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Cloudy clan: Difference between revisions

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{{Technical data page}}
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.


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* [[Blacksmith]] (+28/27 or 49/48) → [[Limmic temperaments #Blacksmith|Limmic temperaments]]
* [[Blacksmith]] (+28/27 or 49/48) → [[Limmic temperaments #Blacksmith|Limmic temperaments]]
* [[Cloudtone]] (+81/80) → [[Meantone family #Cloudtone|Meantone family]]
* [[Cloudtone]] (+81/80) → [[Meantone family #Cloudtone|Meantone family]]
* [[Pental]] (+245/243) → [[Pental family #Pentacloud|Pental family]]
* [[Pental (temperament)|Pental]] (+245/243) → [[Pental family #Pentacloud|Pental family]]
* [[Sengasec]] (+686/675) → [[Quintosec family #Sengasec|Quintosec family]]
* [[Sengasec]] (+686/675) → [[Quintosec family #Sengasec|Quintosec family]]
* [[Warlock]] (+3125/3072) → [[Magic family #Warlock|Magic family]]
* [[Warlock]] (+3125/3072) → [[Magic family #Warlock|Magic family]]
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{{Mapping|legend=1| 5 1 7 14 | 0 3 2 0 }}
{{Mapping|legend=1| 5 1 7 14 | 0 3 2 0 }}
{{Multival|legend=1| 15 10 0 -19 -42 -28 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
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== Decic ==
== Decic ==
{{main| Decic }}
{{Main| Decic }}


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.
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 [[linus comma]], {{monzo| 11 -10 -10 10 }}. This temperament is supported by [[10edo|10-]], [[50edo|50-]], and [[60edo]], 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


[[Comma list]]: 225/224, 16807/16384
[[Comma list]]: 225/224, 16807/16384


[[Mapping]]: [{{val| 10 0 39 28 }}, {{val| 0 1 -1 0 }}]
{{Mapping|legend=1| 10 0 39 28 | 0 1 -1 0 }}


Mapping generators: ~15/14, ~3
: mapping generators: ~15/14, ~3


{{Multival|legend=1| 10 -10 0 -39 -28 28 }}
[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~3/2 = 698.696 (~49/48 = 21.304)
 
[[POTE generator]]: ~3/2 = 698.696


{{Optimal ET sequence|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}
{{Optimal ET sequence|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}
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Comma list: 225/224, 385/384, 3087/3025
Comma list: 225/224, 385/384, 3087/3025


Mapping: [{{val| 10 0 39 28 3 }}, {{val| 0 1 -1 0 2 }}]
Mapping: {{mapping| 10 0 39 28 3 | 0 1 -1 0 2 }}


Mapping generators: ~15/14, ~3
: mapping generators: ~15/14, ~3


POTE generator: ~3/2 = 696.791
Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 696.791 (~56/55 = 23.209)


{{Optimal ET sequence|legend=1| 10, 30be, 40, 50 }}
{{Optimal ET sequence|legend=1| 10, 30be, 40, 50 }}
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Comma list: 105/104, 144/143, 196/195, 2200/2197
Comma list: 105/104, 144/143, 196/195, 2200/2197


Mapping: [{{val| 10 0 39 28 3 37 }}, {{val| 0 1 -1 0 2 0 }}]
Mapping: {{mapping| 10 0 39 28 3 37 | 0 1 -1 0 2 0 }}


Mapping generators: ~14/13, ~3
: mapping generators: ~14/13, ~3


POTE generator: ~3/2 = 696.993
Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 696.993 (~78/77 = 23.007)


{{Optimal ET sequence|legend=1| 10, 30be, 40, 50 }}
{{Optimal ET sequence|legend=1| 10, 30be, 40, 50 }}
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Comma list: 105/104, 144/143, 170/169, 196/195, 221/220
Comma list: 105/104, 144/143, 170/169, 196/195, 221/220


Mapping: [{{val| 10 0 39 28 3 37 25 }}, {{val| 0 1 -1 0 2 0 1 }}]
Mapping: {{mapping| 10 0 39 28 3 37 25 | 0 1 -1 0 2 0 1 }}


Mapping generators: ~14/13, ~3
: mapping generators: ~14/13, ~3


POTE generator: ~3/2 = 697.085
Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 697.085 (~78/77 = 22.915)


{{Optimal ET sequence|legend=1| 10, 30beg, 40, 50 }}
{{Optimal ET sequence|legend=1| 10, 30beg, 40, 50 }}
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=== Splendecic ===
=== Splendecic ===
''Splendecic'' (10e&50) is an alternative extension of decic, tempering out 1617/1600, 2401/2376 and 4375/4356 in the 11-limit. As a subset of the [[Marvel family #Fantastic|fantastic rank-three temperament]], its name is a portmanteau of "[[wiktionary:splendid|splendid]]" (synonym of "[[wiktionary:fantastic|fantastic]]") and "decic".
''Splendecic'' (10e & 50) is an alternative extension of decic, tempering out 1617/1600, 2401/2376 and 4375/4356 in the 11-limit. As a temperament of the [[Marvel family #Fantastic|fantastic rank-3 temperament]], its name is a portmanteau of "[[wiktionary:splendid|splendid]]" (synonym of "[[wiktionary:fantastic|fantastic]]") and "decic".


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
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Comma list: 225/224, 1617/1600, 2401/2376
Comma list: 225/224, 1617/1600, 2401/2376


Mapping: [{{val| 10 0 39 28 82 }}, {{val| 0 1 -1 0 -3 }}]
Mapping: {{mapping| 10 0 39 28 82 | 0 1 -1 0 -3 }}


POTE generator: ~3/2 = 698.518
Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 698.518 (~99/98 = 21.482)


{{Optimal ET sequence|legend=1| 10e, 30bee, 40e, 50, 60e, 110de }}
{{Optimal ET sequence|legend=1| 10e, 30bee, 40e, 50, 60e, 110de }}
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Comma list: 105/104, 196/195, 1001/1000, 1188/1183
Comma list: 105/104, 196/195, 1001/1000, 1188/1183


Mapping: [{{val| 10 0 39 28 82 37 }}, {{val| 0 1 -1 0 -3 0 }}]
Mapping: {{mapping| 10 0 39 28 82 37 | 0 1 -1 0 -3 0 }}


POTE generator: ~3/2 = 698.365
Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 698.365 (~91/90 = 21.635)


{{Optimal ET sequence|legend=1| 10e, 30bee, 40e, 50, 60e, 110de }}
{{Optimal ET sequence|legend=1| 10e, 30bee, 40e, 50, 60e, 110de }}
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Comma list: 105/104, 170/169, 196/195, 289/288, 375/374
Comma list: 105/104, 170/169, 196/195, 289/288, 375/374


Mapping: [{{val| 10 0 39 28 82 37 25 }}, {{val| 0 1 -1 0 -3 0 1 }}]
Mapping: {{mapping| 10 0 39 28 82 37 25 | 0 1 -1 0 -3 0 1 }}


POTE generator: ~3/2 = 698.375
Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 698.375 (~91/90 = 21.625)


{{Optimal ET sequence|legend=1| 10e, 30beeg, 40e, 50, 60e, 110deg }}
{{Optimal ET sequence|legend=1| 10e, 30beeg, 40e, 50, 60e, 110deg }}
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=== Prodecic ===
=== Prodecic ===
''Prodecic'' (10&50e) is an alternative extension of decic, tempering out 441/440, 1375/1372 and 4375/4356 in the 11-limit. As a subset of the [[Marvel family #Prodigy|prodigy rank-three temperament]], its name is a portmanteau of "[[wiktionary:prodigy|prodigy]]" and "decic".
''Prodecic'' (10 & 50e) is an alternative extension of decic, tempering out 441/440, 1375/1372 and 4375/4356 in the 11-limit. As a temperament of the [[Marvel family #Prodigy|prodigy rank-3 temperament]], its name is a portmanteau of "[[wiktionary:prodigy|prodigy]]" and "decic".


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
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Comma list: 225/224, 441/440, 5929/5832
Comma list: 225/224, 441/440, 5929/5832


Mapping: [{{val| 10 0 39 28 -13 }}, {{val| 0 1 -1 0 3 }}]
Mapping: {{mapping| 10 0 39 28 -13 | 0 1 -1 0 3 }}


POTE generator: ~3/2 = 700.210
Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 700.210 (~55/54 = 19.790)


{{Optimal ET sequence|legend=1| 10, 40ee, 50e, 60e }}
{{Optimal ET sequence|legend=1| 10, 40ee, 50e, 60e }}
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Comma list: 105/104, 196/195, 275/273, 5929/5832
Comma list: 105/104, 196/195, 275/273, 5929/5832


Mapping: [{{val| 10 0 39 28 -13 37 }}, {{val| 0 1 -1 0 3 0 }}]
Mapping: {{mapping| 10 0 39 28 -13 37 | 0 1 -1 0 3 0 }}


POTE generator: ~3/2 = 700.503
Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 700.503 (~91/90 = 19.497)


{{Optimal ET sequence|legend=1| 10, 40ee, 50e, 60e }}
{{Optimal ET sequence|legend=1| 10, 40ee, 50e, 60e }}
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Comma list: 105/104, 154/153, 170/169, 196/195, 289/288
Comma list: 105/104, 154/153, 170/169, 196/195, 289/288


Mapping: [{{val| 10 0 39 28 -13 37 25 }}, {{val| 0 1 -1 0 3 0 1 }}]
Mapping: {{mapping| 10 0 39 28 -13 37 25 | 0 1 -1 0 3 0 1 }}


POTE generator: ~3/2 = 700.474
Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 700.474 (~91/90 = 19.526)


{{Optimal ET sequence|legend=1| 10, 40ee, 50e, 60e }}
{{Optimal ET sequence|legend=1| 10, 40ee, 50e, 60e }}
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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.
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: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 875/864, 16807/16384
[[Comma list]]: 875/864, 16807/16384


[[Mapping]]: [{{val|15 0 11 42}}, {{val|0 1 1 0}}]
{{Mapping|legend=1| 15 0 11 42 | 0 1 1 0 }}


Mapping generators: ~21/20, ~3
: mapping generators: ~21/20, ~3


[[POTE generator]]: ~3/2 = 700.223
[[Optimal tuning]] ([[POTE]]): ~21/20 = 1\15, ~3/2 = 700.223 (~126/125 = 19.777)


{{Optimal ET sequence|legend=1| 15, 45, 60 }}
{{Optimal ET sequence|legend=1| 15, 45, 60 }}
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Comma list: 100/99, 385/384, 1372/1331
Comma list: 100/99, 385/384, 1372/1331


Mapping: [{{val|15 0 11 42 52}}, {{val|0 1 1 0 0}}]
Mapping: {{mapping| 15 0 11 42 52 | 0 1 1 0 0 }}


Mapping generators: ~21/20, ~3
: mapping generators: ~21/20, ~3


POTE generator: ~3/2 = 702.733
Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 702.733 (~56/55 = 17.267)


{{Optimal ET sequence|legend=1| 15, 45, 60, 75de, 135de }}
{{Optimal ET sequence|legend=1| 15, 45, 60, 75de, 135de }}
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Comma list: 100/99, 105/104, 144/143, 1372/1331
Comma list: 100/99, 105/104, 144/143, 1372/1331


Mapping: [{{val|15 0 11 42 52 8}}, {{val|0 1 1 0 0 2}}]
Mapping: {{mapping| 15 0 11 42 52 8 | 0 1 1 0 0 2 }}


Mapping generators: ~21/20, ~3
: mapping generators: ~21/20, ~3


POTE generator: ~3/2 = 701.715
Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 701.715 (~91/90 = 18.285)


{{Optimal ET sequence|legend=1| 15, 45f, 60, 135de, 195cddee }}
{{Optimal ET sequence|legend=1| 15, 45f, 60, 135de, 195cddee }}
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Comma list: 121/120, 441/440, 875/864
Comma list: 121/120, 441/440, 875/864


Mapping: [{{val|15 0 11 42 28}}, {{val|0 1 1 0 1}}]
Mapping: {{mapping| 15 0 11 42 28 | 0 1 1 0 1 }}


Mapping generators: ~21/20, ~3
: mapping generators: ~21/20, ~3


POTE generator: ~3/2 = 700.318
Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 700.318 (~126/125 = 19.682)


{{Optimal ET sequence|legend=1| 15, 45e, 60e }}
{{Optimal ET sequence|legend=1| 15, 45e, 60e }}
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Comma list: 121/120, 196/195, 352/351, 875/864
Comma list: 121/120, 196/195, 352/351, 875/864


Mapping: [{{val|15 0 11 42 28 103}}, {{val|0 1 1 0 1 -2}}]
Mapping: {{mapping| 15 0 11 42 28 103 | 0 1 1 0 1 -2 }}


Mapping generators: ~21/20, ~3
: mapping generators: ~21/20, ~3


POTE generator: ~3/2 = 701.647
Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 701.647 (~65/64 = 18.353)


{{Optimal ET sequence|legend=1| 15f, 45e, 60e }}
{{Optimal ET sequence|legend=1| 15f, 45e, 60e }}
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== Quinkee ==
== Quinkee ==
The ''quinkee'' temperament (15&40) has a period of 1/5 octave and tempers out the keega (1029/1000), and from this it derives its name.
The ''quinkee'' temperament (15 & 40) has a period of 1/5 octave and tempers out the keega (1029/1000), and from this it derives its name.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1029/1000, 6144/6125
[[Comma list]]: 1029/1000, 6144/6125


[[Mapping]]: [{{val|5 9 12 14}}, {{val|0 -3 -1 0}}]
{{Mapping|legend=1| 5 9 12 14 | 0 -3 -1 0 }}


[[POTE generator]]: ~5/4 = 393.439
[[Optimal tuning]] ([[POTE]]): ~8/7 = 1\5, ~5/4 = 393.439 (~25/24 = 86.561)


{{Optimal ET sequence|legend=1| 15, 40, 55, 125cd, 180ccdd }}
{{Optimal ET sequence|legend=1| 15, 40, 55, 125cd, 180ccdd }}
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Comma list: 121/120, 176/175, 1029/1000
Comma list: 121/120, 176/175, 1029/1000


Mapping: [{{val|5 9 12 14 18}}, {{val|0 -3 -1 0 -2}}]
Mapping: {{mapping| 5 9 12 14 18 | 0 -3 -1 0 -2 }}


POTE generator: ~5/4 = 393.438
Optimal tuning (POTE): ~8/7 = 1\5, ~5/4 = 393.438 (~22/21 = 86.562)


{{Optimal ET sequence|legend=1| 15, 40, 55, 125cd, 180ccdde }}
{{Optimal ET sequence|legend=1| 15, 40, 55, 125cd, 180ccdde }}
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Comma list: 66/65, 105/104, 121/120, 637/625
Comma list: 66/65, 105/104, 121/120, 637/625


Mapping: [{{val|5 9 12 14 18 20}}, {{val|0 -3 -1 0 -2 -4}}]
Mapping: {{mapping| 5 9 12 14 18 20 | 0 -3 -1 0 -2 -4 }}


POTE generator: ~5/4 = 392.798
Optimal tuning (POTE): ~8/7 = 1\5, ~5/4 = 392.798 (~22/21 = 87.202)


{{Optimal ET sequence|legend=1| 15, 40, 55 }}
{{Optimal ET sequence|legend=1| 15, 40, 55 }}
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[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Pages with mostly numerical content]]
[[Category:Cloudy clan| ]] <!-- main article -->
[[Category:Cloudy clan| ]] <!-- main article -->
[[Category:Cloudy| ]] <!-- key article -->
[[Category:Cloudy| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Cloudy_clan"