¢)
Consistency limit
15
Distinct consistency limit
15
| ← 1124edo | 1125edo | 1126edo → |
1125 equal divisions of the octave (abbreviated 1125edo or 1125ed2), also called 1125-tone equal temperament (1125tet) or 1125 equal temperament (1125et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1125 equal parts of about 1.07 ¢ each. Each step represents a frequency ratio of 21/1125, or the 1125th root of 2.
1125edo is a good 13-limit system, distinctly consistent to the 15-odd-limit, and the no-11 or no-17 29-odd-limit. The equal temperament tempers out 2401/2400, 4375/4374, and 250047/250000 in the 7-limit, supporting ennealimmal.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.088 | -0.180 | -0.293 | +0.149 | +0.006 | -0.422 | +0.087 | -0.008 | -0.244 | -0.502 |
| Relative (%) | +0.0 | -8.3 | -16.9 | -27.4 | +13.9 | +0.5 | -39.6 | +8.2 | -0.7 | -22.9 | -47.1 | |
| Steps (reduced) |
1125 (0) |
1783 (658) |
2612 (362) |
3158 (908) |
3892 (517) |
4163 (788) |
4598 (98) |
4779 (279) |
5089 (589) |
5465 (965) |
5573 (1073) | |
Subsets and supersets
Snce 1125 factors into 32 × 53, 1125edo has subset edos 3, 5, 9, 15, 25, 45, 75, 125, 225, 375.