No-twos subgroup temperaments: Difference between revisions
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== Mebsuta == | == Mebsuta == | ||
Mebsuta is a microtemperament in the 3.7.11 subgroup that sets the relative sizes of [[9/7]] and [[11/9]] to be in the ratio of 5:4; its generator is identifiable as the ratio between these intervals, 81/77. It produces a 21L 1s [[MOS scale]] against the tritave, which serves as a well-temperament of [[22edt]]; that scale's chroma is identified with [[1331/1323]]. | |||
[[Subgroup]]: 3.7.11 | [[Subgroup]]: 3.7.11 | ||
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=== 3.7.11.19 subgroup === | === 3.7.11.19 subgroup === | ||
Mebsuta naturally extends itself with prime 19, identifying the two-generator interval as [[21/19]], since its square differs from [[11/9]] (the four-generator interval) by the small comma [[3971/3969]]. | |||
[[Subgroup]]: 3.7.11.19 | [[Subgroup]]: 3.7.11.19 | ||
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[[Support]]ing [[ET]]s: {{EDs|b22, b175, b197, b153, b131, b219, b372, b109, b328, b241, b87, b21, b65, b43|equave=t}} | [[Support]]ing [[ET]]s: {{EDs|b22, b175, b197, b153, b131, b219, b372, b109, b328, b241, b87, b21, b65, b43|equave=t}} | ||
=== 3.5.7.11.19 subgroup === | |||
Tempering out [[12005/11979]], the unisquary comma, sets the chroma 1331/1323 equal to [[245/243]], producing an accurate if complex mapping for prime 5 at 32 generators up. | |||
[[Subgroup]]: 3.5.7.11.19 | |||
[[Comma list]]: 3971/3969, 12005/11979, 41553/41503 | |||
[[Sval]] [[mapping]]: [{{val| 1 0 2 2 3}}, {{val| 0 32 -5 4 -7}}] | |||
Sval mapping generators: ~3, ~81/77 | |||
[[Optimal tuning]]s: | |||
* PEWE (Pure-Equaves WE): ~3 = 1\1ed3, ~[[81/77]] = 87.065 | |||
* [[CWE]]: ~3 = 1\1ed3, ~[[81/77]] = 87.066 | |||
[[Support]]ing [[ET]]s: {{EDs|b131, b22, b153, b284, b415, b109, b437, b175, b546, b87c, b699, b240, b590, b721|equave=t}} | |||
= Other tritave-based subgroups = | = Other tritave-based subgroups = | ||