User:Aura/4191814edo
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Prime factorization
2 × 11 × 190537
Step size
0.000286272 ¢
Fifth
2452054\4191814 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2)
397122:315172 (113.7 ¢ : 90.22 ¢)
Consistency limit
21
Distinct consistency limit
21
| ← 4191813edo | 4191814edo | 4191815edo → |
Theory
This EDO has a consistency limit of 21, which is the most impressive out of all the 3-2 telic multiples of 190537edo. It tempers out the Archangelic comma in the 3-limit, and though this system's 5-limit and 7-limit are rather lackluster for an EDO this size, the 11-prime, 13-prime, 17-prime, and 19-prime are much better, which helps to bridge the lackluster 5-prime and 7-prime, and thus, it is worthy of a great deal of further exploration in the 19-limit.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000000 | +0.000000 | +0.000087 | +0.000096 | +0.000031 | -0.000005 | +0.000011 | -0.000006 | -0.000097 | +0.000072 | -0.000130 |
| Relative (%) | +0.0 | +0.0 | +30.5 | +33.5 | +10.9 | -1.7 | +3.8 | -2.2 | -33.7 | +25.3 | -45.3 | |
| Steps (reduced) |
4191814 (0) |
6643868 (2452054) |
9733091 (1349463) |
11767910 (3384282) |
14501294 (1925852) |
15511555 (2936113) |
17133884 (366628) |
17806522 (1039266) |
18961930 (2194674) |
20363753 (3596497) |
20767069 (3999813) | |