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| The '''cloudy clan''' tempers out the [[cloudy comma]], 16807/16384, thus splitting the octave into 5 equal parts and mapping the harmonic 7 to 4\5.
| | #redirect [[Cloudy comma]] |
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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]].
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| = Coblack =
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| {{see also|Trisedodge family #Coblack}}
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 126/125, 16807/16384
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| [[POTE generator]]: ~21/20 = 73.044
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| [[Mapping]]: [{{val| 5 1 7 14 }}, {{val| 0 3 2 0 }}]
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| {{Val list|legend=1| 15, 35, 50, 65, 115d }}
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| [[Badness]]: 0.107282
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| == 11-limit ==
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| Subgroup: 2.3.5.7.11
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| Comma list: 126/125, 245/242, 385/384
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| POTE generator: ~21/20 = 73.264
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| Mapping: [{{val| 5 1 7 14 15 }}, {{val| 0 3 2 0 1 }}]
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| Vals: {{Val list| 15, 35, 50, 65, 115d }}
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| Badness: 0.045070
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| = Decic =
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| 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.
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 225/224, 16807/16384
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| [[Mapping]]: [{{val| 10 0 39 28 }}, {{val| 0 1 -1 0 }}]
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| Mapping generators: ~15/14, ~3
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| {{Multival|legend=1| 10 -10 0 -39 -28 28 }}
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| [[POTE generator]]: ~3/2 = 698.696
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| [[Tuning ranges]]:
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| * valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
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| * nice range: ~3/2 = [693.129, 702.512]
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| * strict range: ~3/2 = [696.000, 700.000]
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| {{Val list|legend=1| 10, 50, 60, 110d, 170cdd }}
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| [[Badness]]: 0.089135
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| == 11-limit ==
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| Subgroup: 2.3.5.7.11
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| Comma list: 225/224, 385/384, 3087/3025
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| Mapping: [{{val| 10 0 39 28 3 }}, {{val| 0 1 -1 0 2 }}]
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| Mapping generators: ~15/14, ~3
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| POTE generator: ~3/2 = 696.791
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| Tuning ranges:
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| * valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
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| * nice range: ~3/2 = [689.363, 702.512]
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| * strict range: ~3/2 = [696.000, 700.000]
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| Vals: {{Val list| 10, 50, 160bcdd, 210bcddde, 260bbcddde, 310bbcdddde }}
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| Badness: 0.063900
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| == 13-limit ==
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 105/104, 144/143, 196/195, 2200/2197
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| Mapping: [{{val| 10 0 39 28 3 37 }}, {{val| 0 1 -1 0 2 0 }}]
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| Mapping generators: ~14/13, ~3
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| POTE generator: ~3/2 = 696.993
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| Tuning ranges:
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| * valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
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| * nice range: ~3/2 = [689.363, 702.512]
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| * strict range: ~3/2 = [696.000, 700.000]
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| Vals: {{Val list| 10, 50, 160bcdd, 210bcddde, 260bbcddde }}
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| Badness: 0.036880
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| == 17-limit ==
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 105/104, 144/143, 170/169, 196/195, 221/220
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| Mapping: [{{val| 10 0 39 28 3 37 25 }}, {{val| 0 1 -1 0 2 0 1 }}]
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| Mapping generators: ~14/13, ~3
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| POTE generator: ~3/2 = 697.085
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| Tuning ranges:
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| * valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
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| * nice range: ~3/2 = [689.363, 704.955]
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| * strict range: ~3/2 = [696.000, 700.000]
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| Vals: {{Val list| 10, 50, 160bcddg, 210bcdddegg }}
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| Badness: 0.025064
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| [[Category:Regular temperament theory]]
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| [[Category:Temperament clan]]
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| [[Category:Cloudy]]
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| [[Category:Rank 2]]
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