Cloudy clan: Difference between revisions
Cmloegcmluin (talk | contribs) correct per Milne's comments |
Cmloegcmluin (talk | contribs) update w/r/t final conclusions of discussion with Milne and others |
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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. | 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 [[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 = | ||
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[[POTE generator]]: ~3/2 = 698.696 | [[POTE generator]]: ~3/2 = 698.696 | ||
[[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 | * [[diamond tradeoff]] range: ~3/2 = [693.129, 702.512] | ||
* | * diamond monotone and tradeoff range: ~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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POTE generator: ~3/2 = 696.791 | POTE generator: ~3/2 = 696.791 | ||
Tuning ranges: | Tuning ranges: | ||
* [[diamond | * [[diamond monotone]] range: ~3/2 = [696.000, 700.000] (29\50 to 35\60) | ||
* [[diamond | * [[diamond tradeoff]] range: ~3/2 = [689.363, 702.512] | ||
* | * diamond monotone and tradeoff range: ~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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POTE generator: ~3/2 = 696.993 | POTE generator: ~3/2 = 696.993 | ||
Tuning ranges: | Tuning ranges: | ||
* [[diamond | * [[diamond monotone]] range: ~3/2 = [696.000, 700.000] (29\50 to 35\60) | ||
* [[diamond | * [[diamond tradeoff]] range: ~3/2 = [689.363, 702.512] | ||
* | * diamond monotone and tradeoff range: ~3/2 = [696.000, 700.000] | ||
Vals: {{Val list| 10, 50, 160bcdd, 210bcddde, 260bbcddde }} | Vals: {{Val list| 10, 50, 160bcdd, 210bcddde, 260bbcddde }} | ||
| Line 108: | Line 108: | ||
POTE generator: ~3/2 = 697.085 | POTE generator: ~3/2 = 697.085 | ||
Tuning ranges: | Tuning ranges: | ||
* [[diamond | * [[diamond monotone]] range: ~3/2 = [696.000, 700.000] (29\50 to 35\60) | ||
* [[diamond | * [[diamond tradeoff]] range: ~3/2 = [689.363, 704.955] | ||
* | * diamond monotone and tradeoff range: ~3/2 = [696.000, 700.000] | ||
Vals: {{Val list| 10, 50, 160bcddg, 210bcdddegg }} | Vals: {{Val list| 10, 50, 160bcddg, 210bcdddegg }} | ||
Revision as of 17:59, 31 May 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