200edo: Difference between revisions

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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 divisible 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, {{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.

It [[tempering out|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.

One step of 200edo is close to [[289/288]]. Unfortunately, it is not compatible with any obvious 2.3.17 subgroup mappings of 200edo.

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=== Subsets and supersets ===

200 factorizes as ~~{{factorisation|200}}~~, and has subset edos {{EDOs| 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 }}.

200 factorizes as 23 × 52, and has subset edos {{EDOs| 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 }}.

[[400edo]], which doubles it, provides good correction for the harmonics 5 and 7, and makes for a strong 19-limit system.

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 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 divisible 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, {{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.
+It [[tempering out|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.
 One step of 200edo is close to [[289/288]]. Unfortunately, it is not compatible with any obvious 2.3.17 subgroup mappings of 200edo.
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 === Subsets and supersets ===
-factorizes as {{factorisation|200}}, and has subset edos {{EDOs| 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 }}.
+factorizes as 2<sup>3</sup> × 5<sup>2</sup>, and has subset edos {{EDOs| 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 }}.
 [[400edo]], which doubles it, provides good correction for the harmonics 5 and 7, and makes for a strong 19-limit system.