3558edo
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Prime factorization
2 × 3 × 593
Step size
0.337268¢
Fifth
2081\3558 (701.855¢)
Semitones (A1:m2)
335:269 (113¢ : 90.73¢)
Consistency limit
5
Distinct consistency limit
5
| ← 3557edo | 3558edo | 3559edo → |
3558 equal divisions of the octave (abbreviated 3558edo or 3558ed2), also called 3558-tone equal temperament (3558tet) or 3558 equal temperament (3558et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3558 equal parts of about 0.337 ¢ each. Each step represents a frequency ratio of 21/3558, or the 3558th root of 2.
Theory
3558edo is only consistent to the 5-odd-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.100 | -0.142 | +0.145 | +0.137 | +0.115 | -0.055 | +0.096 | -0.065 | -0.043 | +0.045 | +0.056 |
| Relative (%) | -29.7 | -42.0 | +43.1 | +40.7 | +34.2 | -16.5 | +28.3 | -19.3 | -12.6 | +13.5 | +16.7 | |
| Steps (reduced) |
5639 (2081) |
8261 (1145) |
9989 (2873) |
11279 (605) |
12309 (1635) |
13166 (2492) |
13901 (3227) |
14543 (311) |
15114 (882) |
15628 (1396) |
16095 (1863) | |
Subsets and supersets
Since 3558 factors into 2 × 3 × 593, 3558edo has subset edos 2, 3, 6, 593, 1186, and 1779.
Scales
Some MOS scales: