Cloudy clan: Difference between revisions
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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, 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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[[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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Badness: 0.063900 | Badness: 0.063900 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 97: | Line 97: | ||
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 | ||
Revision as of 18:41, 3 June 2021
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.
Temperaments discussed elsewhere are blacksmith, cloudtone, pentacloud and sengasec.
Coblack
Subgroup: 2.3.5.7
Comma list: 126/125, 16807/16384
Mapping: [⟨5 1 7 14], ⟨0 3 2 0]]
Wedgie: ⟨⟨ 15 10 0 -19 -42 -28 ]]
POTE generator: ~21/20 = 73.044
Badness: 0.107282
11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/242, 385/384
Mapping: [⟨5 1 7 14 15], ⟨0 3 2 0 1]]
POTE generator: ~21/20 = 73.264
Vals: Template:Val list
Badness: 0.045070
Decic
The decic temperament (10&50, named by Xenllium) tempers out the cloudy comma, 16807/16384 and the marvel comma, 225/224 in the 7-limit, as well as the linus comma, [11 -10 -10 10⟩. This temperament is supported by 10, 50, and 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
Comma list: 225/224, 16807/16384
Mapping: [⟨10 0 39 28], ⟨0 1 -1 0]]
Mapping generators: ~15/14, ~3
Wedgie: ⟨⟨ 10 -10 0 -39 -28 28 ]]
POTE generator: ~3/2 = 698.696
- diamond monotone range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
- diamond tradeoff range: ~3/2 = [693.129, 702.512]
- diamond monotone and tradeoff range: ~3/2 = [696.000, 700.000]
Badness: 0.089135
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 3087/3025
Mapping: [⟨10 0 39 28 3], ⟨0 1 -1 0 2]]
Mapping generators: ~15/14, ~3
POTE generator: ~3/2 = 696.791
Tuning ranges:
- diamond monotone range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
- diamond tradeoff range: ~3/2 = [689.363, 702.512]
- diamond monotone and tradeoff range: ~3/2 = [696.000, 700.000]
Vals: Template:Val list
Badness: 0.063900
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 196/195, 2200/2197
Mapping: [⟨10 0 39 28 3 37], ⟨0 1 -1 0 2 0]]
Mapping generators: ~14/13, ~3
POTE generator: ~3/2 = 696.993
Tuning ranges:
- diamond monotone range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
- diamond tradeoff range: ~3/2 = [689.363, 702.512]
- diamond monotone and tradeoff range: ~3/2 = [696.000, 700.000]
Vals: Template:Val list
Badness: 0.036880
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 105/104, 144/143, 170/169, 196/195, 221/220
Mapping: [⟨10 0 39 28 3 37 25], ⟨0 1 -1 0 2 0 1]]
Mapping generators: ~14/13, ~3
POTE generator: ~3/2 = 697.085
Tuning ranges:
- diamond monotone range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
- diamond tradeoff range: ~3/2 = [689.363, 704.955]
- diamond monotone and tradeoff range: ~3/2 = [696.000, 700.000]
Vals: Template:Val list
Badness: 0.025064