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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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| [[Mapping]]: [{{val| 5 1 7 14 }}, {{val| 0 3 2 0 }}]
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| {{Multival|legend=1| 15 10 0 -19 -42 -28 }}
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| [[POTE generator]]: ~21/20 = 73.044
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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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| Mapping: [{{val| 5 1 7 14 15 }}, {{val| 0 3 2 0 1 }}]
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| POTE generator: ~21/20 = 73.264
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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) 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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| * [[Diamond monotone]] range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
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| * [[Diamond tradeoff]] range: ~3/2 = [693.129, 702.512]
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| * Diamond monotone and tradeoff: ~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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| * Diamond monotone range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
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| * Diamond tradeoff range: ~3/2 = [689.363, 702.512]
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| * Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]
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| Vals: {{Val list| 10, 50 }}
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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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| * Diamond monotone range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
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| * Diamond tradeoff range: ~3/2 = [689.363, 702.512]
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| * Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]
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| Vals: {{Val list| 10, 50 }}
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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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| * Diamond monotone range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
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| * Diamond tradeoff range: ~3/2 = [689.363, 704.955]
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| * Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]
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| Vals: {{Val list| 10, 50 }}
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| Badness: 0.025064
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| == Pentadecal ==
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| 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.
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| Subgroup: 2.3.5
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| [[Comma list]]: 30517578125/29386561536
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| [[Mapping]]: [{{val|15 0 11}}, {{val|0 1 1}}]
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| [[POTE generator]]: ~3/2 = 702.652
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| {{Val list|legend=1| 15, 45, 60, 75, 135, 210c, 345cc }}
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| [[Badness]]: 0.692042
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| === 7-limit ===
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 875/864, 16807/16384
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| [[Mapping]]: [{{val|15 0 11 42}}, {{val|0 1 1 0}}]
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| Mapping generators: ~21/20, ~3
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| [[POTE generator]]: ~3/2 = 700.223
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| {{Val list|legend=1| 15, 45, 60 }}
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| [[Badness]]: 0.114833
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 100/99, 385/384, 1372/1331
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| Mapping: [{{val|15 0 11 42 52}}, {{val|0 1 1 0 0}}]
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| Mapping generators: ~21/20, ~3
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| POTE generator: ~3/2 = 702.733
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| Vals: {{Val list| 15, 45, 60, 75de, 135de }}
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| Badness: 0.077420
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| == Quinkee ==
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 1029/1000, 6144/6125
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| [[Mapping]]: [{{val|5 9 12 14}}, {{val|0 -3 -1 0}}]
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| [[POTE generator]]: ~5/4 = 393.439
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| {{Val list|legend=1| 15, 40, 55, 125cd, 180ccdd }}
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| [[Badness]]: 0.184222
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 121/120, 176/175, 1029/1000
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| Mapping: [{{val|5 9 12 14 18}}, {{val|0 -3 -1 0 -2}}]
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| POTE generator: ~5/4 = 393.438
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| Vals: {{Val list| 15, 40, 55, 125cd, 180ccdde }}
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| Badness: 0.065192
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 66/65, 105/104, 121/120, 637/625
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| Mapping: [{{val|5 9 12 14 18 20}}, {{val|0 -3 -1 0 -2 -4}}]
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| POTE generator: ~5/4 = 392.798
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| Vals: {{Val list| 15, 40, 55 }}
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| Badness: 0.048440
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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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