User:Aura/4191814edo: Difference between revisions

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This EDO has a consistency limit of 21, which is the most impressive out of all the 3-2 [[telicity|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.

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.

Meanwhile, although less accurate, the [[5/4]] major third at 1349463\4191814 is divisible by the prime factors of 3 and 449821, while the [[8/5]] minor sixth at 2842351\4191814 is on a prime scale step.

[[Category:Equal divisions of the octave|#######]]

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 This EDO has a consistency limit of 21, which is the most impressive out of all the 3-2 [[telicity|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.
+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.
+Meanwhile, although less accurate, the [[5/4]] major third at 1349463\4191814 is divisible by the prime factors of 3 and 449821, while the [[8/5]] minor sixth at 2842351\4191814 is on a prime scale step.
 {{Harmonics in equal|4191814}}
 [[Category:Equal divisions of the octave|#######]] <!-- 7-digit number -->