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Orwellismic temperaments: Difference between revisions

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{{Technical data page}}
These temper out {{monzo| 6 3 -1 -3 }} = 1728/1715, the orwellisma.
These temper out {{monzo| 6 3 -1 -3 }} = 1728/1715, the orwellisma.


Temperaments not discussed here include:
Temperaments considered below are secant, infraorwell, quartonic, sentinel, diesic, philips, triskaidekic, and pentorwell. Discussed elsewhere are:  
* ''[[beep]]'', {21/20, 27/25} → [[Bug family #Beep]]
* ''[[Beep]]'' (+21/20 or 27/25) → [[Bug family #Beep|Bug family]]
* ''[[doublewide]]'', {50/49, 875/864} → [[Jubilismic clan #Doublewide]]
* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide|Jubilismic clan]]
* [[superpyth]], {64/63, 245/243} → [[Archytas clan #Superpyth]]
* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth|Archytas clan]]
* ''[[mothra]]'', {81/80, 1029/1024} → [[Meantone family #Mothra]]
* ''[[Mothra]]'' (+81/80) → [[Meantone family #Mothra|Meantone family]]
* [[myna]], {126/125, 1728/1715} → [[Starling temperaments #Myna]]
* [[Myna]] (+126/125) → [[Starling temperaments #Myna|Starling temperaments]]
* [[orwell]], {225/224, 1728/1715} → [[Semicomma family #Orwell]]
* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]
* ''[[buzzard]]'', {1728/1715, 5120/5103} → [[Hemifamity temperaments #Buzzard]]
* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]
* ''[[Buzzard]]'' (+5120/5103) → [[Vulture family #Buzzard|Vulture family]]
* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory|Sensipent family]]
* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila|Mabila family]]


== Secant ==
== Secant ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1728/1715, 177147/175000
[[Comma list]]: 1728/1715, 177147/175000


[[Mapping]]: [{{val| 2 1 0 5 }}, {{val| 0 7 15 2 }}]
{{Mapping|legend=1| 2 1 0 5 | 0 7 15 2 }}


{{Multival|legend=1| 14 30 4 15 -33 -75 }}
: Mapping generators: ~567/400, ~10/9


[[POTE generator]]: ~10/9 = 185.885
[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~10/9 = 185.885


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


[[Badness]]: 0.095278
[[Badness]]: 0.095278


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


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


Mapping: [{{val| 2 1 0 5 6 }}, {{val| 0 7 15 2 3 }}]
Mapping: {{mapping| 2 1 0 5 6 | 0 7 15 2 3 }}


POTE genertor: ~10/9 = 185.962
Optimal tuning (POTE): ~99/70 = 1\2, ~10/9 = 185.962


Vals: {{val list| 26, 58, 142e, 200cdee }}
Optimal ET sequence: {{Optimal ET sequence| 26, 58, 142e, 200cdee }}


Badness: 0.046373
Badness: 0.046373


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


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


Mapping: [{{val| 2 1 0 5 6 4 }}, {{val| 0 7 15 2 3 11 }}]
Mapping: {{mapping| 2 1 0 5 6 4 | 0 7 15 2 3 11 }}


POTE generator: ~10/9 = 185.955
Optimal tuning (POTE): ~99/70 = 1\2, ~10/9 = 185.955


Vals: {{val list| 26, 58, 84, 142ef }}
Optimal ET sequence: {{Optimal ET sequence| 26, 58, 84, 142ef }}


Badness: 0.025035
Badness: 0.025035


== Infraorwell  ==
=== 17-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7.11.13.17


[[Comma list]]: 1728/1715, 28672/28125
Comma list: 144/143, 170/169, 221/220, 351/350, 441/440


[[Mapping]]: [{{val| 1 14 0 16 }}, {{val| 0 -16 3 -17 }}]
Mapping: {{mapping| 2 1 0 5 6 4 6 | 0 7 15 2 3 11 7 }}


{{Multival|legend=1| 16 -3 17 -42 -18 48 }}
Optimal tuning (POTE): ~17/12 = 1\2, ~10/9 = 185.916


[[POTE generator]]: ~7/6 = 269.032
Optimal ET sequence: {{Optimal ET sequence| 26, 58, 84, 142ef }}


{{Val list|legend=1| 9, 49, 58, 165cd, 223bcd }}
Badness: 0.021642


[[Badness]]: 0.117073
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19


=== 11-limit  ===
Comma list: 144/143, 153/152, 170/169, 210/209, 221/220, 400/399
Subgroup: 2.3.5.7.11


Comma list: 176/175, 540/539, 1344/1331
Mapping: {{mapping| 2 1 0 5 6 4 6 2 | 0 7 15 2 3 11 7 21 }}


Mapping: [{{val| 1 14 0 16 12 }}, {{val| 0 -16 3 -17 -11 }}]
Optimal tuning (POTE): ~17/12 = 1\2, ~10/9 = 185.858


POTE generator: ~7/6 = 269.036
Optimal ET sequence: {{Optimal ET sequence| 26, 58h, 84, 142efh, 226deefgh }}


Vals: {{val list| 9, 49, 58, 165cdee }}
Badness: 0.018565


Badness: 0.040721
== Infraorwell ==
[[Subgroup]]: 2.3.5.7


=== 13-limit  ===
[[Comma list]]: 1728/1715, 28672/28125
Subgroup: 2.3.5.7.11.13


Comma list: 144/143, 176/175, 196/195, 364/363
{{Mapping|legend=1| 1 14 0 16 | 0 -16 3 -17 }}


Mapping: [{{val| 1 14 0 16 12 20 }}, {{val| 0 -16 3 -17 -11 -21 }}]
: Mapping generators: ~2, ~12/7


POTE generator: ~7/6 = 269.021
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 269.032


Vals: {{val list| 9, 49f, 58 }}
{{Optimal ET sequence|legend=1| 9, 49, 58, 165cd, 223bcd }}


Badness: 0.023683
[[Badness]]: 0.117073


== Quartonic  ==
=== 11-limit ===
{{See also| Turkish maqam music temperaments #Yarman temperament}}
Subgroup: 2.3.5.7.11


Subgroup: 2.3.5
Comma list: 176/175, 540/539, 1344/1331


[[Comma list]]: 390625000/387420489
Mapping: {{mapping| 1 14 0 16 12 | 0 -16 3 -17 -11 }}


[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -11 -18 }}]
Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.036


[[POTE generator]]: ~250/243 = 45.233
Optimal ET sequence: {{Optimal ET sequence| 9, 49, 58, 165cdee }}


{{Val list|legend=1| 26, 27, 53, 239, 292, 345, 398, 451 }}
Badness: 0.040721


[[Badness]]: 0.117250
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=== 7-limit  ===
Comma list: 144/143, 176/175, 196/195, 364/363
Subgroup: 2.3.5.7


[[Comma list]]: 1728/1715, 4000/3969
Mapping: {{mapping| 1 14 0 16 12 20 | 0 -16 3 -17 -11 -21 }}


[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -11 -18 -5 }}]
Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.021


{{Multival|legend=1| 11 18 5 3 -23 -39 }}
Optimal ET sequence: {{Optimal ET sequence| 9, 49f, 58 }}


[[POTE generator]]: ~36/35 = 45.139
Badness: 0.023683


{{Val list|legend=1| 26, 27, 53, 80, 133d, 186d, 319d }}
== Sentinel ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Sentinel]].''


[[Badness]]: 0.042632
[[Subgroup]]: 2.3.5.7


=== 11-limit  ===
[[Comma list]]: 1728/1715, 3645/3584
Subgroup: 2.3.5.7.11


Comma list: 176/175, 540/539, 2200/2187
{{Mapping|legend=1| 1 3 -3 6 | 0 -4 15 -9 }}


Mapping: [{{val| 1 2 3 3 5 }}, {{val| 0 -11 -18 -5 -41 }}]
: Mapping generators: ~2, ~9/7


POTE generator: ~36/35 = 45.041
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.596


Vals: {{val list| 26e, 27e, 53, 80, 213d, 293bcd }}
{{Optimal ET sequence|legend=1| 14, 17, 31, 110, 141, 172b, 375bc }}


Badness: 0.034031
[[Badness]]: 0.093805


==== 13-limit ====
=== 11-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 176/175, 325/324, 540/539
 
Mapping: [{{val| 1 2 3 3 5 4 }}, {{val| 0 -11 -18 -5 -41 -8 }}]
 
POTE generator: ~36/35 = 45.080
 
Vals: {{val list| 26e, 27e, 53, 80, 133d, 213d}}
 
Badness: 0.023875
 
=== Quarto  ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 100/99, 245/242, 864/847
Comma list: 99/98, 243/242, 385/384


Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -11 -18 -5 -14 }}]
Mapping: {{mapping| 1 3 -3 6 7 | 0 -4 15 -9 -10 }}


POTE generator: ~36/35 = 45.132
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.550


Vals: {{val list| 26, 27e, 53e, 80e }}
Optimal ET sequence: {{Optimal ET sequence| 14, 17, 31, 79, 110e, 141e }}


Badness: 0.041786
Badness: 0.039595


==== 13-limit ====
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 78/77, 100/99, 144/143, 245/242
Comma list: 99/98, 105/104, 144/143, 243/242


Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -11 -18 -5 -14 -8 }}]
Mapping: {{mapping| 1 3 -3 6 7 3 | 0 -4 15 -9 -10 2 }}


POTE generator: ~36/35 = 45.205
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.501


Vals: {{val list| 26, 27e, 53e }}
Optimal ET sequence: {{Optimal ET sequence| 14, 17, 31, 79f, 110ef, 141ef }}


Badness: 0.027692
Badness: 0.037408


=== Quartz  ===
== Diesic ==
Subgroup: 2.3.5.7.11
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Diesic]].''


Comma list: 99/98, 385/384, 4000/3969
[[Subgroup]]: 2.3.5.7


Mapping: [{{val| 1 2 3 3 3 }}, {{val| 0 -11 -18 -5 12 }}]
[[Comma list]]: 1728/1715, 5103/5000


POTE generator: ~36/35 = 45.385
{{Mapping|legend=1| 1 2 3 3 | 0 -13 -21 -6 }}


Vals: {{val list| 26, 53 }}
: Mapping generators: ~2, ~36/35


Badness: 0.053285
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 38.567


==== 13-limit  ====
{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
Subgroup: 2.3.5.7.11.13


Comma list: 99/98, 169/168, 275/273, 385/384
[[Badness]]: 0.107348


Mapping: [{{val| 1 2 3 3 3 4 }}, {{val| 0 -11 -18 -5 12 -8 }}]
=== 11-limit ===
Subgroup: 2.3.5.7.11


POTE generator: ~36/35 = 45.387
Comma list: 121/120, 441/440, 891/875


Vals: {{val list| 26, 53, 132e, 185cdef, 238cdef}}
Mapping: {{mapping| 1 2 3 3 4 | 0 -13 -21 -6 -17 }}


Badness: 0.028818
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.565


== Sentinel  ==
Optimal ET sequence: {{Optimal ET sequence| 31, 156ce, 187ce, 218bcee, 249bcee }}
Subgroup: 2.3.5


[[Comma list]]: 8968066875/8589934592
Badness: 0.044186


[[Mapping]]: [{{val| 1 3 -3 }}, {{val| 0 -4 15 }}]
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


[[POTE generator]]: ~512/405 = 425.474
Comma list: 66/65, 121/120, 343/338, 441/440


{{Val list|legend=1| 14, 17, 31, 79, 110, 361bc }}
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -13 -21 -6 -17 -9 }}


[[Badness]]: 0.723413
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.444


=== 7-limit  ===
Optimal ET sequence: {{Optimal ET sequence| 31, 94cff, 125cff }}
Subgroup: 2.3.5.7


[[Comma list]]: 1728/1715, 3645/3584
Badness: 0.038116


[[Mapping]]: [{{val| 1 3 -3 6 }}, {{val| 0 -4 15 -9 }}]
== Phillips ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Phillips]].''


{{Multival|legend=1| 4 -15 9 -33 3 63 }}
[[Subgroup]]: 2.3.5.7


[[POTE generator]]: ~9/7 = 425.596
[[Comma list]]: 1728/1715, 6561/6272


{{Val list|legend=1| 14, 17, 31, 110, 141, 172b, 375bc }}
{{Mapping|legend=1| 2 0 33 -7 | 0 1 -9 4 }}


[[Badness]]: 0.093805
: Mapping generators: ~81/56, ~3


=== 11-limit  ===
[[Optimal tuning]] ([[POTE]]): ~81/56 = 1\2, ~3/2 = 691.174
Subgroup: 2.3.5.7.11


Comma list: 99/98, 243/242, 385/384
{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc }}


Mapping: [{{val| 1 3 -3 6 7 }}, {{val| 0 -4 15 -9 -10 }}]
[[Badness]]: 0.228602


POTE generator: ~9/7 = 425.550
=== 11-limit ===
 
Subgroup: 2.3.5.7.11
Vals: {{val list| 14, 17, 31, 79, 110e, 141e }}


Badness: 0.039595
Comma list: 99/98, 385/384, 729/704


=== 13-limit  ===
Mapping: {{mapping| 2 0 33 -7 -12 | 0 1 -9 4 6 }}
Subgroup: 2.3.5.7.11.13


Comma list: 99/98, 105/104, 144/143, 243/242
Optimal tuning (POTE): ~63/44 = 1\2, ~3/2 = 691.040


Mapping: [{{val| 1 3 -3 6 7 3 }}, {{val| 0 -4 15 -9 -10 2 }}]
Optimal ET sequence: {{Optimal ET sequence| 14, 26, 40, 66b }}


POTE generator: ~9/7 = 425.501
Badness: 0.095777


Vals: {{val list| 14, 17, 31, 79f, 110ef, 141ef }}
== Triskaidekic ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Triskaidekic]].''


Badness: 0.037408
[[Subgroup]]: 2.3.5.7


== Diesic  ==
[[Comma list]]: 1728/1715, 1875/1792
Subgroup: 2.3.5


[[Comma list]]: 10460353203/9765625000
{{Mapping|legend=1| 13 0 30 16 | 0 1 0 1 }}


[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -13 -21 }}]
: Mapping generators: ~15/14, ~3


[[POTE generator]]: ~6561/6250 = 38.571
[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\13, ~3/2 = 694.143


{{Val list|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
{{Optimal ET sequence|legend=1| 13d, 26 }}


[[Badness]]: 1.344681
[[Badness]]: 0.219050


=== 7-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7.11


[[Comma list]]: 1728/1715, 5103/5000
Comma list: 99/98, 125/121, 385/384


[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -13 -21 -6 }}]
Mapping: {{mapping| 13 0 30 16 45 | 0 1 0 1 0 }}


{{Multival|legend=1| 13 21 6 3 -27 -45 }}
Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 696.296


[[POTE generator]]: ~36/35 = 38.567
Optimal ET sequence: {{Optimal ET sequence| 13d, 26, 91cd }}


{{Val list|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
Badness: 0.098847


[[Badness]]: 0.107348
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=== 11-limit  ===
Comma list: 78/77, 99/98, 125/121, 1200/1183
Subgroup: 2.3.5.7.11


Comma list: 121/120, 441/440, 891/875
Mapping: {{mapping| 13 0 30 16 45 48 | 0 1 0 1 0 0 }}


Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -13 -21 -6 -17 }}]
Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 695.879


POTE generator: ~36/35 = 38.565
Optimal ET sequence: {{Optimal ET sequence| 13d, 26, 91cdf }}


Vals: {{val list| 31, 156ce, 187ce, 218bcee, 249bcee }}
Badness: 0.059216


Badness: 0.044186
== Pentorwell ==
[[Subgroup]]: 2.3.5.7


=== 13-limit  ===
[[Comma list]]: 1728/1715, 179200/177147
Subgroup: 2.3.5.7.11.13


Comma list: 66/65, 121/120, 343/338, 441/440
{{Mapping|legend=1| 5 0 -36 22 | 0 1 6 -1 }}


Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -13 -21 -6 -17 -9 }}]
[[Optimal tuning]]s:  
* [[CTE]]: ~280/243 = 1\5, ~3/2 = 704.3709 (~64/63 = 15.6291)
* [[POTE]]: ~280/243 = 1\5, ~3/2 = 704.9128 (~64/63 = 15.0872)


POTE generator: ~36/35 = 38.444
{{Optimal ET sequence|legend=1| 5, 75, 80 }}


Vals: {{val list| 31, 94cff, 125cff }}
[[Badness]]: 0.148665


Badness: 0.038116
=== 11-limit ===
Subgroup: 2.3.5.7.11


== Pentorwell  ==
Comma list: 896/891, 1728/1715, 2200/2187
Subgroup: 2.3.5.7


Comma list: 1728/1715, 179200/177147
Mapping: {{mapping| 5 0 -36 22 57 | 0 1 6 -1 -5 }}


Mapping: [{{val| 5 8 12 14 }}, {{val| 0 -1 -6 1 }}]
Optimal tunings:  
* CTE: ~55/48 = 1\5, ~3/2 = 704.8440 (~99/98 = 15.1560)
* POTE: ~55/48 = 1\5, ~3/2 = 704.8788 (~99/98 = 15.1212)


POTE generator: ~7/4 = 975.0872
Optimal ET sequence: {{Optimal ET sequence| 75e, 80, 315bcdddee }}


{{Val list|legend=1| 5, 75, 80 }}
Badness: 0.071702


Badness: 0.148665
=== 13-limit ===
 
Subgroup: 2.3.5.7.11.13
=== 11-limit ===
Subgroup: 2.3.5.7.11


Comma list: 896/891, 1728/1715, 2200/2187
Comma list: 325/324, 352/351, 364/363, 1728/1715


Mapping: [{{val| 5 8 12 14 17 }}, {{val| 0 -1 -6 1 5 }}]
Mapping: {{mapping| 5 0 -36 22 57 82 | 0 1 6 -1 -5 -8 }}


POTE generator: ~7/4 = 975.1212
Optimal tunings:  
* CTE: ~55/48 = 1\5, ~3/2 = 704.7636 (~99/98 = 15.2364)
* CWE: ~55/48 = 1\5, ~3/2 = 704.7112 (~99/98 = 15.2882)


Vals: {{val list| 5, 75e, 80 }}
Optimal ET sequence: {{Optimal ET sequence| 75e, 80, 155de }}


Badness: 0.071702
Badness: 0.0557


[[Category:Regular temperament theory]]
[[Category:Temperament collections]]
[[Category:Temperament collection]]
[[Category:Pages with mostly numerical content]]
[[Category:Orwellismic temperaments| ]] <!-- main article -->
[[Category:Orwellismic temperaments| ]] <!-- main article -->
[[Category:Orwellismic| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
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