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}}


Line 20: Line 20:
[[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]]

Revision as of 11:45, 5 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

See also: Trisedodge family § 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

Template:Val list

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) 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

Tuning ranges:

  • 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: ~3/2 = [696.000, 700.000]

Template:Val list

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: ~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: ~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: ~3/2 = [696.000, 700.000]

Vals: Template:Val list

Badness: 0.025064

Pentadecal

The pentadecal temperament tempers out the 15-5/3-comma (quintriyo, pentadecatonic minor thirds comma), [-11 -15 15⟩. This temperament can be described as 15&60 temperament, tempering out the cloudy comma, 16807/16384 and the keema, 875/864 in the 7-limit.

Subgroup: 2.3.5

Comma list: 30517578125/29386561536

Mapping: [⟨15 0 11], ⟨0 1 1]]

POTE generator: ~3/2 = 702.652

Template:Val list

Badness: 0.692042

7-limit

Subgroup: 2.3.5.7

Comma list: 875/864, 16807/16384

Mapping: [⟨15 0 11 42], ⟨0 1 1 0]]

Mapping generators: ~21/20, ~3

POTE generator: ~3/2 = 700.223

Template:Val list

Badness: 0.114833

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 385/384, 1372/1331

Mapping: [⟨15 0 11 42 52], ⟨0 1 1 0 0]]

Mapping generators: ~21/20, ~3

POTE generator: ~3/2 = 702.733

Vals: Template:Val list

Badness: 0.077420

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