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 | '''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. | ||
== 200 tone equal modes == | == 200 tone equal modes == | ||
Revision as of 18:40, 25 January 2022
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 supports guiron temperament.
200 tone equal modes
34 34 15 34 34 34 15 = Pythagorean tuning
32 32 20 32 32 32 20 = Meantone tuning in the same way of 50edo
27 27 27 27 27 27 27 11 = Porcupine tuning
26 26 26 9 26 26 26 26 9 = Superdiatonic tuning
24 24 24 16 24 24 24 24 16 = Superdiatonic tuning in the same way of 25edo
22 22 8 22 22 22 8 22 22 22 8 = Sensi
16 16 16 8 16 16 16 16 8 16 16 16 16 8 = Ketradektriatoh tuning
The prime factorization
200 = 23 * 52
leads to these divisors (or: sub edos)
2, 4, 5, 8, 10, 20, 25, 40, 50, 100