200edo: Difference between revisions

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'''200edo''' divides the octave into 200 parts of exactly '''6 cents''' each, and contains a [[perfect fifth]] of exactly '''702 cents''' and a [[perfect fourth]] of exactly '''498''' cents, which is quite accurate, with an error of about 1/22 cent. 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.~~

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

== ~~200 tone equal modes~~ ==

== 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).

~~34 34 15 34 34 34 15 =~~ [[~~5L_2s|Pythagorean tuning~~]]

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.

~~32 32~~ 20 ~~32 32 32 20 = [[5L_2s|Meantone tuning]] in the same way of [[50edo]]~~

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

~~27 27 27 27 27 27 27 11~~ = ~~[[7L_1s~~|~~Porcupine tuning]]~~

=== Odd harmonics ===

~~26 26 26 9 26 26 26 26 9~~ = ~~[[7L_2s|Superdiatonic tuning]]~~

== Scales ==

~~24 24 24 16 24 24 24 24 16~~ = [[~~7L_2s~~|~~Superdiatonic~~ tuning~~]] in the same way of [[25edo~~]]

* 34 34 15 34 34 34 15 = [[5L_2s|Pythagorean tuning]]

~~22 22 8 22 22 22 8 22 22 22 8~~ = [[~~8L_3s~~|~~Sensi~~]]

* 32 32 20 32 32 32 20 = [[5L_2s|Meantone tuning]] in the same way of [[50edo]]

~~16 16 16 8 16 16 16 16 8 16 16 16 16 8~~ = [[~~11L_3s~~|~~Ketradektriatoh~~ tuning]]

* 27 27 27 27 27 27 27 11 = [[7L_1s|Porcupine tuning]]

~~The prime factorization~~

* 26 26 26 9 26 26 26 26 9 = [[7L_2s|Superdiatonic tuning]]

~~200~~ = ~~2<sup>3</sup> * 5<sup>2</sup>~~

* 24 24 24 16 24 24 24 24 16 = [[7L_2s|Superdiatonic tuning]] in the same way of [[25edo]]

~~leads to these divisors (or: ''sub edos'')~~

* 22 22 8 22 22 22 8 22 22 22 8 = [[8L_3s|Sensi]]

~~{{EDOs~~|~~2, 4, 5, 8, 10, 20, 25, 40, 50, 100}}~~

* 16 16 16 8 16 16 16 16 8 16 16 16 16 8 = [[11L_3s|Ketradektriatoh tuning]]

== Music ==

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-'''200edo''' divides the octave into 200 parts of exactly '''6 cents''' each, and contains a [[perfect fifth]] of exactly '''702 cents''' and a [[perfect fourth]] of exactly '''498''' cents, which is quite accurate, with an error of about 1/22 cent. 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.
+{{EDO intro|200}}
 One step of 200edo is close to [[289/288]].
-== 200 tone equal modes ==
+== 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).
-34 15 34 34 34 15 = [[5L_2s|Pythagorean tuning]]
+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.
-32 20 32 32 32 20 = [[5L_2s|Meantone tuning]] in the same way of [[50edo]]
+'s divisors are: {{EDOs|2, 4, 5, 8, 10, 20, 25, 40, 50, 100}}. It factorizes as 2^5 * 3^2.
-27 27 27 27 27 27 11 = [[7L_1s|Porcupine tuning]]
+=== Odd harmonics ===
+{{Harmonics in equal|200}}
-26 26 9 26 26 26 26 9 = [[7L_2s|Superdiatonic tuning]]
+== Scales ==
-24 24 16 24 24 24 24 16 = [[7L_2s|Superdiatonic tuning]] in the same way of [[25edo]]
+* 34 34 15 34 34 34 15 = [[5L_2s|Pythagorean tuning]]
-22 8 22 22 22 8 22 22 22 8 = [[8L_3s|Sensi]]
+* 32 32 20 32 32 32 20 = [[5L_2s|Meantone tuning]] in the same way of [[50edo]]
-16 16 8 16 16 16 16 8 16 16 16 16 8 = [[11L_3s|Ketradektriatoh tuning]]
+* 27 27 27 27 27 27 27 11 = [[7L_1s|Porcupine tuning]]
-The prime factorization
+* 26 26 26 9 26 26 26 26 9 = [[7L_2s|Superdiatonic tuning]]
-= 2<sup>3</sup> * 5<sup>2</sup>
+* 24 24 24 16 24 24 24 24 16 = [[7L_2s|Superdiatonic tuning]] in the same way of [[25edo]]
-leads to these divisors (or: ''sub edos'')
+* 22 22 8 22 22 22 8 22 22 22 8 = [[8L_3s|Sensi]]
-{{EDOs|2, 4, 5, 8, 10, 20, 25, 40, 50, 100}}
+* 16 16 16 8 16 16 16 16 8 16 16 16 16 8 = [[11L_3s|Ketradektriatoh tuning]]
 == Music ==