Orwellismic temperaments: Difference between revisions

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Revision as of 08:16, 9 October 2021

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

Temperaments discussed elsewhere include:

beep, {21/20, 27/25} → Bug family #Beep
doublewide, {50/49, 875/864} → Jubilismic clan #Doublewide
superpyth, {64/63, 245/243} → Archytas clan #Superpyth
mothra, {81/80, 1029/1024} → Meantone family #Mothra
myna, {126/125, 1728/1715} → Starling temperaments #Myna
orwell, {225/224, 1728/1715} → Semicomma family #Orwell
secund, {405/392, 525/512} → Greenwoodmic temperaments #Secund
buzzard, {1728/1715, 5120/5103} → Hemifamity temperaments #Buzzard

Secant

Subgroup: 2.3.5.7

Comma list: 1728/1715, 177147/175000

Mapping: [⟨2 1 0 5], ⟨0 7 15 2]]

Wedgie: ⟨⟨ 14 30 4 15 -33 -75 ]]

POTE generator: ~10/9 = 185.885

Template:Val list

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]]

POTE genertor: ~10/9 = 185.962

Vals: Template:Val list

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]]

POTE generator: ~10/9 = 185.955

Vals: Template:Val list

Badness: 0.025035

Infraorwell

Subgroup: 2.3.5.7

Comma list: 1728/1715, 28672/28125

Mapping: [⟨1 14 0 16], ⟨0 -16 3 -17]]

Wedgie: ⟨⟨ 16 -3 17 -42 -18 48 ]]

POTE generator: ~7/6 = 269.032

Template:Val list

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]]

POTE generator: ~7/6 = 269.036

Vals: Template:Val list

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]]

POTE generator: ~7/6 = 269.021

Vals: Template:Val list

Badness: 0.023683

Quartonic

See also: Turkish maqam music temperaments § Yarman temperament

Subgroup: 2.3.5

Comma list: 390625000/387420489

Mapping: [⟨1 2 3], ⟨0 -11 -18]]

POTE generator: ~250/243 = 45.233

Template:Val list

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 ]]

POTE generator: ~36/35 = 45.139

Template:Val list

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]]

POTE generator: ~36/35 = 45.041

Vals: Template:Val list

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]]

POTE generator: ~36/35 = 45.080

Vals: Template:Val list

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]]

POTE generator: ~36/35 = 45.132

Vals: Template:Val list

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]]

POTE generator: ~36/35 = 45.205

Vals: Template:Val list

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]]

POTE generator: ~36/35 = 45.385

Vals: Template:Val list

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]]

POTE generator: ~36/35 = 45.387

Vals: Template:Val list

Badness: 0.028818

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]]

Wedgie: ⟨⟨ 4 -15 9 -33 3 63 ]]

POTE generator: ~9/7 = 425.596

Template:Val list

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]]

POTE generator: ~9/7 = 425.550

Vals: Template:Val list

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]]

POTE generator: ~9/7 = 425.501

Vals: Template:Val list

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]]

Wedgie: ⟨⟨ 13 21 6 3 -27 -45 ]]

POTE generator: ~36/35 = 38.567

Template:Val list

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]]

POTE generator: ~36/35 = 38.565

Vals: Template:Val list

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]]

POTE generator: ~36/35 = 38.444

Vals: Template:Val list

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]]

Wedgie: ⟨⟨ 2 -18 8 -33 7 69 ]]

POTE generator: ~3/2 = 691.174

Template:Val list

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]]

POTE generator: ~3/2 = 691.040

Vals: Template:Val list

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]]

Wedgie: ⟨⟨ 13 0 13 -30 -16 30 ]]

POTE generator: ~3/2 = 694.143

Template:Val list

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]]

POTE generator: ~3/2 = 696.296

Vals: Template:Val list

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]]

POTE generator: ~3/2 = 695.879

Vals: Template:Val list

Badness: 0.059216

Pentorwell

Subgroup: 2.3.5.7

Comma list: 1728/1715, 179200/177147

Mapping: [⟨5 8 12 14], ⟨0 -1 -6 1]]

POTE generator: ~7/4 = 975.0872

Template:Val list

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]]

POTE generator: ~7/4 = 975.1212

Vals: Template:Val list

Badness: 0.071702

@@ Line 202: / Line 202: @@
 == Sentinel ==
-Subgroup: 2.3.5
+: ''For the 5-limit version of this temperament, see [[High badness temperaments #Sentinel]].''
-[[Comma list]]: 8968066875/8589934592
-[[Mapping]]: [{{val| 1 3 -3 }}, {{val| 0 -4 15 }}]
-[[POTE generator]]: ~512/405 = 425.474
-{{Val list|legend=1| 14, 17, 31, 79, 110, 361bc }}
-[[Badness]]: 0.723413
-=== 7-limit ===
 Subgroup: 2.3.5.7
@@ Line 256: / Line 245: @@
 == Diesic ==
-Subgroup: 2.3.5
+: ''For the 5-limit version of this temperament, see [[High badness temperaments #Diesic]].''
-[[Comma list]]: 10460353203/9765625000
-[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -13 -21 }}]
-[[POTE generator]]: ~6561/6250 = 38.571
-{{Val list|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
-[[Badness]]: 1.344681
-=== 7-limit ===
 Subgroup: 2.3.5.7
@@ Line 308: / Line 286: @@
 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]]: [{{Val|2 0 33 -7}}, {{Val|0 1 -9 4}}]
+{{Multival|legend=1|2 -18 8 -33 7 69}}
+[[POTE generator]]: ~3/2 = 691.174
+{{Val list|legend=1| 14, 26, 66b, 92bc }}
+[[Badness]]: 0.228602
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 99/98, 385/384, 729/704
+Mapping: [{{Val|2 0 33 -7 -12}}, {{Val|0 1 -9 4 6}}]
+POTE generator: ~3/2 = 691.040
+Vals: {{Val list| 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]]: [{{Val|13 0 30 16}}, {{Val|0 1 0 1}}]
+{{Multival|legend=1|13 0 13 -30 -16 30}}
+[[POTE generator]]: ~3/2 = 694.143
+{{Val list|legend=1| 13d, 26 }}
+[[Badness]]: 0.219050
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 99/98, 125/121, 385/384
+Mapping: [{{Val|13 0 30 16 45}}, {{Val|0 1 0 1 0}}]
+POTE generator: ~3/2 = 696.296
+Vals: {{Val list| 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: [{{Val|13 0 30 16 45 48}}, {{Val|0 1 0 1 0 0}}]
+POTE generator: ~3/2 = 695.879
+Vals: {{Val list| 13d, 26, 91cdf }}
+Badness: 0.059216
 == Pentorwell ==

Orwellismic temperaments: Difference between revisions

Revision as of 08:16, 9 October 2021

Contents

Secant

11-limit

13-limit

Infraorwell

11-limit

13-limit

Quartonic

7-limit

11-limit

13-limit

Quarto

13-limit

Quartz

13-limit

Sentinel

11-limit

13-limit

Diesic

11-limit

13-limit

Phillips

11-limit

Triskaidekic

11-limit

13-limit

Pentorwell

11-limit

Navigation menu

Orwellismic temperaments: Difference between revisions

Revision as of 08:16, 9 October 2021

Secant

11-limit

13-limit

Infraorwell

11-limit

13-limit

Quartonic

7-limit

11-limit

13-limit

Quarto

13-limit

Quartz

13-limit

Sentinel

11-limit

13-limit

Diesic

11-limit

13-limit

Phillips

11-limit

Triskaidekic

11-limit

13-limit

Pentorwell

11-limit

Navigation menu

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