User:Aura/4191814edo: Difference between revisions
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In this system, the [[perfect fifth]] at 2452054\4191814 is divisible by the prime factors of 2, 11, 227 and 491. However, the [[perfect fourth]], at 1739760\4191814, has more prime divisors, namely the prime factors of 2^4, 3, 5, 11 and 659. The latter means that just as in [[159edo]], the perfect fourth is divisible by 33, and thus, this system can offer not only a more accurate version of [[Ozan Yarman]]'s original 79-tone system. | In this system, the [[perfect fifth]] at 2452054\4191814 is divisible by the prime factors of 2, 11, 227 and 491. However, the [[perfect fourth]], at 1739760\4191814, has more prime divisors, namely the prime factors of 2^4, 3, 5, 11 and 659. The latter means that just as in [[159edo]], the perfect fourth is divisible by 33, and thus, this system can offer not only a more accurate version of [[Ozan Yarman]]'s original 79-tone system. | ||
{{Harmonics in equal|4191814}} | {{Harmonics in equal|4191814}} | ||
[[Category:Equal divisions of the octave|#######]] <!-- 7-digit number --> | [[Category:Equal divisions of the octave|#######]] <!-- 7-digit number --> | ||
Revision as of 11:55, 23 December 2022
| ← 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 fifth at 2452054\4191814 is divisible by the prime factors of 2, 11, 227 and 491. However, the perfect fourth, at 1739760\4191814, has more prime divisors, namely the prime factors of 2^4, 3, 5, 11 and 659. The latter means that just as in 159edo, the perfect fourth is divisible by 33, and thus, this system can offer not only 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) | |