User:Aura/4191814edo
| ← 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 representation of the 11-prime is a bit better, and the representations of the 13-prime, 17-prime, and 19-prime are excellent, all which help to bridge the lackluster 5-prime and 7-prime. Thus, this system is worthy of a great deal of further exploration in the 19-limit.
In this system, the perfect fourth, at 1739760\4191814 is divisible by the prime factors of 2, 3, 5, 11 and 659. This means that as in 159edo, the perfect fourth is divisible by 66, and thus, this system can offer a more accurate version of Ozan Yarman's original 79-tone system.
| 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) | |