Subgroup temperaments: Difference between revisions

BudjarnLambeth (talk | contribs)
Fractional subgroup temperaments: Changed subheadings to be less chaotic
BudjarnLambeth (talk | contribs)
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= Integer subgroup temperaments =
= Integer subgroup temperaments =


== 2.3.23 subgroup ==
== 2.3.23 subgroup ==


=== Lipsett ===
=== Lipsett ===
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{{Optimal ET sequence|legend=1| 6, 23def, 29f, 35, 41, 47 }}
{{Optimal ET sequence|legend=1| 6, 23def, 29f, 35, 41, 47 }}
== 2.9.11 subgroup ==
=== Demon ===
Demon is a temperament which equates 3 [[11/9]] with [[16/9]], or equivalently 3 [[18/11]] with [[9/8]], tempering out [[1331/1296]]. This results in [[11/9]] being tuned flat to a supraminor third, and [[27/22]] being tuned sharp to a submajor third. It was discovered by [[User:CompactStar|CompactStar]] while searching for temperaments assosciated with the [[7L 4s]] ("daemotonic") MOS, known for its lack of representation of simple temperaments. The optimal tuning for demon temperament is near the basic tuning of 7L 4s (13\18), and indeed [[18edo]] supports demon temperament.
[[Subgroup]]: 2.9.11
[[Comma list]]: [[1331/1296]]
{{Mapping|legend=2|1 1 2|0 3 2}}
[[Optimal tuning]] ([[CTE]]): ~[[18/11]] = 870.060
{{Optimal ET sequence|legend=1|4, 7, 11, 18, 29, 76e}}


== 2.9.7.11 subgroup ==
== 2.9.7.11 subgroup ==
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[[Badness]]: 0.00263
[[Badness]]: 0.00263
== 2.9.11 subgroup ==
=== Demon ===
Demon is a temperament which equates 3 [[11/9]] with [[16/9]], or equivalently 3 [[18/11]] with [[9/8]], tempering out [[1331/1296]]. This results in [[11/9]] being tuned flat to a supraminor third, and [[27/22]] being tuned sharp to a submajor third. It was discovered by [[User:CompactStar|CompactStar]] while searching for temperaments assosciated with the [[7L 4s]] ("daemotonic") MOS, known for its lack of representation of simple temperaments. The optimal tuning for demon temperament is near the basic tuning of 7L 4s (13\18), and indeed [[18edo]] supports demon temperament.
[[Subgroup]]: 2.9.11
[[Comma list]]: [[1331/1296]]
{{Mapping|legend=2|1 1 2|0 3 2}}
[[Optimal tuning]] ([[CTE]]): ~[[18/11]] = 870.060
{{Optimal ET sequence|legend=1|4, 7, 11, 18, 29, 76e}}


== 2.9.15.7 subgroup ==
== 2.9.15.7 subgroup ==