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 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). | 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 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. | |||
One step of 200edo is close to [[289/288]]. Unfortunately, it is not compatible with any obvious 2.3.17 subgroup mappings of 200edo. | 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 === | === Subsets and supersets === | ||
200 factorizes as | 200 factorizes as {{factorisation|200}}, 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. | [[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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| {{monzo| 317 -200 }} | | {{monzo| 317 -200 }} | ||
| {{mapping| 200 317 }} | | {{mapping| 200 317 }} | ||
| | | −0.0142 | ||
| 0.0142 | | 0.0142 | ||
| 0.24 | | 0.24 | ||
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| [[Helmholtz]] | | [[Helmholtz]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Scales == | == Scales == | ||
* 34 34 15 34 34 34 15 = [[ | * 34 34 15 34 34 34 15 = [[5L 2s|Pythagorean tuning]] | ||
* 32 32 20 32 32 32 20 = [[ | * 32 32 20 32 32 32 20 = [[5L 2s|Meantone tuning]] in the same way of [[50edo]] | ||
* 27 27 27 27 27 27 27 11 = [[ | * 27 27 27 27 27 27 27 11 = [[7L 1s|Porcupine tuning]] | ||
* 26 26 26 9 26 26 26 26 9 = [[ | * 26 26 26 9 26 26 26 26 9 = [[7L 2s|Superdiatonic tuning]] | ||
* 24 24 24 16 24 24 24 24 16 = [[ | * 24 24 24 16 24 24 24 24 16 = [[7L 2s|Superdiatonic tuning]] in the same way of [[25edo]] | ||
* 22 22 8 22 22 22 8 22 22 22 8 = [[ | * 22 22 8 22 22 22 8 22 22 22 8 = [[8L 3s|Sensi]] | ||
* 16 16 16 8 16 16 16 16 8 16 16 16 16 8 = [[ | * 16 16 16 8 16 16 16 16 8 16 16 16 16 8 = [[11L 3s|Ketradektriatoh tuning]] | ||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "On Fire" from ''Mysteries'' (2023) | * "On Fire" from ''Mysteries'' (2023) – [https://open.spotify.com/track/6janPwh3S8FLgIzWf9S0oQ Spotify] | [https://francium223.bandcamp.com/track/on-fire Bandcamp] | [https://www.youtube.com/watch?v=S1NKb_EoYrw YouTube] | ||
; [[Claudi Meneghin]] | ; [[Claudi Meneghin]] | ||
* ''Fugue on Elgar’s Enigma Theme'' | * ''Fugue on Elgar’s Enigma Theme'' – [https://www.youtube.com/watch?v=h4rjMFAzjow YouTube] | [http://soonlabel.com/xenharmonic/archives/1324 soonlabel archive]{{dead link}} | [http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Claudi_Meneghin_Enigma_Fugue.mp3 play]{{dead link}} | ||
[[Category:Listen]] | [[Category:Listen]] | ||