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Semicomma family: Difference between revisions

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[[Tuning ranges]]:
[[Tuning ranges]]:
* [[Diamond monotone]] range: [257.143, 276.923] (3\14 to 3\13)
* 5-odd-limit [[diamond monotone]]: ~75/64 = [257.143, 276.923] (3\14 to 3\13)
* [[Diamond tradeoff]] range: [271.229, 271.708]
* 5-odd-limit [[diamond tradeoff]]: ~75/64 = [271.229, 271.708]
* Diamond monotone and tradeoff: [271.229, 271.708]
* 5-odd-limit diamond monotone and tradeoff: ~75/64 = [271.229, 271.708]


{{Val list|legend=1| 22, 31, 53, 190, 243, 296, 645c }}
{{Val list|legend=1| 22, 31, 53, 190, 243, 296, 645c }}
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[[Tuning ranges]]:
[[Tuning ranges]]:
* [[Diamond monotone]] range: [266.667, 272.727] (2\9 to 5\22)
* 7-odd-limit [[diamond monotone]]: ~7/6 = [266.667, 272.727] (2\9 to 5\22)
* [[Diamond tradeoff]] range: [266.871, 271.708]
* 9-odd-limit diamond monotone: ~7/6 = [270.968, 272.727] (7\31 to 5\22)
* Diamond monotone and tradeoff: [266.871, 271.708]
* 7-odd-limit [[diamond tradeoff]]: ~7/6 = [266.871, 271.708]
* 9-odd-limit diamond tradeoff: ~7/6 = [266.871, 272.514]
* 7-odd-limit diamond monotone and tradeoff: ~7/6 = [266.871, 271.708]
* 9-odd-limit diamond monotone and tradeoff: ~7/6 = [270.968, 272.514]


[[Algebraic generator]]: Sabra3, the real root of 12''x<sup>3</sup> - 7''x'' - 48.
[[Algebraic generator]]: Sabra3, the real root of 12''x<sup>3</sup> - 7''x'' - 48.
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Tuning ranges:
Tuning ranges:
* Diamond monotone range: [270.968, 272.727] (7\31 to 5\22)
* 11-odd-limit diamond monotone: ~7/6 = [270.968, 272.727] (7\31 to 5\22)
* Diamond tradeoff range: [266.871, 275.659]
* 11-odd-limit diamond tradeoff: ~7/6 = [266.871, 275.659]
* Diamond monotone and tradeoff: [270.968, 272.727]
* 11-odd-limit diamond monotone and tradeoff: ~7/6 = [270.968, 272.727]


Vals: {{Val list| 9, 22, 31, 53, 84e }}
Vals: {{Val list| 9, 22, 31, 53, 84e }}
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Tuning ranges:
Tuning ranges:
* Diamond monotone range: [270.968, 271.698] (7\31 to 12\53)
* 13- and 15-odd-limit diamond monotone: ~7/6 = [270.968, 271.698] (7\31 to 12\53)
* Diamond tradeoff range: [266.871, 275.659]
* 13- and 15-odd-limit diamond tradeoff: ~7/6 = [266.871, 275.659]
* Diamond monotone and tradeoff: [270.968, 271.698]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~7/6 = [270.968, 271.698]


Vals: {{Val list| 22, 31, 53, 84e, 137e }}
Vals: {{Val list| 22, 31, 53, 84e, 137e }}
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Tuning ranges:
Tuning ranges:
* Diamond monotone range: [270.968, 272.727] (7\31 to 5\22)
* 13- and 15-odd-limit diamond monotone: ~7/6 = [270.968, 272.727] (7\31 to 5\22)
* Diamond tradeoff range: [266.871, 281.691]
* 13- and 15-odd-limit diamond tradeoff: ~7/6 = [266.871, 281.691]
* Diamond monotone and tradeoff: [270.968, 272.727]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~7/6 = [270.968, 272.727]


Vals: {{Val list| 22f, 31 }}
Vals: {{Val list| 22f, 31 }}
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Tuning ranges:
Tuning ranges:
* Diamond monotone range: [135.484, 136.364] (7\62 to 5\44)
* 13- and 15-odd-limit diamond monotone: ~13/12 = [135.484, 136.364] (7\62 to 5\44)
* Diamond tradeoff range: [128.298, 138.573]
* 13- and 15-odd-limit diamond tradeoff: ~13/12 = [128.298, 138.573]
* Diamond monotone and tradeoff: [135.484, 136.364]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~13/12 = [135.484, 136.364]


Vals: {{Val list| 9, 35bd, 44, 53, 62, 115ef, 168eef }}
Vals: {{Val list| 9, 35bd, 44, 53, 62, 115ef, 168eef }}
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Tuning ranges:
Tuning ranges:
* Diamond monotone range: [270.968, 271.698] (7\31 to 12\53)
* 11-odd-limit diamond monotone: ~7/6 = [270.968, 271.698] (7\31 to 12\53)
* Diamond tradeoff range: [266.871, 272.514]
* 11-odd-limit diamond tradeoff: ~7/6 = [266.871, 272.514]
* Diamond monotone and tradeoff: [270.968, 271.698]
* 11-odd-limit diamond monotone and tradeoff: ~7/6 = [270.968, 271.698]


Vals: {{Val list| 31, 84, 115, 376b, 491bd, 606bde }}
Vals: {{Val list| 31, 84, 115, 376b, 491bd, 606bde }}
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{{Val list|legend=1| 31, 172, 203, 234, 265, 296 }}
{{Val list|legend=1| 31, 172, 203, 234, 265, 296 }}


Badness: 0.143488
[[Badness]]: 0.143488


=== 11-limit ===
=== 11-limit ===
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Badness: 0.052774
Badness: 0.052774
== Quinwell ==
The ''quinwell'' temperament (22&amp;265) slices orwell minor third into five generators and tempers out the wizma, 421075/419904.
Subgroup: 2.3.5.7
[[Comma list]]: 421075/419904, 2109375/2097152
[[Mapping]]: [{{val| 1 0 3 0 }}, {{val| 0 35 -15 62 }}]
{{Multival|legend=1| 35 -15 62 -105 0 186 }}
[[POTE generator]]: ~405/392 = 54.324
{{Val list|legend=1| 22, 221, 243, 751c, 994cd, 1237bccd, 1480bccd }}
[[Badness]]: 0.168897


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
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