Cloudy clan: Difference between revisions

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{{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 [[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.
Decic tempers out the [[cloudy comma]], 16807/16384 and the [[marvel comma]], 225/224 in the 7-limit, as well as the [[linus comma]], {{monzo| 11 -10 -10 10 }}. It maybe described as the {{nowrap| 50 & 60 }} temperament, [[support]]ed by [[10edo|10-]], [[50edo|50-]], and [[60edo]]. It 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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{{Mapping|legend=1| 10 0 39 28 | 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


[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~3/2 = 698.696 (~49/48 = 21.304)
[[Optimal tuning]] ([[POTE]]): ~15/14 = 120.000{{c}}, ~3/2 = 698.696{{c}} (~49/48 = 21.304{{c}})


{{Optimal ET sequence|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]] (Smith): 0.089135


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 10 0 39 28 3 | 0 1 -1 0 2 }}
Mapping: {{mapping| 10 0 39 28 3 | 0 1 -1 0 2 }}


: mapping generators: ~15/14, ~3
Optimal tuning (POTE): ~15/14 = 120.000{{c}}, ~3/2 = 696.791{{c}} (~56/55 = 23.209{{c}})
 
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=0| 10, 30be, 40, 50 }}


Badness: 0.063900
Badness (Smith): 0.063900


==== 13-limit ====
==== 13-limit ====
Line 50: Line 47:
Mapping: {{mapping| 10 0 39 28 3 37 | 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
Optimal tuning (POTE): ~15/14 = 120.000{{c}}, ~3/2 = 696.993{{c}} (~78/77 = 23.007{{c}})
 
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=0| 10, 30be, 40, 50 }}


Badness: 0.036880
Badness (Smith): 0.036880


==== 17-limit ====
==== 17-limit ====
Line 65: Line 60:
Mapping: {{mapping| 10 0 39 28 3 37 25 | 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
Optimal tuning (POTE): ~15/14 = 120.000{{c}}, ~3/2 = 697.085{{c}} (~78/77 = 22.915{{c}})
 
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=0| 10, 30beg, 40, 50 }}


Badness: 0.025064
Badness (Smith): 0.025064


=== 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 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".
Splendecic (50 & 60e) 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'' and ''decic''.


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 82: Line 75:
Mapping: {{mapping| 10 0 39 28 82 | 0 1 -1 0 -3 }}
Mapping: {{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 tuning (POTE): ~15/14 = 120.000{{c}}, ~3/2 = 698.518{{c}} (~99/98 = 21.482{{c}})


{{Optimal ET sequence|legend=1| 10e, 30bee, 40e, 50, 60e, 110de }}
{{Optimal ET sequence|legend=0| 10e, 30bee, 40e, 50, 60e, 110de }}


Badness: 0.059802
Badness (Smith): 0.059802


==== 13-limit ====
==== 13-limit ====
Line 95: Line 88:
Mapping: {{mapping| 10 0 39 28 82 37 | 0 1 -1 0 -3 0 }}
Mapping: {{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 tuning (POTE): ~15/14 = 120.000{{c}}, ~3/2 = 698.365{{c}} (~91/90 = 21.635{{c}})


{{Optimal ET sequence|legend=1| 10e, 30bee, 40e, 50, 60e, 110de }}
{{Optimal ET sequence|legend=0| 10e, 30bee, 40e, 50, 60e, 110de }}


Badness: 0.037989
Badness (Smith): 0.037989


==== 17-limit ====
==== 17-limit ====
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Mapping: {{mapping| 10 0 39 28 82 37 25 | 0 1 -1 0 -3 0 1 }}
Mapping: {{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 tuning (POTE): ~15/14 = 120.000{{c}}, ~3/2 = 698.375{{c}} (~91/90 = 21.625{{c}})


{{Optimal ET sequence|legend=1| 10e, 30beeg, 40e, 50, 60e, 110deg }}
{{Optimal ET sequence|legend=0| 10e, 30beeg, 40e, 50, 60e, 110deg }}


Badness: 0.026050
Badness (Smith): 0.026050


=== 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 temperament of the [[Marvel family #Prodigy|prodigy rank-3 temperament]], its name is a portmanteau of "[[wiktionary:prodigy|prodigy]]" and "decic".
Prodecic (50e & 60e) 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
Subgroup: 2.3.5.7.11
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Mapping: {{mapping| 10 0 39 28 -13 | 0 1 -1 0 3 }}
Mapping: {{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 tuning (POTE): ~15/14 = 120.000{{c}}, ~3/2 = 700.210{{c}} (~55/54 = 19.790{{c}})


{{Optimal ET sequence|legend=1| 10, 40ee, 50e, 60e }}
{{Optimal ET sequence|legend=0| 10, 40ee, 50e, 60e }}


Badness: 0.066600
Badness (Smith): 0.066600


==== 13-limit ====
==== 13-limit ====
Line 136: Line 129:
Mapping: {{mapping| 10 0 39 28 -13 37 | 0 1 -1 0 3 0 }}
Mapping: {{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 tuning (POTE): ~15/14 = 120.000{{c}}, ~3/2 = 700.503{{c}} (~91/90 = 19.497{{c}})


{{Optimal ET sequence|legend=1| 10, 40ee, 50e, 60e }}
{{Optimal ET sequence|legend=0| 10, 40ee, 50e, 60e }}


Badness: 0.041788
Badness (Smith): 0.041788


==== 17-limit ====
==== 17-limit ====
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Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 700.474 (~91/90 = 19.526)
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=0| 10, 40ee, 50e, 60e }}


Badness: 0.027590
Badness (Smith): 0.027590


== Pentadecal ==
== Pentadecal ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Pentadecal]].''
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #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.
Pentadecal tempers out the 15-5/3-comma, {{monzo| -11 -15 15 }} in the 5-limit. This temperament can be described as {{nowrap| 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
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{{Mapping|legend=1| 15 0 11 42 | 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


[[Optimal tuning]] ([[POTE]]): ~21/20 = 1\15, ~3/2 = 700.223 (~126/125 = 19.777)
[[Optimal tuning]] ([[POTE]]): ~21/20 = 80.000{{c}}, ~3/2 = 700.223{{c}} (~126/125 = 19.777{{c}})


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


[[Badness]]: 0.114833
[[Badness]] (Smith): 0.114833


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 15 0 11 42 52 | 0 1 1 0 0 }}
Mapping: {{mapping| 15 0 11 42 52 | 0 1 1 0 0 }}


: mapping generators: ~21/20, ~3
Optimal tuning (POTE): ~21/20 = 80.000{{c}}, ~3/2 = 702.733{{c}} (~56/55 = 17.267{{c}})
 
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=0| 15, 45, 60, 75de, 135de }}


Badness: 0.077420
Badness (Smith): 0.077420


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 15 0 11 42 52 8 | 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
Optimal tuning (POTE): ~21/20 = 80.000{{c}}, ~3/2 = 701.715{{c}} (~91/90 = 18.285{{c}})
 
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=0| 15, 45f, 60, 135de, 195cddee }}


Badness: 0.051740
Badness (Smith): 0.051740


=== Quindecal ===
=== Quindecal ===
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Mapping: {{mapping| 15 0 11 42 28 | 0 1 1 0 1 }}
Mapping: {{mapping| 15 0 11 42 28 | 0 1 1 0 1 }}


: mapping generators: ~21/20, ~3
Optimal tuning (POTE): ~21/20 = 80.000{{c}}, ~3/2 = 700.318{{c}} (~126/125 = 19.682{{c}})
 
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=0| 15, 45e, 60e }}


Badness: 0.044405
Badness (Smith): 0.044405


==== 13-limit ====
==== 13-limit ====
Line 226: Line 212:
Mapping: {{mapping| 15 0 11 42 28 103 | 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
Optimal tuning (POTE): ~21/20 = 80.000{{c}}, ~3/2 = 701.647{{c}} (~65/64 = 18.353{{c}})


Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 701.647 (~65/64 = 18.353)
{{Optimal ET sequence|legend=0| 15f, 45e, 60e }}


{{Optimal ET sequence|legend=1| 15f, 45e, 60e }}
Badness (Smith): 0.055361
 
Badness: 0.055361


== 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.
Quinkee has a period of 1/5 octave and tempers out the keega (1029/1000), from which it derives its name. It may be described as the {{nowrap| 15 & 40 }} temperament.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 243: Line 227:
{{Mapping|legend=1| 5 9 12 14 | 0 -3 -1 0 }}
{{Mapping|legend=1| 5 9 12 14 | 0 -3 -1 0 }}


[[Optimal tuning]] ([[POTE]]): ~8/7 = 1\5, ~5/4 = 393.439 (~25/24 = 86.561)
[[Optimal tuning]] ([[POTE]]): ~8/7 = 240.000{{c}}, ~5/4 = 393.439{{c}} (~25/24 = 86.561{{c}})


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


[[Badness]]: 0.184222
[[Badness]] (Smith): 0.184222


=== 11-limit ===
=== 11-limit ===
Line 256: Line 240:
Mapping: {{mapping| 5 9 12 14 18 | 0 -3 -1 0 -2 }}
Mapping: {{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 tuning (POTE): ~8/7 = 240.000{{c}}, ~5/4 = 393.438{{c}} (~22/21 = 86.562{{c}})


{{Optimal ET sequence|legend=1| 15, 40, 55, 125cd, 180ccdde }}
{{Optimal ET sequence|legend=0| 15, 40, 55, 125cd, 180ccdde }}


Badness: 0.065192
Badness (Smith): 0.065192


=== 13-limit ===
=== 13-limit ===
Line 269: Line 253:
Mapping: {{mapping| 5 9 12 14 18 20 | 0 -3 -1 0 -2 -4 }}
Mapping: {{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 tuning (POTE): ~8/7 = 240.000{{c}}, ~5/4 = 392.798{{c}} (~22/21 = 87.202{{c}})
 
{{Optimal ET sequence|legend=1| 15, 40, 55 }}


Badness: 0.048440
{{Optimal ET sequence|legend=0| 15, 40, 55 }}


== References ==
Badness (Smith): 0.048440


[[Category:Temperament clans]]
[[Category:Temperament clans]]

Revision as of 08:22, 25 June 2026

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:

Decic

Main article: Decic

Decic 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⟩. It maybe described as the 50 & 60 temperament, supported by 10-, 50-, and 60edo. It 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 = 120.000 ¢, ~3/2 = 698.696 ¢ (~49/48 = 21.304 ¢)

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

Badness (Smith): 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]]

Optimal tuning (POTE): ~15/14 = 120.000 ¢, ~3/2 = 696.791 ¢ (~56/55 = 23.209 ¢)

Optimal ET sequence: 10, 30be, 40, 50

Badness (Smith): 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]]

Optimal tuning (POTE): ~15/14 = 120.000 ¢, ~3/2 = 696.993 ¢ (~78/77 = 23.007 ¢)

Optimal ET sequence: 10, 30be, 40, 50

Badness (Smith): 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]]

Optimal tuning (POTE): ~15/14 = 120.000 ¢, ~3/2 = 697.085 ¢ (~78/77 = 22.915 ¢)

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

Badness (Smith): 0.025064

Splendecic

Splendecic (50 & 60e) 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 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 = 120.000 ¢, ~3/2 = 698.518 ¢ (~99/98 = 21.482 ¢)

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

Badness (Smith): 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 = 120.000 ¢, ~3/2 = 698.365 ¢ (~91/90 = 21.635 ¢)

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

Badness (Smith): 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 = 120.000 ¢, ~3/2 = 698.375 ¢ (~91/90 = 21.625 ¢)

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

Badness (Smith): 0.026050

Prodecic

Prodecic (50e & 60e) 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 = 120.000 ¢, ~3/2 = 700.210 ¢ (~55/54 = 19.790 ¢)

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

Badness (Smith): 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 = 120.000 ¢, ~3/2 = 700.503 ¢ (~91/90 = 19.497 ¢)

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

Badness (Smith): 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 (Smith): 0.027590

Pentadecal

For the 5-limit version, see Miscellaneous 5-limit temperaments #Pentadecal.

Pentadecal tempers out the 15-5/3-comma, [-11 -15 15⟩ in the 5-limit. 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 = 80.000 ¢, ~3/2 = 700.223 ¢ (~126/125 = 19.777 ¢)

Optimal ET sequence: 15, 45, 60

Badness (Smith): 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]]

Optimal tuning (POTE): ~21/20 = 80.000 ¢, ~3/2 = 702.733 ¢ (~56/55 = 17.267 ¢)

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

Badness (Smith): 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]]

Optimal tuning (POTE): ~21/20 = 80.000 ¢, ~3/2 = 701.715 ¢ (~91/90 = 18.285 ¢)

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

Badness (Smith): 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]]

Optimal tuning (POTE): ~21/20 = 80.000 ¢, ~3/2 = 700.318 ¢ (~126/125 = 19.682 ¢)

Optimal ET sequence: 15, 45e, 60e

Badness (Smith): 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]]

Optimal tuning (POTE): ~21/20 = 80.000 ¢, ~3/2 = 701.647 ¢ (~65/64 = 18.353 ¢)

Optimal ET sequence: 15f, 45e, 60e

Badness (Smith): 0.055361

Quinkee

Quinkee has a period of 1/5 octave and tempers out the keega (1029/1000), from which it derives its name. It may be described as the 15 & 40 temperament.

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 = 240.000 ¢, ~5/4 = 393.439 ¢ (~25/24 = 86.561 ¢)

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

Badness (Smith): 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 = 240.000 ¢, ~5/4 = 393.438 ¢ (~22/21 = 86.562 ¢)

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

Badness (Smith): 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 = 240.000 ¢, ~5/4 = 392.798 ¢ (~22/21 = 87.202 ¢)

Optimal ET sequence: 15, 40, 55

Badness (Smith): 0.048440

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