User:Overthink/3426edo
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Prime factorization
2 × 3 × 571
Step size
0.350263 ¢
Fifth
2004\3426 (701.926 ¢) (→ 334\571)
Semitones (A1:m2)
324:258 (113.5 ¢ : 90.37 ¢)
Consistency limit
15
Distinct consistency limit
15
| ← 3425edo | 3426edo | 3427edo → |
3426 equal divisions of the octave (abbreviated 3426edo or 3426ed2), also called 3426-tone equal temperament (3426tet) or 3426 equal temperament (3426et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3426 equal parts of about 0.35 ¢ each. Each step represents a frequency ratio of 21/3426, or the 3426th root of 2.
Theory
3426edo is consistent to the 15-odd-limit and is overall a strong 11- and 13-limit system.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.029 | +0.026 | +0.001 | -0.004 | +0.103 | +0.123 | -0.140 | +0.097 | -0.155 | -0.027 |
| Relative (%) | +0.0 | -8.2 | +7.4 | +0.2 | -1.3 | +29.4 | +35.2 | -40.0 | +27.7 | -44.3 | -7.7 | |
| Steps (reduced) |
3426 (0) |
5430 (2004) |
7955 (1103) |
9618 (2766) |
11852 (1574) |
12678 (2400) |
14004 (300) |
14553 (849) |
15498 (1794) |
16643 (2939) |
16973 (3269) | |