Orwellismic temperaments: Difference between revisions

Revision as of 10:49, 17 September 2023

These temper out [6 3 -1 -3⟩ = 1728/1715, the orwellisma.

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

Beep (+21/20 or 27/25) → Bug family
Doublewide (+50/49) → Jubilismic clan
Superpyth (+64/63) → Archytas clan
Mothra (+81/80) → Meantone family
Myna (+126/125) → Starling temperaments
Orwell (+225/224) → Semicomma family
Secund (+405/392 or 525/512) → Greenwoodmic temperaments
Buzzard (+5120/5103) → Vulture family
Trisensory (+78732/78125) → Sensipent family
Trimabila (+268435456/263671875) → Mabila family

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

Wedgie: ⟨⟨ 14 30 4 15 -33 -75 ]]

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

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

Badness: 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 = 1\2, ~10/9 = 185.962

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

Badness: 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 = 1\2, ~10/9 = 185.955

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

Badness: 0.025035

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

Wedgie: ⟨⟨ 16 -3 17 -42 -18 48 ]]

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

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

Badness: 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 = 1\1, ~7/6 = 269.036

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

Badness: 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 = 1\1, ~7/6 = 269.021

Optimal ET sequence: 9, 49f, 58

Badness: 0.023683

Quartonic

Quartonic tempers out the quartonic comma, [3 -18 11⟩ = 390625000/387420489 in the 5-limit. This temperament can be described as 26 & 27 temperament, which tempers out the orwellisma and the octagar comma, 4000/3969. The name "quartonic" means quarter-tone, which is the generator of this temperament (representing ~36/35 and ~40/39). Alternative extension yarman (80 & 159) slices the quartonic generator in three.

Subgroup: 2.3.5

Comma list: 390625000/387420489

Mapping: [⟨1 2 3], ⟨0 -11 -18]]

mapping generators: ~2, ~250/243

Optimal tuning (POTE): ~2 = 1\1, ~250/243 = 45.233

Optimal ET sequence: 26, 27, 53, 239, 292, 345, 398, 451

Badness: 0.117250

7-limit

Subgroup: 2.3.5.7

Comma list: 1728/1715, 4000/3969

Mapping: [⟨1 2 3 3], ⟨0 -11 -18 -5]]

Wedgie: ⟨⟨ 11 18 5 3 -23 -39 ]]

Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.139

Optimal ET sequence: 26, 27, 53, 80, 133d, 186d, 319d

Badness: 0.042632

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 540/539, 2200/2187

Mapping: [⟨1 2 3 3 5], ⟨0 -11 -18 -5 -41]]

Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.041

Optimal ET sequence: 26e, 27e, 53, 80, 213d, 293bcd

Badness: 0.034031

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 176/175, 325/324, 540/539

Mapping: [⟨1 2 3 3 5 4], ⟨0 -11 -18 -5 -41 -8]]

Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.080

Optimal ET sequence: 26e, 27e, 53, 80, 133d, 213d

Badness: 0.023875

Quarto

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/242, 864/847

Mapping: [⟨1 2 3 3 4], ⟨0 -11 -18 -5 -14]]

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

Optimal ET sequence: 26, 27e, 53e, 80e

Badness: 0.041786

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 78/77, 100/99, 144/143, 245/242

Mapping: [⟨1 2 3 3 4 4], ⟨0 -11 -18 -5 -14 -8]]

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

Optimal ET sequence: 26, 27e, 53e

Badness: 0.027692

Quartz

Subgroup: 2.3.5.7.11

Comma list: 99/98, 385/384, 4000/3969

Mapping: [⟨1 2 3 3 3], ⟨0 -11 -18 -5 12]]

Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.385

Optimal ET sequence: 26, 53

Badness: 0.053285

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 169/168, 275/273, 385/384

Mapping: [⟨1 2 3 3 3 4], ⟨0 -11 -18 -5 12 -8]]

Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.387

Optimal ET sequence: 26, 53, 132e, 185cdef, 238cdef

Badness: 0.028818

Biquartonic

Subgroup: 2.3.5.7.11

Comma list: 1728/1715, 2420/2401, 2560/2541

Mapping: [⟨2 4 6 6 7], ⟨0 -11 -18 -5 -1]]

Optimal tuning (POTE): ~99/70 = 1\2, ~36/35 = 45.129

Optimal ET sequence: 26, 54c, 80, 186de, 266dde

Badness: 0.060737

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 325/324, 364/363, 640/637

Mapping: [⟨2 4 6 6 7 8], ⟨0 -11 -18 -5 -1 -8]]

Optimal tuning (POTE): ~55/39 = 1\2, ~36/35 = 45.153

Optimal ET sequence: 26, 54c, 80, 106, 186de

Badness: 0.039891

Yarm

Subgroup: 2.3.5.7.11

Comma list: 1331/1323, 1728/1715, 4000/3969

Mapping: [⟨1 2 3 3 4], ⟨0 -33 -54 -15 -43]]

Optimal tuning (POTE): ~2 = 1\1, ~100/99 = 15.046

Optimal ET sequence: 79, 80, 239dd, 319dd

Badness: 0.099950

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 325/324, 640/637, 1331/1323

Mapping: [⟨1 2 3 3 4 4], ⟨0 -33 -54 -15 -43 -24]]

Optimal tuning (POTE): ~2 = 1\1, ~100/99 = 15.060

Optimal ET sequence: 79, 80, 159d, 239dd

Badness: 0.061645

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 169/168, 325/324, 561/560, 640/637, 850/847

Mapping: [⟨1 2 3 3 4 4 4], ⟨0 -33 -54 -15 -43 -24 7]]

Optimal tuning (POTE): ~2 = 1\1, ~100/99 = 15.066

Optimal ET sequence: 79, 80, 159d, 239dd

Badness: 0.046718

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

Wedgie: ⟨⟨ 4 -15 9 -33 3 63 ]]

Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.596

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

Badness: 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 = 1\1, ~9/7 = 425.550

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

Badness: 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 = 1\1, ~9/7 = 425.501

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

Badness: 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

Wedgie: ⟨⟨ 13 21 6 3 -27 -45 ]]

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

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

Badness: 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 = 1\1, ~36/35 = 38.565

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

Badness: 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 = 1\1, ~36/35 = 38.444

Optimal ET sequence: 31, 94cff, 125cff

Badness: 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

Wedgie: ⟨⟨ 2 -18 8 -33 7 69 ]]

Optimal tuning (POTE): ~81/56 = 1\2, ~3/2 = 691.174

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

Badness: 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 = 1\2, ~3/2 = 691.040

Optimal ET sequence: 14, 26, 40, 66b

Badness: 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

Wedgie: ⟨⟨ 13 0 13 -30 -16 30 ]]

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

Optimal ET sequence: 13d, 26

Badness: 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 = 1\13, ~3/2 = 696.296

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: [⟨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: 13d, 26, 91cdf

Badness: 0.059216

Pentorwell

Subgroup: 2.3.5.7

Comma list: 1728/1715, 179200/177147

Mapping: [⟨5 8 12 14], ⟨0 -1 -6 1]]

Optimal tuning (POTE): ~280/243 = 1\5, ~7/4 = 975.0872

Optimal ET sequence: 5, 75, 80

Badness: 0.148665

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨5 8 12 14 17], ⟨0 -1 -6 1 5]]

Optimal tuning (POTE): ~55/48 = 1\5, ~7/4 = 975.1212

Optimal ET sequence: 5, 75e, 80

Badness: 0.071702

Orwellismic temperaments: Difference between revisions

Revision as of 10:49, 17 September 2023

Contents

Secant

11-limit

13-limit

Infraorwell

11-limit

13-limit

Quartonic

7-limit

11-limit

13-limit

Quarto

13-limit

Quartz

13-limit

Biquartonic

13-limit

Yarm

13-limit

17-limit

Sentinel

11-limit

13-limit

Diesic

11-limit

13-limit

Phillips

11-limit

Triskaidekic

11-limit

13-limit

Pentorwell

11-limit

Navigation menu

@@ Line 1: / Line 1: @@
 These temper out {{monzo| 6 3 -1 -3 }} = 1728/1715, the orwellisma.
-Temperaments discussed elsewhere 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|Bug family]]
+* ''[[Beep]]'' (+21/20 or 27/25) → [[Bug family #Beep|Bug family]]
-* ''[[Doublewide]]'', {50/49, 875/864} → [[Jubilismic clan #Doublewide|Jubilismic clan]]
+* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide|Jubilismic clan]]
-* [[Superpyth]], {64/63, 245/243} → [[Archytas clan #Superpyth|Archytas clan]]
+* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth|Archytas clan]]
-* ''[[Mothra]]'', {81/80, 1029/1024} → [[Meantone family #Mothra|Meantone family]]
+* ''[[Mothra]]'' (+81/80) → [[Meantone family #Mothra|Meantone family]]
-* [[Myna]], {126/125, 1728/1715} → [[Starling temperaments #Myna|Starling temperaments]]
+* [[Myna]] (+126/125) → [[Starling temperaments #Myna|Starling temperaments]]
-* [[Orwell]], {225/224, 1728/1715} → [[Semicomma family #Orwell|Semicomma family]]
+* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]
-* ''[[Secund]]'', {405/392, 525/512} → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
+* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
-* ''[[Buzzard]]'', {1728/1715, 5120/5103} → [[Hemifamity temperaments #Buzzard|Hemifamity temperaments]]
+* ''[[Buzzard]]'' (+5120/5103) → [[Vulture family #Buzzard|Vulture family]]
-* ''[[Trisensory]]'', {1728/1715, 78732/78125} → [[Sensipent family #Trisensory|Sensipent family]]
+* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory|Sensipent family]]
-* ''[[Trimabila]]'', {1728/1715, 268435456/263671875} → [[Mabila family #Trimabila|Mabila family]]
+* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila|Mabila family]]
 == Secant ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[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 }}
+: mapping generators: ~567/400, ~10/9
 {{Multival|legend=1| 14 30 4 15 -33 -75 }}
-[[POTE generator]]: ~10/9 = 185.885
+[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~10/9 = 185.885
 {{Optimal ET sequence|legend=1| 26, 58, 84, 142, 368cd }}
@@ Line 33: / Line 35: @@
 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
 {{Optimal ET sequence|legend=1| 26, 58, 142e, 200cdee }}
@@ Line 46: / Line 48: @@
 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
 {{Optimal ET sequence|legend=1| 26, 58, 84, 142ef }}
@@ Line 55: / Line 57: @@
 == Infraorwell ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 1728/1715, 28672/28125
-[[Mapping]]: [{{val| 1 14 0 16 }}, {{val| 0 -16 3 -17 }}]
+{{Mapping|legend=1| 1 14 0 16 | 0 -16 3 -17 }}
+: mapping generators: ~2, ~12/7
 {{Multival|legend=1| 16 -3 17 -42 -18 48 }}
-[[POTE generator]]: ~7/6 = 269.032
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 269.032
 {{Optimal ET sequence|legend=1| 9, 49, 58, 165cd, 223bcd }}
@@ Line 74: / Line 78: @@
 Comma list: 176/175, 540/539, 1344/1331
-Mapping: [{{val| 1 14 0 16 12 }}, {{val| 0 -16 3 -17 -11 }}]
+Mapping: {{mapping| 1 14 0 16 12 | 0 -16 3 -17 -11 }}
-POTE generator: ~7/6 = 269.036
+Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.036
 {{Optimal ET sequence|legend=1| 9, 49, 58, 165cdee }}
@@ Line 87: / Line 91: @@
 Comma list: 144/143, 176/175, 196/195, 364/363
-Mapping: [{{val| 1 14 0 16 12 20 }}, {{val| 0 -16 3 -17 -11 -21 }}]
+Mapping: {{mapping| 1 14 0 16 12 20 | 0 -16 3 -17 -11 -21 }}
-POTE generator: ~7/6 = 269.021
+Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.021
 {{Optimal ET sequence|legend=1| 9, 49f, 58 }}
@@ Line 96: / Line 100: @@
 == Quartonic ==
-Quartonic tempers out saleyo comma, {{monzo|3 -18 11}} = 390625000/387420489 in the 5-limit. This temperament can be described as 26&amp;27 temperament, which tempers out the orwellisma and the octagar comma, 4000/3969. The name "quartonic" means quarter-tone, which is the generator of this temperament (representing ~[[36/35]] and ~[[40/39]]). Alternative extension [[Turkish maqam music temperaments|yarman]] (80&amp;159) slices the quartonic generator in three.
+Quartonic tempers out the quartonic comma, {{monzo| 3 -18 11 }} = 390625000/387420489 in the 5-limit. This temperament can be described as 26 &amp; 27 temperament, which tempers out the orwellisma and the octagar comma, 4000/3969. The name "quartonic" means quarter-tone, which is the generator of this temperament (representing ~[[36/35]] and ~[[40/39]]). Alternative extension [[Turkish maqam music temperaments|yarman]] (80 &amp; 159) slices the quartonic generator in three.
-Subgroup: 2.3.5
+[[Subgroup]]: 2.3.5
 [[Comma list]]: 390625000/387420489
-[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -11 -18 }}]
+{{Mapping|legend=1| 1 2 3 | 0 -11 -18 }}
+: mapping generators: ~2, ~250/243
-[[POTE generator]]: ~250/243 = 45.233
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~250/243 = 45.233
 {{Optimal ET sequence|legend=1| 26, 27, 53, 239, 292, 345, 398, 451 }}
@@ Line 111: / Line 117: @@
 === 7-limit ===
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 1728/1715, 4000/3969
-[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -11 -18 -5 }}]
+{{Mapping|legend=1| 1 2 3 3 | 0 -11 -18 -5 }}
 {{Multival|legend=1| 11 18 5 3 -23 -39 }}
-[[POTE generator]]: ~36/35 = 45.139
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 45.139
 {{Optimal ET sequence|legend=1| 26, 27, 53, 80, 133d, 186d, 319d }}
@@ Line 130: / Line 136: @@
 Comma list: 176/175, 540/539, 2200/2187
-Mapping: [{{val| 1 2 3 3 5 }}, {{val| 0 -11 -18 -5 -41 }}]
+Mapping: {{mapping| 1 2 3 3 5 | 0 -11 -18 -5 -41 }}
-POTE generator: ~36/35 = 45.041
+Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.041
 {{Optimal ET sequence|legend=1| 26e, 27e, 53, 80, 213d, 293bcd }}
@@ Line 143: / Line 149: @@
 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 }}]
+Mapping: {{mapping| 1 2 3 3 5 4 | 0 -11 -18 -5 -41 -8 }}
-POTE generator: ~36/35 = 45.080
+Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.080
 {{Optimal ET sequence|legend=1| 26e, 27e, 53, 80, 133d, 213d}}
@@ Line 156: / Line 162: @@
 Comma list: 100/99, 245/242, 864/847
-Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -11 -18 -5 -14 }}]
+Mapping: {{mapping| 1 2 3 3 4 | 0 -11 -18 -5 -14 }}
-POTE generator: ~36/35 = 45.132
+Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.132
 {{Optimal ET sequence|legend=1| 26, 27e, 53e, 80e }}
@@ Line 169: / Line 175: @@
 Comma list: 78/77, 100/99, 144/143, 245/242
-Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -11 -18 -5 -14 -8 }}]
+Mapping: {{mapping| 1 2 3 3 4 4 | 0 -11 -18 -5 -14 -8 }}
-POTE generator: ~36/35 = 45.205
+Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.205
 {{Optimal ET sequence|legend=1| 26, 27e, 53e }}
@@ Line 182: / Line 188: @@
 Comma list: 99/98, 385/384, 4000/3969
-Mapping: [{{val| 1 2 3 3 3 }}, {{val| 0 -11 -18 -5 12 }}]
+Mapping: {{mapping| 1 2 3 3 3 | 0 -11 -18 -5 12 }}
-POTE generator: ~36/35 = 45.385
+Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.385
 {{Optimal ET sequence|legend=1| 26, 53 }}
@@ Line 195: / Line 201: @@
 Comma list: 99/98, 169/168, 275/273, 385/384
-Mapping: [{{val| 1 2 3 3 3 4 }}, {{val| 0 -11 -18 -5 12 -8 }}]
+Mapping: {{mapping| 1 2 3 3 3 4 | 0 -11 -18 -5 12 -8 }}
-POTE generator: ~36/35 = 45.387
+Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.387
 {{Optimal ET sequence|legend=1| 26, 53, 132e, 185cdef, 238cdef}}
@@ Line 208: / Line 214: @@
 Comma list: 1728/1715, 2420/2401, 2560/2541
-Mapping: [{{val|2 4 6 6 7}}, {{val|0 -11 -18 -5 -1}}]
+Mapping: {{mapping| 2 4 6 6 7 | 0 -11 -18 -5 -1 }}
-POTE generator: ~36/35 = 45.129
+Optimal tuning (POTE): ~99/70 = 1\2, ~36/35 = 45.129
 {{Optimal ET sequence|legend=1| 26, 54c, 80, 186de, 266dde }}
@@ Line 221: / Line 227: @@
 Comma list: 169/168, 325/324, 364/363, 640/637
-Mapping: [{{val|2 4 6 6 7 8}}, {{val|0 -11 -18 -5 -1 -8}}]
+Mapping: {{mapping| 2 4 6 6 7 8 | 0 -11 -18 -5 -1 -8 }}
-POTE generator: ~36/35 = 45.153
+Optimal tuning (POTE): ~55/39 = 1\2, ~36/35 = 45.153
 {{Optimal ET sequence|legend=1| 26, 54c, 80, 106, 186de }}
@@ Line 234: / Line 240: @@
 Comma list: 1331/1323, 1728/1715, 4000/3969
-Mapping: [{{val|1 2 3 3 4}}, {{val|0 -33 -54 -15 -43}}]
+Mapping: {{mapping| 1 2 3 3 4 | 0 -33 -54 -15 -43 }}
-POTE generator: ~100/99 = 15.046
+Optimal tuning (POTE): ~2 = 1\1, ~100/99 = 15.046
 {{Optimal ET sequence|legend=1| 79, 80, 239dd, 319dd }}
@@ Line 247: / Line 253: @@
 Comma list: 169/168, 325/324, 640/637, 1331/1323
-Mapping: [{{val|1 2 3 3 4 4}}, {{val|0 -33 -54 -15 -43 -24}}]
+Mapping: {{mapping| 1 2 3 3 4 4 | 0 -33 -54 -15 -43 -24 }}
-POTE generator: ~100/99 = 15.060
+Optimal tuning (POTE): ~2 = 1\1, ~100/99 = 15.060
 {{Optimal ET sequence|legend=1| 79, 80, 159d, 239dd }}
@@ Line 260: / Line 266: @@
 Comma list: 169/168, 325/324, 561/560, 640/637, 850/847
-Mapping: [{{val|1 2 3 3 4 4 4}}, {{val|0 -33 -54 -15 -43 -24 7}}]
+Mapping: {{mapping| 1 2 3 3 4 4 4 | 0 -33 -54 -15 -43 -24 7 }}
-POTE generator: ~100/99 = 15.066
+Optimal tuning (POTE): ~2 = 1\1, ~100/99 = 15.066
 {{Optimal ET sequence|legend=1| 79, 80, 159d, 239dd }}
@@ Line 271: / Line 277: @@
 : ''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
-[[Mapping]]: [{{val| 1 3 -3 6 }}, {{val| 0 -4 15 -9 }}]
+{{Mapping|legend=1| 1 3 -3 6 | 0 -4 15 -9 }}
+: mapping generators: ~2, ~9/7
 {{Multival|legend=1| 4 -15 9 -33 3 63 }}
-[[POTE generator]]: ~9/7 = 425.596
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.596
 {{Optimal ET sequence|legend=1| 14, 17, 31, 110, 141, 172b, 375bc }}
@@ Line 290: / Line 298: @@
 Comma list: 99/98, 243/242, 385/384
-Mapping: [{{val| 1 3 -3 6 7 }}, {{val| 0 -4 15 -9 -10 }}]
+Mapping: {{mapping| 1 3 -3 6 7 | 0 -4 15 -9 -10 }}
-POTE generator: ~9/7 = 425.550
+Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.550
 {{Optimal ET sequence|legend=1| 14, 17, 31, 79, 110e, 141e }}
@@ Line 303: / Line 311: @@
 Comma list: 99/98, 105/104, 144/143, 243/242
-Mapping: [{{val| 1 3 -3 6 7 3 }}, {{val| 0 -4 15 -9 -10 2 }}]
+Mapping: {{mapping| 1 3 -3 6 7 3 | 0 -4 15 -9 -10 2 }}
-POTE generator: ~9/7 = 425.501
+Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.501
 {{Optimal ET sequence|legend=1| 14, 17, 31, 79f, 110ef, 141ef }}
@@ Line 314: / Line 322: @@
 : ''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
-[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -13 -21 -6 }}]
+{{Mapping|legend=1| 1 2 3 3 | 0 -13 -21 -6 }}
+: mapping generators: ~2, ~36/35
 {{Multival|legend=1| 13 21 6 3 -27 -45 }}
-[[POTE generator]]: ~36/35 = 38.567
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 38.567
 {{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
@@ Line 333: / Line 343: @@
 Comma list: 121/120, 441/440, 891/875
-Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -13 -21 -6 -17 }}]
+Mapping: {{mapping| 1 2 3 3 4 | 0 -13 -21 -6 -17 }}
-POTE generator: ~36/35 = 38.565
+Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.565
 {{Optimal ET sequence|legend=1| 31, 156ce, 187ce, 218bcee, 249bcee }}
@@ Line 346: / Line 356: @@
 Comma list: 66/65, 121/120, 343/338, 441/440
-Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -13 -21 -6 -17 -9 }}]
+Mapping: {{mapping| 1 2 3 3 4 4 | 0 -13 -21 -6 -17 -9 }}
-POTE generator: ~36/35 = 38.444
+Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.444
 {{Optimal ET sequence|legend=1| 31, 94cff, 125cff }}
@@ Line 357: / Line 367: @@
 : ''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
-[[Mapping]]: [{{Val|2 0 33 -7}}, {{Val|0 1 -9 4}}]
+{{Mapping|legend=1| 2 0 33 -7 | 0 1 -9 4 }}
-{{Multival|legend=1|2 -18 8 -33 7 69}}
+: mapping generators: ~81/56, ~3
-[[POTE generator]]: ~3/2 = 691.174
+{{Multival|legend=1| 2 -18 8 -33 7 69 }}
+[[Optimal tuning]] ([[POTE]]): ~81/56 = 1\2, ~3/2 = 691.174
 {{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc }}
@@ Line 376: / Line 388: @@
 Comma list: 99/98, 385/384, 729/704
-Mapping: [{{Val|2 0 33 -7 -12}}, {{Val|0 1 -9 4 6}}]
+Mapping: {{mapping| 2 0 33 -7 -12 | 0 1 -9 4 6 }}
-POTE generator: ~3/2 = 691.040
+Optimal tuning (POTE): ~63/44 = 1\2, ~3/2 = 691.040
 {{Optimal ET sequence|legend=1| 14, 26, 40, 66b }}
@@ Line 387: / Line 399: @@
 : ''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
-[[Mapping]]: [{{Val|13 0 30 16}}, {{Val|0 1 0 1}}]
+{{Mapping|legend=1| 13 0 30 16 | 0 1 0 1 }}
+: mapping generators: ~15/14, ~3
-{{Multival|legend=1|13 0 13 -30 -16 30}}
+{{Multival|legend=1| 13 0 13 -30 -16 30 }}
-[[POTE generator]]: ~3/2 = 694.143
+[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\13, ~3/2 = 694.143
 {{Optimal ET sequence|legend=1| 13d, 26 }}
@@ Line 406: / Line 420: @@
 Comma list: 99/98, 125/121, 385/384
-Mapping: [{{Val|13 0 30 16 45}}, {{Val|0 1 0 1 0}}]
+Mapping: {{mapping| 13 0 30 16 45 | 0 1 0 1 0 }}
-POTE generator: ~3/2 = 696.296
+Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 696.296
 {{Optimal ET sequence|legend=1| 13d, 26, 91cd }}
@@ Line 419: / Line 433: @@
 Comma list: 78/77, 99/98, 125/121, 1200/1183
-Mapping: [{{Val|13 0 30 16 45 48}}, {{Val|0 1 0 1 0 0}}]
+Mapping: {{mapping| 13 0 30 16 45 48 | 0 1 0 1 0 0 }}
-POTE generator: ~3/2 = 695.879
+Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 695.879
 {{Optimal ET sequence|legend=1| 13d, 26, 91cdf }}
@@ Line 428: / Line 442: @@
 == Pentorwell ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 1728/1715, 179200/177147
-[[Mapping]]: [{{val| 5 8 12 14 }}, {{val| 0 -1 -6 1 }}]
+{{Mapping|legend=1| 5 8 12 14 | 0 -1 -6 1 }}
-[[POTE generator]]: ~7/4 = 975.0872
+[[Optimal tuning]] ([[POTE]]): ~280/243 = 1\5, ~7/4 = 975.0872
 {{Optimal ET sequence|legend=1| 5, 75, 80 }}
@@ Line 445: / Line 459: @@
 Comma list: 896/891, 1728/1715, 2200/2187
-Mapping: [{{val| 5 8 12 14 17 }}, {{val| 0 -1 -6 1 5 }}]
+Mapping: {{mapping| 5 8 12 14 17 | 0 -1 -6 1 5 }}
-POTE generator: ~7/4 = 975.1212
+Optimal tuning (POTE): ~55/48 = 1\5, ~7/4 = 975.1212
 {{Optimal ET sequence|legend=1| 5, 75e, 80 }}
@@ Line 455: / Line 469: @@
 [[Category:Temperament collections]]
 [[Category:Orwellismic temperaments| ]] <!-- main article -->
+[[Category:Orwellismic| ]] <!-- key article -->
 [[Category:Rank 2]]

Orwellismic temperaments: Difference between revisions

Revision as of 10:49, 17 September 2023

Secant

11-limit

13-limit

Infraorwell

11-limit

13-limit

Quartonic

7-limit

11-limit

13-limit

Quarto

13-limit

Quartz

13-limit

Biquartonic

13-limit

Yarm

13-limit

17-limit

Sentinel

11-limit

13-limit

Diesic

11-limit

13-limit

Phillips

11-limit

Triskaidekic

11-limit

13-limit

Pentorwell

11-limit

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