Orwellismic temperaments: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
These temper out {{monzo| 6 3 -1 -3 }} = 1728/1715, the orwellisma.
This is a collection of [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] that [[tempering out|temper out]] the [[orwellisma]] ({{monzo|legend=1| 6 3 -1 -3 }}, [[ratio]]: 1728/1715).


Temperaments considered below are secant, infraorwell, quartonic, sentinel, diesic, philips, triskaidekic, and pentorwell. Discussed elsewhere are:  
Temperaments considered below are secant, infraorwell, quartonic, sentinel, diesic, philips, triskaidekic, and pentorwell. Discussed elsewhere are:  
* ''[[Beep]]'' (+21/20 or 27/25) → [[Bug family #Beep|Bug family]]
* [[Beep]] (+21/20 or 27/25) → [[Bug family #Beep|Bug family]]
* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide|Jubilismic clan]]
* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide|Jubilismic clan]]
* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth|Archytas clan]]
* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth|Archytas clan]]
* ''[[Mothra]]'' (+81/80) → [[Meantone family #Mothra|Meantone family]]
* [[Mothra]] (+81/80) → [[Meantone family #Mothra|Meantone family]]
* [[Myna]] (+126/125) → [[Starling temperaments #Myna|Starling temperaments]]
* [[Myna]] (+126/125) → [[Starling temperaments #Myna|Starling temperaments]]
* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]
* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]
* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]
* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]
* ''[[Buzzard]]'' (+5120/5103) → [[Vulture family #Buzzard|Vulture family]]
* [[Buzzard]] (+5120/5103) → [[Vulture family #Buzzard|Vulture family]]
* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory|Sensipent family]]
* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory|Sensipent family]]
* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila|Mabila family]]
* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila|Mabila family]]
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{{Mapping|legend=1| 2 1 0 5 | 0 7 15 2 }}
{{Mapping|legend=1| 2 1 0 5 | 0 7 15 2 }}
: mapping generators: ~567/400, ~10/9


: Mapping generators: ~567/400, ~10/9
[[Optimal tuning]] ([[POTE]]): ~567/400 = 600.000{{c}}, ~10/9 = 185.885{{c}}
 
[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~10/9 = 185.885


{{Optimal ET sequence|legend=1| 26, 58, 84, 142, 368cd }}
{{Optimal ET sequence|legend=1| 26, 58, 84, 142, 368cd }}


[[Badness]]: 0.095278
[[Badness]] (Smith): 0.095278


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 2 1 0 5 6 | 0 7 15 2 3 }}
Mapping: {{mapping| 2 1 0 5 6 | 0 7 15 2 3 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~10/9 = 185.962
Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~10/9 = 185.962{{c}}


Optimal ET sequence: {{Optimal ET sequence| 26, 58, 142e, 200cdee }}
{{Optimal ET sequence|legend=0| 26, 58, 142e, 200cdee }}


Badness: 0.046373
Badness (Smith): 0.046373


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 2 1 0 5 6 4 | 0 7 15 2 3 11 }}
Mapping: {{mapping| 2 1 0 5 6 4 | 0 7 15 2 3 11 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~10/9 = 185.955
Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~10/9 = 185.955{{c}}


Optimal ET sequence: {{Optimal ET sequence| 26, 58, 84, 142ef }}
{{Optimal ET sequence|legend=0| 26, 58, 84, 142ef }}


Badness: 0.025035
Badness (Smith): 0.025035


=== 17-limit ===
=== 17-limit ===
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Mapping: {{mapping| 2 1 0 5 6 4 6 | 0 7 15 2 3 11 7 }}
Mapping: {{mapping| 2 1 0 5 6 4 6 | 0 7 15 2 3 11 7 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~10/9 = 185.916
Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~10/9 = 185.916{{c}}


Optimal ET sequence: {{Optimal ET sequence| 26, 58, 84, 142ef }}
{{Optimal ET sequence|legend=0| 26, 58, 84, 142ef }}


Badness: 0.021642
Badness (Smith): 0.021642


=== 19-limit ===
=== 19-limit ===
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Mapping: {{mapping| 2 1 0 5 6 4 6 2 | 0 7 15 2 3 11 7 21 }}
Mapping: {{mapping| 2 1 0 5 6 4 6 2 | 0 7 15 2 3 11 7 21 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~10/9 = 185.858
Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~10/9 = 185.858{{c}}


Optimal ET sequence: {{Optimal ET sequence| 26, 58h, 84, 142efh, 226deefgh }}
{{Optimal ET sequence|legend=0| 26, 58h, 84, 142efh, 226deefgh }}


Badness: 0.018565
Badness (Smith): 0.018565


== Infraorwell ==
== Infraorwell ==
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{{Mapping|legend=1| 1 14 0 16 | 0 -16 3 -17 }}
{{Mapping|legend=1| 1 14 0 16 | 0 -16 3 -17 }}
: mapping generators: ~2, ~12/7


: Mapping generators: ~2, ~12/7
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/6 = 269.032{{c}}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 269.032


{{Optimal ET sequence|legend=1| 9, 49, 58, 165cd, 223bcd }}
{{Optimal ET sequence|legend=1| 9, 49, 58, 165cd, 223bcd }}


[[Badness]]: 0.117073
[[Badness]] (Smith): 0.117073


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 14 0 16 12 | 0 -16 3 -17 -11 }}
Mapping: {{mapping| 1 14 0 16 12 | 0 -16 3 -17 -11 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.036
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 269.036{{c}}


Optimal ET sequence: {{Optimal ET sequence| 9, 49, 58, 165cdee }}
{{Optimal ET sequence|legend=0| 9, 49, 58, 165cdee }}


Badness: 0.040721
Badness (Smith): 0.040721


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 14 0 16 12 20 | 0 -16 3 -17 -11 -21 }}
Mapping: {{mapping| 1 14 0 16 12 20 | 0 -16 3 -17 -11 -21 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.021
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 269.021{{c}}


Optimal ET sequence: {{Optimal ET sequence| 9, 49f, 58 }}
{{Optimal ET sequence|legend=0| 9, 49f, 58 }}


Badness: 0.023683
Badness (Smith): 0.023683


== Sentinel ==
== Sentinel ==
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{{Mapping|legend=1| 1 3 -3 6 | 0 -4 15 -9 }}
{{Mapping|legend=1| 1 3 -3 6 | 0 -4 15 -9 }}
: mapping generators: ~2, ~9/7


: Mapping generators: ~2, ~9/7
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~9/7 = 425.596{{c}}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.596


{{Optimal ET sequence|legend=1| 14, 17, 31, 110, 141, 172b, 375bc }}
{{Optimal ET sequence|legend=1| 14, 17, 31, 110, 141, 172b, 375bc }}


[[Badness]]: 0.093805
[[Badness]] (Smith): 0.093805


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 3 -3 6 7 | 0 -4 15 -9 -10 }}
Mapping: {{mapping| 1 3 -3 6 7 | 0 -4 15 -9 -10 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.550
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~9/7 = 425.550{{c}}


Optimal ET sequence: {{Optimal ET sequence| 14, 17, 31, 79, 110e, 141e }}
{{Optimal ET sequence|legend=0| 14, 17, 31, 79, 110e, 141e }}


Badness: 0.039595
Badness (Smith): 0.039595


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 3 -3 6 7 3 | 0 -4 15 -9 -10 2 }}
Mapping: {{mapping| 1 3 -3 6 7 3 | 0 -4 15 -9 -10 2 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.501
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~9/7 = 425.501{{c}}


Optimal ET sequence: {{Optimal ET sequence| 14, 17, 31, 79f, 110ef, 141ef }}
{{Optimal ET sequence|legend=0| 14, 17, 31, 79f, 110ef, 141ef }}


Badness: 0.037408
Badness (Smith): 0.037408


== Diesic ==
== Diesic ==
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{{Mapping|legend=1| 1 2 3 3 | 0 -13 -21 -6 }}
{{Mapping|legend=1| 1 2 3 3 | 0 -13 -21 -6 }}
: mapping generators: ~2, ~36/35


: Mapping generators: ~2, ~36/35
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~36/35 = 38.567{{c}}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 38.567


{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}


[[Badness]]: 0.107348
[[Badness]] (Smith): 0.107348


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 2 3 3 4 | 0 -13 -21 -6 -17 }}
Mapping: {{mapping| 1 2 3 3 4 | 0 -13 -21 -6 -17 }}


Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.565
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~36/35 = 38.565{{c}}


Optimal ET sequence: {{Optimal ET sequence| 31, 156ce, 187ce, 218bcee, 249bcee }}
{{Optimal ET sequence|legend=0| 31, 156ce, 187ce, 218bcee, 249bcee }}


Badness: 0.044186
Badness (Smith): 0.044186


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 2 3 3 4 4 | 0 -13 -21 -6 -17 -9 }}
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -13 -21 -6 -17 -9 }}


Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.444
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~36/35 = 38.444{{c}}


Optimal ET sequence: {{Optimal ET sequence| 31, 94cff, 125cff }}
{{Optimal ET sequence|legend=0| 31, 94cff, 125cff }}


Badness: 0.038116
Badness (Smith): 0.038116


== Phillips ==
== Phillips ==
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{{Mapping|legend=1| 2 0 33 -7 | 0 1 -9 4 }}
{{Mapping|legend=1| 2 0 33 -7 | 0 1 -9 4 }}
: mapping generators: ~81/56, ~3


: Mapping generators: ~81/56, ~3
[[Optimal tuning]] ([[POTE]]): ~81/56 = 600.000{{c}}, ~3/2 = 691.174{{c}}
 
[[Optimal tuning]] ([[POTE]]): ~81/56 = 1\2, ~3/2 = 691.174


{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc }}
{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc }}


[[Badness]]: 0.228602
[[Badness]] (Smith): 0.228602


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 2 0 33 -7 -12 | 0 1 -9 4 6 }}
Mapping: {{mapping| 2 0 33 -7 -12 | 0 1 -9 4 6 }}


Optimal tuning (POTE): ~63/44 = 1\2, ~3/2 = 691.040
Optimal tuning (POTE): ~63/44 = 600.000{{c}}, ~3/2 = 691.040{{c}}


Optimal ET sequence: {{Optimal ET sequence| 14, 26, 40, 66b }}
{{Optimal ET sequence|legend=0| 14, 26, 40, 66b }}


Badness: 0.095777
Badness (Smith): 0.095777


== Triskaidekic ==
== Triskaidekic ==
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{{Mapping|legend=1| 13 0 30 16 | 0 1 0 1 }}
{{Mapping|legend=1| 13 0 30 16 | 0 1 0 1 }}
: mapping generators: ~15/14, ~3


: Mapping generators: ~15/14, ~3
[[Optimal tuning]] ([[POTE]]): ~15/14 = 92.308{{c}}, ~3/2 = 694.143{{c}}
 
[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\13, ~3/2 = 694.143


{{Optimal ET sequence|legend=1| 13d, 26 }}
{{Optimal ET sequence|legend=1| 13d, 26 }}


[[Badness]]: 0.219050
[[Badness]] (Smith): 0.219050


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 13 0 30 16 45 | 0 1 0 1 0 }}
Mapping: {{mapping| 13 0 30 16 45 | 0 1 0 1 0 }}


Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 696.296
Optimal tuning (POTE): ~15/14 = 92.308{{c}}, ~3/2 = 696.296{{c}}


Optimal ET sequence: {{Optimal ET sequence| 13d, 26, 91cd }}
{{Optimal ET sequence|legend=0| 13d, 26, 91cd }}


Badness: 0.098847
Badness (Smith): 0.098847


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 13 0 30 16 45 48 | 0 1 0 1 0 0 }}
Mapping: {{mapping| 13 0 30 16 45 48 | 0 1 0 1 0 0 }}


Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 695.879
Optimal tuning (POTE): ~15/14 = 92.308{{c}}, ~3/2 = 695.879{{c}}


Optimal ET sequence: {{Optimal ET sequence| 13d, 26, 91cdf }}
{{Optimal ET sequence|legend=0| 13d, 26, 91cdf }}


Badness: 0.059216
Badness (Smith): 0.059216


== Pentorwell ==
== Pentorwell ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~280/243 = 1\5, ~3/2 = 704.3709 (~64/63 = 15.6291)
* [[CTE]]: ~280/243 = 240.000{{c}}, ~3/2 = 704.3709{{c}} (~64/63 = 15.6291{{c}})
* [[POTE]]: ~280/243 = 1\5, ~3/2 = 704.9128 (~64/63 = 15.0872)
* [[POTE]]: ~280/243 = 240.000{{c}}, ~3/2 = 704.9128{{c}} (~64/63 = 15.0872{{c}})


{{Optimal ET sequence|legend=1| 5, 75, 80 }}
{{Optimal ET sequence|legend=1| 5, 75, 80 }}


[[Badness]]: 0.148665
[[Badness]] (Smith): 0.148665


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~55/48 = 1\5, ~3/2 = 704.8440 (~99/98 = 15.1560)
* CTE: ~55/48 = 240.000{{c}}, ~3/2 = 704.8440{{c}} (~99/98 = 15.1560{{c}})
* POTE: ~55/48 = 1\5, ~3/2 = 704.8788 (~99/98 = 15.1212)
* POTE: ~55/48 = 240.000{{c}}, ~3/2 = 704.8788{{c}} (~99/98 = 15.1212{{c}})


Optimal ET sequence: {{Optimal ET sequence| 75e, 80, 315bcdddee }}
{{Optimal ET sequence|legend=0| 75e, 80, 315bcdddee }}


Badness: 0.071702
Badness (Smith): 0.071702


=== 13-limit ===
=== 13-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~55/48 = 1\5, ~3/2 = 704.7636 (~99/98 = 15.2364)
* CTE: ~55/48 = 240.000{{c}}, ~3/2 = 704.7636{{c}} (~99/98 = 15.2364{{c}})
* CWE: ~55/48 = 1\5, ~3/2 = 704.7112 (~99/98 = 15.2882)
* CWE: ~55/48 = 240.000{{c}}, ~3/2 = 704.7112{{c}} (~99/98 = 15.2882{{c}})


Optimal ET sequence: {{Optimal ET sequence| 75e, 80, 155de }}
{{Optimal ET sequence|legend=0| 75e, 80, 155de }}


Badness: 0.0557
Badness (Smith): 0.0557


[[Category:Temperament collections]]
[[Category:Temperament collections]]

Revision as of 10:52, 13 October 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.

This is a collection of rank-2 temperaments that temper out the orwellisma (monzo: [6 3 -1 -3⟩, ratio: 1728/1715).

Temperaments considered below are secant, infraorwell, quartonic, sentinel, diesic, philips, triskaidekic, and pentorwell. Discussed elsewhere are:

Secant

Subgroup: 2.3.5.7

Comma list: 1728/1715, 177147/175000

Mapping: [⟨2 1 0 5], ⟨0 7 15 2]]

mapping generators: ~567/400, ~10/9

Optimal tuning (POTE): ~567/400 = 600.000 ¢, ~10/9 = 185.885 ¢

Optimal ET sequence: 26, 58, 84, 142, 368cd

Badness (Smith): 0.095278

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 1344/1331, 1728/1715

Mapping: [⟨2 1 0 5 6], ⟨0 7 15 2 3]]

Optimal tuning (POTE): ~99/70 = 600.000 ¢, ~10/9 = 185.962 ¢

Optimal ET sequence: 26, 58, 142e, 200cdee

Badness (Smith): 0.046373

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 351/350, 364/363, 441/440

Mapping: [⟨2 1 0 5 6 4], ⟨0 7 15 2 3 11]]

Optimal tuning (POTE): ~99/70 = 600.000 ¢, ~10/9 = 185.955 ¢

Optimal ET sequence: 26, 58, 84, 142ef

Badness (Smith): 0.025035

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 144/143, 170/169, 221/220, 351/350, 441/440

Mapping: [⟨2 1 0 5 6 4 6], ⟨0 7 15 2 3 11 7]]

Optimal tuning (POTE): ~17/12 = 600.000 ¢, ~10/9 = 185.916 ¢

Optimal ET sequence: 26, 58, 84, 142ef

Badness (Smith): 0.021642

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 144/143, 153/152, 170/169, 210/209, 221/220, 400/399

Mapping: [⟨2 1 0 5 6 4 6 2], ⟨0 7 15 2 3 11 7 21]]

Optimal tuning (POTE): ~17/12 = 600.000 ¢, ~10/9 = 185.858 ¢

Optimal ET sequence: 26, 58h, 84, 142efh, 226deefgh

Badness (Smith): 0.018565

Infraorwell

Subgroup: 2.3.5.7

Comma list: 1728/1715, 28672/28125

Mapping: [⟨1 14 0 16], ⟨0 -16 3 -17]]

mapping generators: ~2, ~12/7

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/6 = 269.032 ¢

Optimal ET sequence: 9, 49, 58, 165cd, 223bcd

Badness (Smith): 0.117073

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 540/539, 1344/1331

Mapping: [⟨1 14 0 16 12], ⟨0 -16 3 -17 -11]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/6 = 269.036 ¢

Optimal ET sequence: 9, 49, 58, 165cdee

Badness (Smith): 0.040721

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 176/175, 196/195, 364/363

Mapping: [⟨1 14 0 16 12 20], ⟨0 -16 3 -17 -11 -21]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/6 = 269.021 ¢

Optimal ET sequence: 9, 49f, 58

Badness (Smith): 0.023683

Sentinel

For the 5-limit version of this temperament, see High badness temperaments #Sentinel.

Subgroup: 2.3.5.7

Comma list: 1728/1715, 3645/3584

Mapping: [⟨1 3 -3 6], ⟨0 -4 15 -9]]

mapping generators: ~2, ~9/7

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~9/7 = 425.596 ¢

Optimal ET sequence: 14, 17, 31, 110, 141, 172b, 375bc

Badness (Smith): 0.093805

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 243/242, 385/384

Mapping: [⟨1 3 -3 6 7], ⟨0 -4 15 -9 -10]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~9/7 = 425.550 ¢

Optimal ET sequence: 14, 17, 31, 79, 110e, 141e

Badness (Smith): 0.039595

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 105/104, 144/143, 243/242

Mapping: [⟨1 3 -3 6 7 3], ⟨0 -4 15 -9 -10 2]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~9/7 = 425.501 ¢

Optimal ET sequence: 14, 17, 31, 79f, 110ef, 141ef

Badness (Smith): 0.037408

Diesic

For the 5-limit version of this temperament, see High badness temperaments #Diesic.

Subgroup: 2.3.5.7

Comma list: 1728/1715, 5103/5000

Mapping: [⟨1 2 3 3], ⟨0 -13 -21 -6]]

mapping generators: ~2, ~36/35

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~36/35 = 38.567 ¢

Optimal ET sequence: 31, 156c, 187c, 218bc, 249bc, 280bc

Badness (Smith): 0.107348

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 441/440, 891/875

Mapping: [⟨1 2 3 3 4], ⟨0 -13 -21 -6 -17]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~36/35 = 38.565 ¢

Optimal ET sequence: 31, 156ce, 187ce, 218bcee, 249bcee

Badness (Smith): 0.044186

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 121/120, 343/338, 441/440

Mapping: [⟨1 2 3 3 4 4], ⟨0 -13 -21 -6 -17 -9]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~36/35 = 38.444 ¢

Optimal ET sequence: 31, 94cff, 125cff

Badness (Smith): 0.038116

Phillips

For the 5-limit version of this temperament, see High badness temperaments #Phillips.

Subgroup: 2.3.5.7

Comma list: 1728/1715, 6561/6272

Mapping: [⟨2 0 33 -7], ⟨0 1 -9 4]]

mapping generators: ~81/56, ~3

Optimal tuning (POTE): ~81/56 = 600.000 ¢, ~3/2 = 691.174 ¢

Optimal ET sequence: 14, 26, 66b, 92bc

Badness (Smith): 0.228602

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 385/384, 729/704

Mapping: [⟨2 0 33 -7 -12], ⟨0 1 -9 4 6]]

Optimal tuning (POTE): ~63/44 = 600.000 ¢, ~3/2 = 691.040 ¢

Optimal ET sequence: 14, 26, 40, 66b

Badness (Smith): 0.095777

Triskaidekic

For the 5-limit version of this temperament, see High badness temperaments #Triskaidekic.

Subgroup: 2.3.5.7

Comma list: 1728/1715, 1875/1792

Mapping: [⟨13 0 30 16], ⟨0 1 0 1]]

mapping generators: ~15/14, ~3

Optimal tuning (POTE): ~15/14 = 92.308 ¢, ~3/2 = 694.143 ¢

Optimal ET sequence: 13d, 26

Badness (Smith): 0.219050

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 125/121, 385/384

Mapping: [⟨13 0 30 16 45], ⟨0 1 0 1 0]]

Optimal tuning (POTE): ~15/14 = 92.308 ¢, ~3/2 = 696.296 ¢

Optimal ET sequence: 13d, 26, 91cd

Badness (Smith): 0.098847

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 78/77, 99/98, 125/121, 1200/1183

Mapping: [⟨13 0 30 16 45 48], ⟨0 1 0 1 0 0]]

Optimal tuning (POTE): ~15/14 = 92.308 ¢, ~3/2 = 695.879 ¢

Optimal ET sequence: 13d, 26, 91cdf

Badness (Smith): 0.059216

Pentorwell

Subgroup: 2.3.5.7

Comma list: 1728/1715, 179200/177147

Mapping: [⟨5 0 -36 22], ⟨0 1 6 -1]]

Optimal tunings:

  • CTE: ~280/243 = 240.000 ¢, ~3/2 = 704.3709 ¢ (~64/63 = 15.6291 ¢)
  • POTE: ~280/243 = 240.000 ¢, ~3/2 = 704.9128 ¢ (~64/63 = 15.0872 ¢)

Optimal ET sequence: 5, 75, 80

Badness (Smith): 0.148665

11-limit

Subgroup: 2.3.5.7.11

Comma list: 896/891, 1728/1715, 2200/2187

Mapping: [⟨5 0 -36 22 57], ⟨0 1 6 -1 -5]]

Optimal tunings:

  • CTE: ~55/48 = 240.000 ¢, ~3/2 = 704.8440 ¢ (~99/98 = 15.1560 ¢)
  • POTE: ~55/48 = 240.000 ¢, ~3/2 = 704.8788 ¢ (~99/98 = 15.1212 ¢)

Optimal ET sequence: 75e, 80, 315bcdddee

Badness (Smith): 0.071702

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 352/351, 364/363, 1728/1715

Mapping: [⟨5 0 -36 22 57 82], ⟨0 1 6 -1 -5 -8]]

Optimal tunings:

  • CTE: ~55/48 = 240.000 ¢, ~3/2 = 704.7636 ¢ (~99/98 = 15.2364 ¢)
  • CWE: ~55/48 = 240.000 ¢, ~3/2 = 704.7112 ¢ (~99/98 = 15.2882 ¢)

Optimal ET sequence: 75e, 80, 155de

Badness (Smith): 0.0557

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