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Orwellismic temperaments: Difference between revisions

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__FORCETOC__
{{Technical data page}}
These temper out |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 [[Meantone family|cynder]], [[Archytas clan|superpyth]], [[Starling temperaments|myna]], [[Hemifamity temperaments|buzzard]], [[Jubilismic clan|doublewide]], [[Bug family|beep]], and [[Semicomma family|orwell]].
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]]
* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide|Jubilismic clan]]
* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth|Archytas clan]]
* ''[[Mothra]]'' (+81/80) → [[Meantone family #Mothra|Meantone family]]
* [[Myna]] (+126/125) → [[Starling temperaments #Myna|Starling temperaments]]
* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]
* ''[[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 ==
Commas: 1728/1715, 177147/175000
[[Subgroup]]: 2.3.5.7


POTE generator: ~10/9 = 185.885
[[Comma list]]: 1728/1715, 177147/175000


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


Wedgie: <<14 30 4 15 -33 -75|
: Mapping generators: ~567/400, ~10/9


EDOs: {{EDOs|26, 58, 84, 142, 368cd}}
[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~10/9 = 185.885


Badness: 0.0953
{{Optimal ET sequence|legend=1| 26, 58, 84, 142, 368cd }}


==11-limit==
[[Badness]]: 0.095278
Commas: 441/440, 1344/1331, 1728/1715


POTE genertor: ~10/9 = 185.962
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [<2 1 0 5 6|, <0 7 15 2 3|]
Comma list: 441/440, 1344/1331, 1728/1715


EDOs: {{EDOs|26, 58, 142e, 200cde}}
Mapping: {{mapping| 2 1 0 5 6 | 0 7 15 2 3 }}


Badness: 0.0464
Optimal tuning (POTE): ~99/70 = 1\2, ~10/9 = 185.962


==13-limit==
Optimal ET sequence: {{Optimal ET sequence| 26, 58, 142e, 200cdee }}
Commas: 144/143, 351/350, 364/363, 441/440


POTE generator: ~10/9 = 185.955
Badness: 0.046373


Map: [<2 1 0 5 6 4|, <0 7 15 2 3 11|]
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


EDOs: {{EDOs|26, 58, 84, 142ef}}
Comma list: 144/143, 351/350, 364/363, 441/440


Badness: 0.0250
Mapping: {{mapping| 2 1 0 5 6 4 | 0 7 15 2 3 11 }}


=Infraorwell=
Optimal tuning (POTE): ~99/70 = 1\2, ~10/9 = 185.955
Commas: 1728/1715, 28672/28125


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


Map: [<1 14 0 16|, <0 -16 3 -17|]
Badness: 0.025035


Wedgie: <<16 -3 17 -42 -18 48||
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


EDOs: {{EDOs|9, 49, 58, 165cd, 223bcd}}
Comma list: 144/143, 170/169, 221/220, 351/350, 441/440


Badness: 0.1171
Mapping: {{mapping| 2 1 0 5 6 4 6 | 0 7 15 2 3 11 7 }}


==11-limit==
Optimal tuning (POTE): ~17/12 = 1\2, ~10/9 = 185.916
Commas: 176/175, 540/539, 1344/1331


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


Map: [<1 14 0 16 12|, <0 -16 3 -17 -11|]
Badness: 0.021642


EDOs: {{EDOs|9, 49, 58, 165cde}}
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19


Badness: 0.0407
Comma list: 144/143, 153/152, 170/169, 210/209, 221/220, 400/399


==13-limit==
Mapping: {{mapping| 2 1 0 5 6 4 6 2 | 0 7 15 2 3 11 7 21 }}
Commas: 144/143, 176/175, 196/195, 364/363


POTE generator: ~7/6 = 269.021
Optimal tuning (POTE): ~17/12 = 1\2, ~10/9 = 185.858


Map: [<1 14 0 16 12 20|, <0 -16 3 -17 -11 -21|]
Optimal ET sequence: {{Optimal ET sequence| 26, 58h, 84, 142efh, 226deefgh }}


EDOs: {{EDOs|9, 49f, 58}}
Badness: 0.018565


Badness: 0.0237
== Infraorwell ==
[[Subgroup]]: 2.3.5.7


=Quartonic=
[[Comma list]]: 1728/1715, 28672/28125
Comma: 390625000/387420489


POTE generator: ~250/243 = 45.233
{{Mapping|legend=1| 1 14 0 16 | 0 -16 3 -17 }}


Map: [<1 2 3|, <0 -11 -18|]
: Mapping generators: ~2, ~12/7


EDOs: {{EDOs|26, 27, 53, 239, 292, 345, 398, 451}}
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 269.032


Badness: 0.1172
{{Optimal ET sequence|legend=1| 9, 49, 58, 165cd, 223bcd }}


==7-limit==
[[Badness]]: 0.117073
Commas: 1728/1715, 4000/3969


POTE generator: ~36/35 = 45.139
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [<1 2 3 3|, <0 -11 -18 -5|]
Comma list: 176/175, 540/539, 1344/1331


Wedgie: <<11 18 5 3 -23 -39||
Mapping: {{mapping| 1 14 0 16 12 | 0 -16 3 -17 -11 }}


EDOs: {{EDOs|26, 27, 53, 80, 133d, 186d, 319d}}
Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.036


Badness: 0.0426
Optimal ET sequence: {{Optimal ET sequence| 9, 49, 58, 165cdee }}


==11-limit==
Badness: 0.040721
Commas: 176/175, 540/539, 2200/2187


POTE generator: ~36/35 = 45.041
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Map: [<1 2 3 3 5|, <0 -11 -18 -5 -41|]
Comma list: 144/143, 176/175, 196/195, 364/363


EDOs: {{EDOs|53, 80, 213d, 293bcd}}
Mapping: {{mapping| 1 14 0 16 12 20 | 0 -16 3 -17 -11 -21 }}


Badness: 0.034
Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.021


==13-limit==
Optimal ET sequence: {{Optimal ET sequence| 9, 49f, 58 }}
Commas: 169/168, 176/175, 325/324, 540/539


POTE generator: ~36/35 = 45.080
Badness: 0.023683


Map: [<1 2 3 3 5 4|, <0 -11 -18 -5 -41 -8|]
== Sentinel ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Sentinel]].''


EDOs: {{EDOs|53, 80, 133d, 213d}}
[[Subgroup]]: 2.3.5.7


Badness: 0.0239
[[Comma list]]: 1728/1715, 3645/3584


==Quarto==
{{Mapping|legend=1| 1 3 -3 6 | 0 -4 15 -9 }}
Commmas: 100/99, 245/242, 864/847


POTE generator: ~36/35 = 45.132
: Mapping generators: ~2, ~9/7


Map: [<1 2 3 3 4|, <0 -11 -18 -5 -14|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.596


EDOs: {{EDOs|26, 27e, 53e, 80e}}
{{Optimal ET sequence|legend=1| 14, 17, 31, 110, 141, 172b, 375bc }}


Badness: 0.0418
[[Badness]]: 0.093805


===13-limit===
=== 11-limit ===
Commas: 78/77, 100/99, 144/143, 245/242
Subgroup: 2.3.5.7.11


POTE generator: ~36/35 = 45.205
Comma list: 99/98, 243/242, 385/384


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


EDOs: {{EDOs|26, 27e, 53e}}
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.550


Badness: 0.0277
Optimal ET sequence: {{Optimal ET sequence| 14, 17, 31, 79, 110e, 141e }}


==Quartz==
Badness: 0.039595
Commas: 99/98, 385/384, 4000/3969


POTE generator: ~36/35 = 45.385
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Map: [<1 2 3 3 3|, <0 -11 -18 -5 12|]
Comma list: 99/98, 105/104, 144/143, 243/242


EDOs: {{EDOs|26, 53}}
Mapping: {{mapping| 1 3 -3 6 7 3 | 0 -4 15 -9 -10 2 }}


Badness: 0.0533
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.501


===13-limit===
Optimal ET sequence: {{Optimal ET sequence| 14, 17, 31, 79f, 110ef, 141ef }}
Commas: 99/98, 169/168, 275/273, 385/384


POTE generator: ~36/35 = 45.387
Badness: 0.037408


Map: [<1 2 3 3 3 4|, <0 -11 -18 -5 12 -8|]
== Diesic ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Diesic]].''


EDOs: {{EDOs|26, 53, 132e, 185cdef, 238cdef}}
[[Subgroup]]: 2.3.5.7


Badness: 0.0288
[[Comma list]]: 1728/1715, 5103/5000


=Sentinel=
{{Mapping|legend=1| 1 2 3 3 | 0 -13 -21 -6 }}
Comma: 8968066875/8589934592


POTE generator: ~512/405 = 425.474
: Mapping generators: ~2, ~36/35


Map: [<1 3 -3|, <0 -4 15|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 38.567


EDOs: {{EDOs|14, 17, 31, 79, 110, 361bc}}
{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}


Badness: 0.7234
[[Badness]]: 0.107348


==7-limit==
=== 11-limit ===
Commas: 1728/1715, 3645/3584
Subgroup: 2.3.5.7.11


POTE generator: ~9/7 = 425.596
Comma list: 121/120, 441/440, 891/875


Map: [<1 3 -3 6|, <0 -4 15 -9|]
Mapping: {{mapping| 1 2 3 3 4 | 0 -13 -21 -6 -17 }}


Wedgie: <<4 -15 9 -33 3 63||
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.565


EDOs: {{EDOs|14, 17, 31, 110, 141, 172b, 375bc}}
Optimal ET sequence: {{Optimal ET sequence| 31, 156ce, 187ce, 218bcee, 249bcee }}


Badness: 0.0938
Badness: 0.044186


==11-limit==
=== 13-limit ===
Commas: 99/98, 243/242, 385/384
Subgroup: 2.3.5.7.11.13


POTE generator: ~9/7 = 425.550
Comma list: 66/65, 121/120, 343/338, 441/440


Map: [<1 3 -3 6 7|, <0 -4 15 -9 -10|]
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -13 -21 -6 -17 -9 }}


EDOs: {{EDOs|14, 17, 31, 79, 110e, 141e}}
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.444


Badness: 0.0396
Optimal ET sequence: {{Optimal ET sequence| 31, 94cff, 125cff }}


==13-limit==
Badness: 0.038116
Commas: 99/98, 105/104, 144/143, 243/242


POTE generator: ~9/7 = 425.501
== Phillips ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Phillips]].''


Map: [<1 3 -3 6 7 3|, <0 -4 15 -9 -10 2|]
[[Subgroup]]: 2.3.5.7


EDOs: {{EDOs|14, 17, 31, 79f, 110ef, 141ef}}
[[Comma list]]: 1728/1715, 6561/6272


Badness: 0.0374
{{Mapping|legend=1| 2 0 33 -7 | 0 1 -9 4 }}


=Diesic=
: Mapping generators: ~81/56, ~3
Comma: 10460353203/9765625000


POTE generator: ~6561/6250 = 38.571
[[Optimal tuning]] ([[POTE]]): ~81/56 = 1\2, ~3/2 = 691.174


Map: [<1 2 3|, <0 -13 -21|]
{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc }}


EDOs: {{EDOs|31, 156c, 187c, 218bc, 249bc, 280bc}}
[[Badness]]: 0.228602


Badness: 1.3447
=== 11-limit ===
Subgroup: 2.3.5.7.11


==7-limit==
Comma list: 99/98, 385/384, 729/704
Commas: 1728/1715, 5103/5000


POTE generator: ~36/35 = 38.567
Mapping: {{mapping| 2 0 33 -7 -12 | 0 1 -9 4 6 }}


Map: [<1 2 3 3|, <0 -13 -21 -6|]
Optimal tuning (POTE): ~63/44 = 1\2, ~3/2 = 691.040


Wedgie: <<13 21 6 3 -27 -45||
Optimal ET sequence: {{Optimal ET sequence| 14, 26, 40, 66b }}


EDOs: {{EDOs|31, 156c, 187c, 218bc, 249bc, 280bc}}
Badness: 0.095777


Badness: 0.1073
== Triskaidekic ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Triskaidekic]].''


==11-limit==
[[Subgroup]]: 2.3.5.7
Commas: 121/120, 441/440, 891/875


POTE generator: ~36/35 = 38.565
[[Comma list]]: 1728/1715, 1875/1792


Map: [<1 2 3 3 4|, <0 -13 -21 -6 -17|]
{{Mapping|legend=1| 13 0 30 16 | 0 1 0 1 }}


EDOs: {{EDOs|31, 156ce, 187ce, 218bce, 249bce}}
: Mapping generators: ~15/14, ~3


Badness: 0.0442
[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\13, ~3/2 = 694.143


==13-limit==
{{Optimal ET sequence|legend=1| 13d, 26 }}
Commas: 66/65, 121/120, 343/338, 441/440


POTE generator: ~36/35 = 38.444
[[Badness]]: 0.219050


Map: [<1 2 3 3 4 4|, <0 -13 -21 -6 -17 -9|]
=== 11-limit ===
Subgroup: 2.3.5.7.11


EDOs: {{EDOs|31, 94cf, 125cf}}
Comma list: 99/98, 125/121, 385/384


Badness: 0.0381
Mapping: {{mapping| 13 0 30 16 45 | 0 1 0 1 0 }}


[[Category:Temperament]]
Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 696.296
 
Optimal ET sequence: {{Optimal ET sequence| 13d, 26, 91cd }}
 
Badness: 0.098847
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 78/77, 99/98, 125/121, 1200/1183
 
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 ET sequence: {{Optimal ET sequence| 13d, 26, 91cdf }}
 
Badness: 0.059216
 
== Pentorwell ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1728/1715, 179200/177147
 
{{Mapping|legend=1| 5 0 -36 22 | 0 1 6 -1 }}
 
[[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)
 
{{Optimal ET sequence|legend=1| 5, 75, 80 }}
 
[[Badness]]: 0.148665
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 896/891, 1728/1715, 2200/2187
 
Mapping: {{mapping| 5 0 -36 22 57 | 0 1 6 -1 -5 }}
 
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)
 
Optimal ET sequence: {{Optimal ET sequence| 75e, 80, 315bcdddee }}
 
Badness: 0.071702
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 352/351, 364/363, 1728/1715
 
Mapping: {{mapping| 5 0 -36 22 57 82 | 0 1 6 -1 -5 -8 }}
 
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)
 
Optimal ET sequence: {{Optimal ET sequence| 75e, 80, 155de }}
 
Badness: 0.0557
 
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]
[[Category:Orwellismic temperaments| ]] <!-- main article -->
[[Category:Orwellismic| ]] <!-- key article -->
[[Category:Rank 2]]
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