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=<span style="color: #007261; font-family: Consolas; font-size: 113%;">200 tone equal temperament</span>=
{{Infobox ET}}
{{ED intro}}


==<span style="font-size: 13px; font-weight: normal; line-height: 19px;">200 [[EDO|EDO]] divides the octave into 200 parts of exactly '''6 cents''' each, and contains a [[perfect_fifth|perfect fifth]] of exactly '''702 cents''' and a [[Perfect_fourth|perfect fourth]] of exactly '''498''' cents, which is quite accurate, with an error of about 1/22 cent. It tempers out the schisma, 32805/32768, in the 5-limit and the gamelisma, 1029/1024, in the 7-limit, so that it supports [[Schismatic_family#Guiron|guiron temperament]].</span>==
== 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 log<sub>2</sub>(3/2). Only about 0.045 cents sharp, it is the next best fifth in absolute error after [[53edo]]'s. 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).  


<u>'''200 tone equal modes:'''</u>
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.


34 34 15 34 34 34 15 = [[5L_2s|Pythagorean tuning]]
One step of 200edo is close to [[289/288]]. Unfortunately, it is not compatible with any obvious 2.3.17 subgroup mappings of 200edo.


32 32 20 32 32 32 20 = [[5L_2s|Meantone tuning]] in the same way of [[50edo|50edo]]
=== Prime harmonics ===
{{Harmonics in equal|200}}


27 27 27 27 27 27 27 11 = [[7L_1s|Porcupine tuning]]
=== Subsets and supersets ===
200 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 }}.


26 26 26 9 26 26 26 26 9 = [[7L_2s|Superdiatonic tuning]]
[[400edo]], which doubles it, provides good correction for the harmonics 5 and 7, and makes for a strong 19-limit system.


24 24 24 16 24 24 24 24 16 = [[7L_2s|Superdiatonic tuning]] in the same way of [[25edo|25edo]]
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 317 -200 }}
| {{mapping| 200 317 }}
| −0.0142
| 0.0142
| 0.24
|-
| 2.3.5
| 32805/32768, {{monzo| 2 -32 21 }}
| {{mapping| 200 317 464 }}
| +0.3226
| 0.4767
| 7.95
|-
| 2.3.5.7
| 1029/1024, 10976/10935, 390625/387072
| {{mapping| 200 317 464 561 }}
| +0.4937
| 0.5082
| 8.47
|}


22 22 8 22 22 22 8 22 22 22 8 = [[8L_3s|Sensi]]
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br />per 8ve
! Generator*
! Cents*
! Associated<br />ratio*
! Temperaments
|-
| 1
| 23\200
| 138.00
| 27/25
| [[Quartemka]]
|-
| 1
| 39\200
| 234.00
| 8/7
| [[Guiron]]
|-
| 1
| 83\200
| 498.00
| 4/3
| [[Helmholtz (temperament)|Helmholtz]]
|}
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct


16 16 16 8 16 16 16 16 8 16 16 16 16 8 = [[11L_3s|Ketradektriatoh tuning]]
== Scales ==
* 34 34 15 34 34 34 15 = [[5L 2s|Pythagorean tuning]]
* 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 = [[7L 1s|Porcupine tuning]]
* 26 26 26 9 26 26 26 26 9 = [[7L 2s|Superdiatonic tuning]]
* 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 = [[8L 3s|Sensi]]
* 16 16 16 8 16 16 16 16 8 16 16 16 16 8 = [[11L 3s|Ketradektriatoh tuning]]


The prime factorization
== Music ==
; [[Francium]]
* "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]


200 = [[2edo|2]]<span style="vertical-align: super;">3</span> * [[5edo|5]]<span style="vertical-align: super;">2</span>
; [[Claudi Meneghin]]
* ''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}}


leads to these further divisors
[[Category:3-limit record edos|###]] <!-- 3-digit number -->
 
[[Category:Listen]]
[[4edo|4]], [[8edo|8]], [[10edo|10]], [[20edo|20]], [[25edo|25]], [[40edo|40]], [[50edo|50]], [[100edo|100]]
 
=Music=
[http://soonlabel.com/xenharmonic/archives/1324 Fugue on Elgar’s Enigma Theme] [http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Claudi_Meneghin_Enigma_Fugue.mp3 play] by Claudi Meneghin
[[Category:edo]]
[[Category:todo:intro]]
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