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Temperaments discussed elsewhere are [[Archytas clan #Blacksmith|blacksmith]], [[Meantone family #Cloudtone|cloudtone]], [[Pental family #Pentacloud|pentacloud]] and [[Qintosec family #Sengasec|sengasec]].
Temperaments discussed elsewhere are [[Archytas clan #Blacksmith|blacksmith]], [[Meantone family #Cloudtone|cloudtone]], [[Pental family #Pentacloud|pentacloud]] and [[Qintosec family #Sengasec|sengasec]].


== Coblack ==
== Coblack ==
{{see also|Trisedodge family #Coblack}}
{{see also|Trisedodge family #Coblack}}


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[[Badness]]: 0.107282
[[Badness]]: 0.107282


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


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Badness: 0.045070
Badness: 0.045070


== Decic ==
== Decic ==
The ''decic'' temperament (10&50, named by [[User:Xenllium|Xenllium]]) tempers out the [[cloudy comma]], 16807/16384 and the [[225/224|marvel comma]], 225/224 in the 7-limit, as well as the [[15/14ths equal temperament|linus comma]], {{monzo|11 -10 -10 10}}. This temperament is supported by [[10edo|10]], [[50edo|50]], and [[60edo|60]] EDOs, and can be extended naturally to the 11-, 13-, and 17-limit by adding 385/384, 105/104, and 170/169 to the comma list in this order.
The ''decic'' temperament (10&50) tempers out the [[cloudy comma]], 16807/16384 and the [[225/224|marvel comma]], 225/224 in the 7-limit, as well as the [[15/14ths equal temperament|linus comma]], {{monzo|11 -10 -10 10}}. This temperament is supported by [[10edo|10]], [[50edo|50]], and [[60edo|60]] EDOs, and can be extended naturally to the 11-, 13-, and 17-limit by adding 385/384, 105/104, and 170/169 to the comma list in this order.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
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[[Tuning ranges]]:
[[Tuning ranges]]:
* [[diamond monotone]] range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* [[Diamond monotone]] range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* [[diamond tradeoff]] range: ~3/2 = [693.129, 702.512]
* [[Diamond tradeoff]] range: ~3/2 = [693.129, 702.512]
* diamond monotone and tradeoff range: ~3/2 = [696.000, 700.000]
* Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]


{{Val list|legend=1| 10, 50, 60, 110d, 170cdd }}
{{Val list|legend=1| 10, 50, 60, 110d, 170cdd }}
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[[Badness]]: 0.089135
[[Badness]]: 0.089135


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


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Tuning ranges:
Tuning ranges:
* [[diamond monotone]] range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* Diamond monotone range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* [[diamond tradeoff]] range: ~3/2 = [689.363, 702.512]
* Diamond tradeoff range: ~3/2 = [689.363, 702.512]
* diamond monotone and tradeoff range: ~3/2 = [696.000, 700.000]
* Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]


Vals: {{Val list| 10, 50, 160bcdd, 210bcddde, 260bbcddde, 310bbcdddde }}
Vals: {{Val list| 10, 50, 160bcdd, 210bcddde, 260bbcddde, 310bbcdddde }}
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Badness: 0.063900
Badness: 0.063900


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


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Tuning ranges:
Tuning ranges:
* [[diamond monotone]] range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* Diamond monotone range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* [[diamond tradeoff]] range: ~3/2 = [689.363, 702.512]
* Diamond tradeoff range: ~3/2 = [689.363, 702.512]
* diamond monotone and tradeoff range: ~3/2 = [696.000, 700.000]
* Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]


Vals: {{Val list| 10, 50, 160bcdd, 210bcddde, 260bbcddde }}
Vals: {{Val list| 10, 50, 160bcdd, 210bcddde, 260bbcddde }}
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Badness: 0.036880
Badness: 0.036880


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


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Tuning ranges:
Tuning ranges:
* [[diamond monotone]] range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* Diamond monotone range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* [[diamond tradeoff]] range: ~3/2 = [689.363, 704.955]
* Diamond tradeoff range: ~3/2 = [689.363, 704.955]
* diamond monotone and tradeoff range: ~3/2 = [696.000, 700.000]
* Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]


Vals: {{Val list| 10, 50, 160bcddg, 210bcdddegg }}
Vals: {{Val list| 10, 50, 160bcddg, 210bcdddegg }}


Badness: 0.025064
Badness: 0.025064
== Pentadecal ==
The ''pentadecal'' temperament tempers out the 15-5/3-comma (quintriyo, pentadecatonic minor thirds comma), {{monzo|-11 -15 15}}. This temperament can be described as 15&60 temperament, tempering out the [[cloudy comma]], 16807/16384 and the [[875/864|keema]], 875/864 in the 7-limit.
Subgroup: 2.3.5
[[Comma list]]: 30517578125/29386561536
[[Mapping]]: [{{val|15 0 11}}, {{val|0 1 1}}]
[[POTE generator]]: ~3/2 = 702.652
{{Val list|legend=1| 15, 45, 60, 75, 135, 210c, 345cc }}
[[Badness]]: 0.692042
=== 7-limit ===
Subgroup: 2.3.5.7
[[Comma list]]: 875/864, 16807/16384
[[Mapping]]: [{{val|15 0 11 42}}, {{val|0 1 1 0}}]
Mapping generators: ~21/20, ~3
[[POTE generator]]: ~3/2 = 700.223
{{Val list|legend=1| 15, 45, 60 }}
[[Badness]]: 0.114833
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 1372/1331
Mapping: [{{val|15 0 11 42 52}}, {{val|0 1 1 0 0}}]
Mapping generators: ~21/20, ~3
POTE generator: ~3/2 = 702.733
Vals: {{Val list| 15, 45, 60, 75de, 135de }}
Badness: 0.077420


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
Retrieved from "https://en.xen.wiki/w/Cloudy_clan"