User:Francium/1427edo
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Prime factorization
1427 (prime)
Step size
0.840925 ¢
Fifth
835\1427 (702.172 ¢)
Semitones (A1:m2)
137:106 (115.2 ¢ : 89.14 ¢)
Consistency limit
3
Distinct consistency limit
3
| ← 1426edo | 1427edo | 1428edo → |
1427 equal divisions of the octave (abbreviated 1427edo or 1427ed2), also called 1427-tone equal temperament (1427tet) or 1427 equal temperament (1427et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1427 equal parts of about 0.841 ¢ each. Each step represents a frequency ratio of 21/1427, or the 1427th root of 2.
Theory
1427edo is only consistent to the 3-limit. It is strong in the 2.15.7.17.23 subgroup, tempering out 9132503625/9126805504, 11664000000/11662192423, 12762815625/12758024192 and 1973822685184/1973598159375.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.217 | -0.329 | -0.080 | -0.406 | +0.329 | +0.397 | -0.112 | +0.160 | +0.174 | +0.137 | -0.103 |
| Relative (%) | +25.9 | -39.1 | -9.5 | -48.3 | +39.1 | +47.3 | -13.3 | +19.1 | +20.7 | +16.3 | -12.3 | |
| Steps (reduced) |
2262 (835) |
3313 (459) |
4006 (1152) |
4523 (242) |
4937 (656) |
5281 (1000) |
5575 (1294) |
5833 (125) |
6062 (354) |
6268 (560) |
6455 (747) | |
Subsets and supersets
1427edo is the 225th prime edo. 4281edo, which triples it, gives a good correction to its harmonic 5.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [2262 -1427⟩ | [⟨1427 2262]] | −0.0686 | 0.0686 | 8.16 |