200edo: Difference between revisions

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One step of 200edo is close to [[289/288]].

== Theory ==

200edo contains a [[perfect fifth]] of exactly 702 cents and a [[perfect fourth]] of exactly 498 cents, which is accurate due to 200 being the denominator of a continued fraction convergent to ~~log2~~(3/2). The error is only about 1/22 ~~cent~~. In light of having its perfect fifth precise and the step divisibly by 9, it is essentially a perfect ~~EDO~~ for [[Carlos Alpha]], even up many octaves (the difference between 13 steps of 200edo and 1 step of Carlos Alpha is only 0.03501 cents).

200edo contains a [[perfect fifth]] of exactly 702 cents and a [[perfect fourth]] of exactly 498 cents, which is accurate due to 200 being the denominator of a continued fraction convergent to log2(3/2). The error is only about 1/22 cents. In light of having its perfect fifth precise and the step divisibly by 9, it is essentially a perfect edo for [[Carlos Alpha]], even up many octaves (the difference between 13 steps of 200edo and 1 step of Carlos Alpha is only 0.03501 cents).

It tempers out the schisma, 32805/32768 and the quartemka, |2 -32 21~~>~~ in the 5-limit and the gamelisma, 1029/1024, in the [[7-limit]], so that it [[support]]s [[guiron]] temperament.

It tempers out the [[schisma]], 32805/32768 and the quartemka, {{monzo| 2 -32 21 }} in the 5-limit, and the [[gamelisma]], 1029/1024, in the [[7-limit]], so that it [[support]]s the [[guiron]] temperament.

~~200's divisors are: {{EDOs|2, 4, 5, 8, 10, 20, 25, 40, 50, 100}}. It factorizes as 5^2 * 2^3~~.

=== Odd harmonics ===

=== Miscellaneous properties ===

200's divisors are: {{EDOs| 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 }}. It factorizes as 52 × 23.

== Scales ==

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 {{EDO intro|200}}
 One step of 200edo is close to [[289/288]].
 == Theory ==
-edo  contains a [[perfect fifth]] of exactly 702 cents and a [[perfect fourth]] of exactly 498 cents, which is accurate due to 200 being the denominator of a continued fraction convergent to log2(3/2). The error is only about 1/22 cent. In light of having its perfect fifth precise and the step divisibly by 9, it is essentially a perfect EDO for [[Carlos Alpha]], even up many octaves (the difference between 13 steps of 200edo and 1 step of Carlos Alpha is only 0.03501 cents).
+edo contains a [[perfect fifth]] of exactly 702 cents and a [[perfect fourth]] of exactly 498 cents, which is accurate due to 200 being the denominator of a continued fraction convergent to log<sub>2</sub>(3/2). The error is only about 1/22 cents. In light of having its perfect fifth precise and the step divisibly by 9, it is essentially a perfect edo for [[Carlos Alpha]], even up many octaves (the difference between 13 steps of 200edo and 1 step of Carlos Alpha is only 0.03501 cents).
-It tempers out the schisma, 32805/32768 and the quartemka, |2 -32 21&gt; in the 5-limit and the gamelisma, 1029/1024, in the [[7-limit]], so that it [[support]]s [[guiron]] temperament.
+It tempers out the [[schisma]], 32805/32768 and the quartemka, {{monzo| 2 -32 21 }} in the 5-limit, and the [[gamelisma]], 1029/1024, in the [[7-limit]], so that it [[support]]s the [[guiron]] temperament.
-'s divisors are: {{EDOs|2, 4, 5, 8, 10, 20, 25, 40, 50, 100}}. It factorizes as 5^2 * 2^3.
 === Odd harmonics ===
 {{Harmonics in equal|200}}
+=== Miscellaneous properties ===
+'s divisors are: {{EDOs| 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 }}. It factorizes as 5<sup>2</sup> × 2<sup>3</sup>.
 == Scales ==