200edo: Difference between revisions
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{{EDO intro|200}} | {{EDO intro|200}} | ||
One step of 200edo is close to [[289/288]]. | One step of 200edo is close to [[289/288]]. | ||
== Theory == | == Theory == | ||
200edo | 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 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). | ||
It tempers out the schisma, 32805/32768 and the quartemka, |2 -32 21 | 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. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|200}} | {{Harmonics in equal|200}} | ||
=== Miscellaneous properties === | |||
200's divisors are: {{EDOs| 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 }}. It factorizes as 5<sup>2</sup> × 2<sup>3</sup>. | |||
== Scales == | == Scales == | ||
Revision as of 15:53, 4 October 2022
One step of 200edo is close to 289/288.
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 cents. 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).
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 the guiron temperament.
Odd harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.04 | -2.31 | -2.83 | +0.68 | -0.53 | -2.96 | +2.49 | +1.73 | +2.42 | +0.96 |
| Relative (%) | +0.0 | +0.7 | -38.6 | -47.1 | +11.4 | -8.8 | -49.3 | +41.4 | +28.8 | +40.4 | +16.1 | |
| Steps (reduced) |
200 (0) |
317 (117) |
464 (64) |
561 (161) |
692 (92) |
740 (140) |
817 (17) |
850 (50) |
905 (105) |
972 (172) |
991 (191) | |
Miscellaneous properties
200's divisors are: 2, 4, 5, 8, 10, 20, 25, 40, 50, 100. It factorizes as 52 × 23.
Scales
- 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