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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.


Temperaments discussed elsewhere are:  
Temperaments discussed elsewhere are:  
* [[Blacksmith]], {28/27, 49/48} → [[Limmic temperaments #Blacksmith|Limmic temperaments]]
* [[Blacksmith]] (+28/27 or 49/48) → [[Limmic temperaments #Blacksmith|Limmic temperaments]]
* [[Cloudtone]], {81/80, 16807/16384} → [[Meantone family #Cloudtone|Meantone family]]
* [[Cloudtone]] (+81/80) → [[Meantone family #Cloudtone|Meantone family]]
* [[Pental]], {245/243, 16807/16384} → [[Pental family #Pentacloud|Pental family]]
* [[Pental (temperament)|Pental]] (+245/243) → [[Pental family #Pentacloud|Pental family]]
* [[Sengasec]], {686/675, 16807/16384} → [[Qintosec family #Sengasec|Qintosec family]]
* [[Sengasec]] (+686/675) → [[Quintosec family #Sengasec|Quintosec family]]
* [[Warlock]], {3125/3072, 16807/16384} → [[Magic family #Warlock|Magic family]]
* [[Warlock]] (+3125/3072) → [[Magic family #Warlock|Magic family]]


== Coblack ==
== Coblack ==
{{See also| Trisedodge family #Coblack }}
{{See also| Trisedodge family #Coblack }}


Subgroup: 2.3.5.7
In addition to the [[cloudy comma]], the coblack temperament tempers out the [[126/125|starling comma (126/125)]]. Coblack was named by [[Petr Pařízek]] in 2011, who considered it a counterpart of [[blacksmith]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>.
 
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 126/125, 16807/16384
[[Comma list]]: 126/125, 16807/16384


[[Mapping]]: [{{val| 5 7 11 14 }}, {{val| 0 3 2 0 }}]
{{Mapping|legend=1| 5 1 7 14 | 0 3 2 0 }}
 
{{Multival|legend=1| 15 10 0 -19 -42 -28 }}


[[POTE generator]]: ~21/20 = 73.044
[[Optimal tuning]]s:
* [[CTE]]: ~8/7 = 1\5, ~48/35 = 553.8429 (~21/20 = 73.8429)
* [[POTE]]: ~8/7 = 1\5, ~48/35 = 553.044 (~21/20 = 73.044)


{{Val list|legend=1| 15, 35, 50, 65, 115d }}
{{Optimal ET sequence|legend=1| 15, 35, 50, 65, 115d }}


[[Badness]]: 0.107282
[[Badness]]: 0.107282
Line 30: Line 33:
Comma list: 126/125, 245/242, 385/384
Comma list: 126/125, 245/242, 385/384


Mapping: [{{val| 5 7 11 14 17 }}, {{val| 0 3 2 0 1 }}]
Mapping: {{mapping| 5 1 7 14 15 | 0 3 2 0 1 }}


POTE generator: ~21/20 = 73.264
Optimal tunings:
* CTE: ~8/7 = 1\5, ~11/8 = 553.7951 (~21/20 = 73.7951)
* POTE: ~8/7 = 1\5, ~11/8 = 553.264 (~21/20 = 73.264)


Optimal GPV sequence: {{Val list| 15, 35, 50, 65, 115d }}
Optimal ET sequence: {{Optimal ET sequence| 15, 35, 50, 65, 115d }}


Badness: 0.045070
Badness: 0.045070


== Decic ==
== Decic ==
{{main| Decic }}
{{Main| Decic }}


The ''decic'' temperament (10&amp;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 &amp; 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


{{Multival|legend=1| 10 -10 0 -39 -28 28 }}
: mapping generators: ~15/14, ~3


[[POTE generator]]: ~3/2 = 698.696
[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~3/2 = 698.696 (~49/48 = 21.304)


{{Val list|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}
{{Optimal ET sequence|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}


[[Badness]]: 0.089135
[[Badness]]: 0.089135
Line 64: Line 67:
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 GPV sequence: {{Val list| 10, 30be, 40, 50 }}
{{Optimal ET sequence|legend=1| 10, 30be, 40, 50 }}


Badness: 0.063900
Badness: 0.063900
Line 79: Line 82:
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 GPV sequence: {{Val list| 10, 30be, 40, 50 }}
{{Optimal ET sequence|legend=1| 10, 30be, 40, 50 }}


Badness: 0.036880
Badness: 0.036880
Line 94: Line 97:
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 GPV sequence: {{Val list| 10, 30beg, 40, 50 }}
{{Optimal ET sequence|legend=1| 10, 30beg, 40, 50 }}


Badness: 0.025064
Badness: 0.025064


=== Splendecic ===
=== Splendecic ===
''Splendecic'' (10e&amp;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 &amp; 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
Line 111: Line 114:
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 GPV sequence: {{Val list| 10e, 30bee, 40e, 50, 60e, 110de }}
{{Optimal ET sequence|legend=1| 10e, 30bee, 40e, 50, 60e, 110de }}


Badness: 0.059802
Badness: 0.059802
Line 124: Line 127:
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 GPV sequence: {{Val list| 10e, 30bee, 40e, 50, 60e, 110de }}
{{Optimal ET sequence|legend=1| 10e, 30bee, 40e, 50, 60e, 110de }}


Badness: 0.037989
Badness: 0.037989
Line 137: Line 140:
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 GPV sequence: {{Val list| 10e, 30beeg, 40e, 50, 60e, 110deg }}
{{Optimal ET sequence|legend=1| 10e, 30beeg, 40e, 50, 60e, 110deg }}


Badness: 0.026050
Badness: 0.026050


=== Prodecic ===
=== Prodecic ===
''Prodecic'' (10&amp;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 &amp; 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
Line 152: Line 155:
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 GPV sequence: {{Val list| 10, 40ee, 50e, 60e }}
{{Optimal ET sequence|legend=1| 10, 40ee, 50e, 60e }}


Badness: 0.066600
Badness: 0.066600
Line 165: Line 168:
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 GPV sequence: {{Val list| 10, 40ee, 50e, 60e }}
{{Optimal ET sequence|legend=1| 10, 40ee, 50e, 60e }}


Badness: 0.041788
Badness: 0.041788
Line 178: Line 181:
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 GPV sequence: {{Val list| 10, 40ee, 50e, 60e }}
{{Optimal ET sequence|legend=1| 10, 40ee, 50e, 60e }}


Badness: 0.027590
Badness: 0.027590
Line 191: Line 194:
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&amp;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&amp;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)


{{Val list|legend=1| 15, 45, 60 }}
{{Optimal ET sequence|legend=1| 15, 45, 60 }}


[[Badness]]: 0.114833
[[Badness]]: 0.114833
Line 210: Line 213:
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 GPV sequence: {{Val list| 15, 45, 60, 75de, 135de }}
{{Optimal ET sequence|legend=1| 15, 45, 60, 75de, 135de }}


Badness: 0.077420
Badness: 0.077420
Line 225: Line 228:
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 GPV sequence: {{Val list| 15, 45f, 60, 135de, 195cddee }}
{{Optimal ET sequence|legend=1| 15, 45f, 60, 135de, 195cddee }}


Badness: 0.051740
Badness: 0.051740
Line 240: Line 243:
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 GPV sequence: {{Val list| 15, 45e, 60e }}
{{Optimal ET sequence|legend=1| 15, 45e, 60e }}


Badness: 0.044405
Badness: 0.044405
Line 255: Line 258:
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 GPV sequence: {{Val list| 15f, 45e, 60e }}
{{Optimal ET sequence|legend=1| 15f, 45e, 60e }}


Badness: 0.055361
Badness: 0.055361


== Quinkee ==
== Quinkee ==
The ''quinkee'' temperament (15&amp;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 &amp; 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)


{{Val list|legend=1| 15, 40, 55, 125cd, 180ccdd }}
{{Optimal ET sequence|legend=1| 15, 40, 55, 125cd, 180ccdd }}


[[Badness]]: 0.184222
[[Badness]]: 0.184222
Line 285: Line 288:
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 GPV sequence: {{Val list| 15, 40, 55, 125cd, 180ccdde }}
{{Optimal ET sequence|legend=1| 15, 40, 55, 125cd, 180ccdde }}


Badness: 0.065192
Badness: 0.065192
Line 298: Line 301:
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 GPV sequence: {{Val list| 15, 40, 55 }}
{{Optimal ET sequence|legend=1| 15, 40, 55 }}


Badness: 0.048440
Badness: 0.048440


[[Category:Regular temperament theory]]
== Notes ==
[[Category:Temperament clan]]
 
[[Category:Cloudy]]
[[Category:Temperament clans]]
[[Category:Pages with mostly numerical content]]
[[Category:Cloudy clan| ]] <!-- main article -->
[[Category:Cloudy| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Latest revision as of 00:27, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

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:

Coblack

See also: Trisedodge family § Coblack

In addition to the cloudy comma, the coblack temperament tempers out the starling comma (126/125). Coblack was named by Petr Pařízek in 2011, who considered it a counterpart of blacksmith[1].

Subgroup: 2.3.5.7

Comma list: 126/125, 16807/16384

Mapping: [⟨5 1 7 14], ⟨0 3 2 0]]

Optimal tunings:

  • CTE: ~8/7 = 1\5, ~48/35 = 553.8429 (~21/20 = 73.8429)
  • POTE: ~8/7 = 1\5, ~48/35 = 553.044 (~21/20 = 73.044)

Optimal ET sequence: 15, 35, 50, 65, 115d

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]]

Optimal tunings:

  • CTE: ~8/7 = 1\5, ~11/8 = 553.7951 (~21/20 = 73.7951)
  • POTE: ~8/7 = 1\5, ~11/8 = 553.264 (~21/20 = 73.264)

Optimal ET sequence: 15, 35, 50, 65, 115d

Badness: 0.045070

Decic

Main article: 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 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

Comma list: 225/224, 16807/16384

Mapping: [⟨10 0 39 28], ⟨0 1 -1 0]]

mapping generators: ~15/14, ~3

Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 698.696 (~49/48 = 21.304)

Optimal ET sequence: 10, 30b, 40, 50, 60, 110d, 170cdd

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

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

Optimal ET sequence: 10, 30be, 40, 50

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

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

Optimal ET sequence: 10, 30be, 40, 50

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

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

Optimal ET sequence: 10, 30beg, 40, 50

Badness: 0.025064

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 temperament of the fantastic rank-3 temperament, its name is a portmanteau of "splendid" (synonym of "fantastic") and "decic".

Subgroup: 2.3.5.7.11

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

Mapping: [⟨10 0 39 28 82], ⟨0 1 -1 0 -3]]

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

Optimal ET sequence: 10e, 30bee, 40e, 50, 60e, 110de

Badness: 0.059802

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 196/195, 1001/1000, 1188/1183

Mapping: [⟨10 0 39 28 82 37], ⟨0 1 -1 0 -3 0]]

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

Optimal ET sequence: 10e, 30bee, 40e, 50, 60e, 110de

Badness: 0.037989

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 105/104, 170/169, 196/195, 289/288, 375/374

Mapping: [⟨10 0 39 28 82 37 25], ⟨0 1 -1 0 -3 0 1]]

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

Optimal ET sequence: 10e, 30beeg, 40e, 50, 60e, 110deg

Badness: 0.026050

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 temperament of the prodigy rank-3 temperament, its name is a portmanteau of "prodigy" and "decic".

Subgroup: 2.3.5.7.11

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

Mapping: [⟨10 0 39 28 -13], ⟨0 1 -1 0 3]]

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

Optimal ET sequence: 10, 40ee, 50e, 60e

Badness: 0.066600

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 196/195, 275/273, 5929/5832

Mapping: [⟨10 0 39 28 -13 37], ⟨0 1 -1 0 3 0]]

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

Optimal ET sequence: 10, 40ee, 50e, 60e

Badness: 0.041788

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 105/104, 154/153, 170/169, 196/195, 289/288

Mapping: [⟨10 0 39 28 -13 37 25], ⟨0 1 -1 0 3 0 1]]

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

Optimal ET sequence: 10, 40ee, 50e, 60e

Badness: 0.027590

Pentadecal

For the 5-limit version of this temperament, see High badness temperaments #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: 2.3.5.7

Comma list: 875/864, 16807/16384

Mapping: [⟨15 0 11 42], ⟨0 1 1 0]]

mapping generators: ~21/20, ~3

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

Optimal ET sequence: 15, 45, 60

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

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

Optimal ET sequence: 15, 45, 60, 75de, 135de

Badness: 0.077420

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 105/104, 144/143, 1372/1331

Mapping: [⟨15 0 11 42 52 8], ⟨0 1 1 0 0 2]]

mapping generators: ~21/20, ~3

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

Optimal ET sequence: 15, 45f, 60, 135de, 195cddee

Badness: 0.051740

Quindecal

Subgroup: 2.3.5.7.11

Comma list: 121/120, 441/440, 875/864

Mapping: [⟨15 0 11 42 28], ⟨0 1 1 0 1]]

mapping generators: ~21/20, ~3

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

Optimal ET sequence: 15, 45e, 60e

Badness: 0.044405

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 196/195, 352/351, 875/864

Mapping: [⟨15 0 11 42 28 103], ⟨0 1 1 0 1 -2]]

mapping generators: ~21/20, ~3

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

Optimal ET sequence: 15f, 45e, 60e

Badness: 0.055361

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.

Subgroup: 2.3.5.7

Comma list: 1029/1000, 6144/6125

Mapping: [⟨5 9 12 14], ⟨0 -3 -1 0]]

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

Optimal ET sequence: 15, 40, 55, 125cd, 180ccdd

Badness: 0.184222

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 1029/1000

Mapping: [⟨5 9 12 14 18], ⟨0 -3 -1 0 -2]]

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

Optimal ET sequence: 15, 40, 55, 125cd, 180ccdde

Badness: 0.065192

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 105/104, 121/120, 637/625

Mapping: [⟨5 9 12 14 18 20], ⟨0 -3 -1 0 -2 -4]]

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

Optimal ET sequence: 15, 40, 55

Badness: 0.048440

Notes

  1. ↑ Yahoo! Tuning Group | Suggested names for the unclasified temperaments
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