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 | Temperaments considered below are secant, infraorwell, quartonic, sentinel, diesic, philips, triskaidekic, and pentorwell. Discussed elsewhere are: | ||
* ''[[Beep]]'' | * ''[[Beep]]'' (+21/20 or 27/25) → [[Bug family #Beep|Bug family]] | ||
* ''[[Doublewide]]'' | * ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide|Jubilismic clan]] | ||
* [[Superpyth]] | * [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth|Archytas clan]] | ||
* ''[[Mothra]]'' | * ''[[Mothra]]'' (+81/80) → [[Meantone family #Mothra|Meantone family]] | ||
* [[Myna]] | * [[Myna]] (+126/125) → [[Starling temperaments #Myna|Starling temperaments]] | ||
* [[Orwell]] | * [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]] | ||
* ''[[Secund]]'' | * ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]] | ||
* ''[[Buzzard]]'' | * ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]] | ||
* ''[[Trimabila]]'' | * ''[[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|legend=1| 2 1 0 5 | 0 7 15 2 }} | |||
: Mapping generators: ~567/400, ~10/9 | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~10/9 = 185.885 | ||
{{ | {{Optimal ET sequence|legend=1| 26, 58, 84, 142, 368cd }} | ||
[[Badness]]: 0.095278 | [[Badness]]: 0.095278 | ||
Line 32: | Line 35: | ||
Comma list: 441/440, 1344/1331, 1728/1715 | Comma list: 441/440, 1344/1331, 1728/1715 | ||
Mapping: | Mapping: {{mapping| 2 1 0 5 6 | 0 7 15 2 3 }} | ||
POTE | Optimal tuning (POTE): ~99/70 = 1\2, ~10/9 = 185.962 | ||
Optimal | Optimal ET sequence: {{Optimal ET sequence| 26, 58, 142e, 200cdee }} | ||
Badness: 0.046373 | Badness: 0.046373 | ||
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Comma list: 144/143, 351/350, 364/363, 441/440 | Comma list: 144/143, 351/350, 364/363, 441/440 | ||
Mapping: | Mapping: {{mapping| 2 1 0 5 6 4 | 0 7 15 2 3 11 }} | ||
POTE | Optimal tuning (POTE): ~99/70 = 1\2, ~10/9 = 185.955 | ||
Optimal | Optimal ET sequence: {{Optimal ET sequence| 26, 58, 84, 142ef }} | ||
Badness: 0.025035 | Badness: 0.025035 | ||
== | === 17-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7.11.13.17 | ||
Comma list: 144/143, 170/169, 221/220, 351/350, 441/440 | |||
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 ET sequence: {{Optimal ET sequence| 26, 58, 84, 142ef }} | |||
Badness: 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: {{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 ET sequence: {{Optimal ET sequence| 26, 58h, 84, 142efh, 226deefgh }} | |||
Badness: 0.018565 | |||
== Infraorwell == | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 1728/1715, 28672/28125 | |||
{{Mapping|legend=1| 1 14 0 16 | 0 -16 3 -17 }} | |||
Mapping: | : Mapping generators: ~2, ~12/7 | ||
POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 269.032 | ||
Optimal | {{Optimal ET sequence|legend=1| 9, 49, 58, 165cd, 223bcd }} | ||
[[Badness]]: 0.117073 | |||
[[Badness]]: 0. | |||
=== 11-limit === | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: 176/175, 540/539, | Comma list: 176/175, 540/539, 1344/1331 | ||
Mapping: | Mapping: {{mapping| 1 14 0 16 12 | 0 -16 3 -17 -11 }} | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.036 | ||
Optimal | Optimal ET sequence: {{Optimal ET sequence| 9, 49, 58, 165cdee }} | ||
Badness: 0. | Badness: 0.040721 | ||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Comma list: | Comma list: 144/143, 176/175, 196/195, 364/363 | ||
Mapping: | Mapping: {{mapping| 1 14 0 16 12 20 | 0 -16 3 -17 -11 -21 }} | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.021 | ||
Optimal | Optimal ET sequence: {{Optimal ET sequence| 9, 49f, 58 }} | ||
Badness: 0. | Badness: 0.023683 | ||
== Sentinel == | == Sentinel == | ||
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Sentinel]].'' | : ''For the 5-limit version of this temperament, see [[High badness temperaments #Sentinel]].'' | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 1728/1715, 3645/3584 | [[Comma list]]: 1728/1715, 3645/3584 | ||
{{Mapping|legend=1| 1 3 -3 6 | 0 -4 15 -9 }} | |||
: Mapping generators: ~2, ~9/7 | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.596 | ||
{{ | {{Optimal ET sequence|legend=1| 14, 17, 31, 110, 141, 172b, 375bc }} | ||
[[Badness]]: 0.093805 | [[Badness]]: 0.093805 | ||
Line 250: | Line 145: | ||
Comma list: 99/98, 243/242, 385/384 | Comma list: 99/98, 243/242, 385/384 | ||
Mapping: | Mapping: {{mapping| 1 3 -3 6 7 | 0 -4 15 -9 -10 }} | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.550 | ||
Optimal | Optimal ET sequence: {{Optimal ET sequence| 14, 17, 31, 79, 110e, 141e }} | ||
Badness: 0.039595 | Badness: 0.039595 | ||
Line 263: | Line 158: | ||
Comma list: 99/98, 105/104, 144/143, 243/242 | Comma list: 99/98, 105/104, 144/143, 243/242 | ||
Mapping: | Mapping: {{mapping| 1 3 -3 6 7 3 | 0 -4 15 -9 -10 2 }} | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.501 | ||
Optimal | Optimal ET sequence: {{Optimal ET sequence| 14, 17, 31, 79f, 110ef, 141ef }} | ||
Badness: 0.037408 | Badness: 0.037408 | ||
Line 274: | Line 169: | ||
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Diesic]].'' | : ''For the 5-limit version of this temperament, see [[High badness temperaments #Diesic]].'' | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 1728/1715, 5103/5000 | [[Comma list]]: 1728/1715, 5103/5000 | ||
{{Mapping|legend=1| 1 2 3 3 | 0 -13 -21 -6 }} | |||
: Mapping generators: ~2, ~36/35 | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 38.567 | ||
{{ | {{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }} | ||
[[Badness]]: 0.107348 | [[Badness]]: 0.107348 | ||
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Comma list: 121/120, 441/440, 891/875 | Comma list: 121/120, 441/440, 891/875 | ||
Mapping: | Mapping: {{mapping| 1 2 3 3 4 | 0 -13 -21 -6 -17 }} | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.565 | ||
Optimal | Optimal ET sequence: {{Optimal ET sequence| 31, 156ce, 187ce, 218bcee, 249bcee }} | ||
Badness: 0.044186 | Badness: 0.044186 | ||
Line 306: | Line 201: | ||
Comma list: 66/65, 121/120, 343/338, 441/440 | Comma list: 66/65, 121/120, 343/338, 441/440 | ||
Mapping: | Mapping: {{mapping| 1 2 3 3 4 4 | 0 -13 -21 -6 -17 -9 }} | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.444 | ||
Optimal | Optimal ET sequence: {{Optimal ET sequence| 31, 94cff, 125cff }} | ||
Badness: 0.038116 | Badness: 0.038116 | ||
Line 317: | Line 212: | ||
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Phillips]].'' | : ''For the 5-limit version of this temperament, see [[High badness temperaments #Phillips]].'' | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 1728/1715, 6561/6272 | [[Comma list]]: 1728/1715, 6561/6272 | ||
{{Mapping|legend=1| 2 0 33 -7 | 0 1 -9 4 }} | |||
: Mapping generators: ~81/56, ~3 | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~81/56 = 1\2, ~3/2 = 691.174 | ||
{{ | {{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc }} | ||
[[Badness]]: 0.228602 | [[Badness]]: 0.228602 | ||
Line 336: | Line 231: | ||
Comma list: 99/98, 385/384, 729/704 | Comma list: 99/98, 385/384, 729/704 | ||
Mapping: | Mapping: {{mapping| 2 0 33 -7 -12 | 0 1 -9 4 6 }} | ||
POTE | Optimal tuning (POTE): ~63/44 = 1\2, ~3/2 = 691.040 | ||
Optimal | Optimal ET sequence: {{Optimal ET sequence| 14, 26, 40, 66b }} | ||
Badness: 0.095777 | Badness: 0.095777 | ||
Line 347: | Line 242: | ||
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Triskaidekic]].'' | : ''For the 5-limit version of this temperament, see [[High badness temperaments #Triskaidekic]].'' | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 1728/1715, 1875/1792 | [[Comma list]]: 1728/1715, 1875/1792 | ||
{{Mapping|legend=1| 13 0 30 16 | 0 1 0 1 }} | |||
: Mapping generators: ~15/14, ~3 | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~15/14 = 1\13, ~3/2 = 694.143 | ||
{{ | {{Optimal ET sequence|legend=1| 13d, 26 }} | ||
[[Badness]]: 0.219050 | [[Badness]]: 0.219050 | ||
Line 366: | Line 261: | ||
Comma list: 99/98, 125/121, 385/384 | Comma list: 99/98, 125/121, 385/384 | ||
Mapping: | Mapping: {{mapping| 13 0 30 16 45 | 0 1 0 1 0 }} | ||
POTE | Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 696.296 | ||
Optimal | Optimal ET sequence: {{Optimal ET sequence| 13d, 26, 91cd }} | ||
Badness: 0.098847 | Badness: 0.098847 | ||
Line 379: | Line 274: | ||
Comma list: 78/77, 99/98, 125/121, 1200/1183 | Comma list: 78/77, 99/98, 125/121, 1200/1183 | ||
Mapping: | Mapping: {{mapping| 13 0 30 16 45 48 | 0 1 0 1 0 0 }} | ||
POTE | Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 695.879 | ||
Optimal | Optimal ET sequence: {{Optimal ET sequence| 13d, 26, 91cdf }} | ||
Badness: 0.059216 | Badness: 0.059216 | ||
== Pentorwell == | == Pentorwell == | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 1728/1715, 179200/177147 | [[Comma list]]: 1728/1715, 179200/177147 | ||
{{Mapping|legend=1| 5 0 -36 22 | 0 1 6 -1 }} | |||
[[POTE | [[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 | [[Badness]]: 0.148665 | ||
Line 405: | Line 302: | ||
Comma list: 896/891, 1728/1715, 2200/2187 | Comma list: 896/891, 1728/1715, 2200/2187 | ||
Mapping: | Mapping: {{mapping| 5 0 -36 22 57 | 0 1 6 -1 -5 }} | ||
POTE | 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 | Optimal ET sequence: {{Optimal ET sequence| 75e, 80, 315bcdddee }} | ||
Badness: 0.071702 | Badness: 0.071702 | ||
[[Category: | === 13-limit === | ||
[[Category: | 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 temperaments| ]] <!-- main article --> | ||
[[Category:Orwellismic| ]] <!-- key article --> | |||
[[Category:Rank 2]] | [[Category:Rank 2]] |