Orwellismic temperaments: Difference between revisions

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Line 23: Line 23:
{{Val list|legend=1| 26, 58, 84, 142, 368cd }}
{{Val list|legend=1| 26, 58, 84, 142, 368cd }}


[[Badness]]: 0.0953
[[Badness]]: 0.095278


== 11-limit ==
== 11-limit ==
Line 36: Line 36:
Vals: {{val list| 26, 58, 142e, 200cdee }}
Vals: {{val list| 26, 58, 142e, 200cdee }}


Badness: 0.0464
Badness: 0.046373


== 13-limit ==
== 13-limit ==
Line 49: Line 49:
Vals: {{val list| 26, 58, 84, 142ef }}
Vals: {{val list| 26, 58, 84, 142ef }}


Badness: 0.0250
Badness: 0.025035


= Infraorwell =
= Infraorwell =
Line 62: Line 62:
[[POTE generator]]: ~7/6 = 269.032
[[POTE generator]]: ~7/6 = 269.032


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


[[Badness]]: 0.1171
[[Badness]]: 0.117073


== 11-limit ==
== 11-limit ==
Line 75: Line 75:
POTE generator: ~7/6 = 269.036
POTE generator: ~7/6 = 269.036


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


Badness: 0.0407
Badness: 0.040721


== 13-limit ==
== 13-limit ==
Line 88: Line 88:
POTE generator: ~7/6 = 269.021
POTE generator: ~7/6 = 269.021


Vals: {{val list| 9, … , 49f, 58 }}
Vals: {{val list| 9, 49f, 58 }}


Badness: 0.0237
Badness: 0.023683


= Quartonic =
= Quartonic =
== 5-limit ==
{{See also| Turkish maqam music temperaments #Yarman temperament}}
 
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 104: Line 105:
{{Val list|legend=1| 26, 27, 53, 239, 292, 345, 398, 451 }}
{{Val list|legend=1| 26, 27, 53, 239, 292, 345, 398, 451 }}


[[Badness]]: 0.1172
[[Badness]]: 0.117250


== 7-limit ==
== 7-limit ==
Line 119: Line 120:
{{Val list|legend=1| 26, 27, 53, 80, 133d, 186d, 319d }}
{{Val list|legend=1| 26, 27, 53, 80, 133d, 186d, 319d }}


[[Badness]]: 0.0426
[[Badness]]: 0.042632


== 11-limit ==
== 11-limit ==
Line 130: Line 131:
POTE generator: ~36/35 = 45.041
POTE generator: ~36/35 = 45.041


Vals: {{val list| 26e, 27e, 53, 80, 213d, 293bcd}}
Vals: {{val list| 26e, 27e, 53, 80, 213d, 293bcd }}


Badness: 0.034
Badness: 0.034031


=== 13-limit ===
=== 13-limit ===
Line 145: Line 146:
Vals: {{val list| 26e, 27e, 53, 80, 133d, 213d}}
Vals: {{val list| 26e, 27e, 53, 80, 133d, 213d}}


Badness: 0.0239
Badness: 0.023875


== Quarto ==
== Quarto ==
Line 158: Line 159:
Vals: {{val list| 26, 27e, 53e, 80e }}
Vals: {{val list| 26, 27e, 53e, 80e }}


Badness: 0.0418
Badness: 0.041786


=== 13-limit ===
=== 13-limit ===
Line 169: Line 170:
POTE generator: ~36/35 = 45.205
POTE generator: ~36/35 = 45.205


Vals: {{val list| 26, 27e, 53e}}
Vals: {{val list| 26, 27e, 53e }}


Badness: 0.0277
Badness: 0.027692


== Quartz ==
== Quartz ==
Line 184: Line 185:
Vals: {{val list| 26, 53 }}
Vals: {{val list| 26, 53 }}


Badness: 0.0533
Badness: 0.053285


=== 13-limit ===
=== 13-limit ===
Line 197: Line 198:
Vals: {{val list| 26, 53, 132e, 185cdef, 238cdef}}
Vals: {{val list| 26, 53, 132e, 185cdef, 238cdef}}


Badness: 0.0288
Badness: 0.028818


= Sentinel =
= Sentinel =
== 5-limit ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 211: Line 211:
{{Val list|legend=1| 14, 17, 31, 79, 110, 361bc }}
{{Val list|legend=1| 14, 17, 31, 79, 110, 361bc }}


[[Badness]]: 0.7234
[[Badness]]: 0.723413


== 7-limit ==
== 7-limit ==
Line 226: Line 226:
{{Val list|legend=1| 14, 17, 31, 110, 141, 172b, 375bc }}
{{Val list|legend=1| 14, 17, 31, 110, 141, 172b, 375bc }}


[[Badness]]: 0.0938
[[Badness]]: 0.093805


== 11-limit ==
== 11-limit ==
Line 239: Line 239:
Vals: {{val list| 14, 17, 31, 79, 110e, 141e }}
Vals: {{val list| 14, 17, 31, 79, 110e, 141e }}


Badness: 0.0396
Badness: 0.039595


== 13-limit ==
== 13-limit ==
Line 252: Line 252:
Vals: {{val list| 14, 17, 31, 79f, 110ef, 141ef }}
Vals: {{val list| 14, 17, 31, 79f, 110ef, 141ef }}


Badness: 0.0374
Badness: 0.037408


= Diesic =
= Diesic =
== 5-limit ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 266: Line 265:
{{Val list|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
{{Val list|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}


[[Badness]]: 1.3447
[[Badness]]: 1.344681


== 7-limit ==
== 7-limit ==
Line 281: Line 280:
{{Val list|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
{{Val list|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}


[[Badness]]: 0.1073
[[Badness]]: 0.107348


== 11-limit ==
== 11-limit ==
Line 294: Line 293:
Vals: {{val list| 31, 156ce, 187ce, 218bcee, 249bcee }}
Vals: {{val list| 31, 156ce, 187ce, 218bcee, 249bcee }}


Badness: 0.0442
Badness: 0.044186


== 13-limit ==
== 13-limit ==
Line 307: Line 306:
Vals: {{val list| 31, 94cff, 125cff }}
Vals: {{val list| 31, 94cff, 125cff }}


Badness: 0.0381
Badness: 0.038116


= Pentorwell =
= Pentorwell =
Line 318: Line 317:
POTE generator: ~7/4 = 975.0872
POTE generator: ~7/4 = 975.0872


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


Badness: 0.148665
Badness: 0.148665
Line 331: Line 330:
POTE generator: ~7/4 = 975.1212
POTE generator: ~7/4 = 975.1212


Vals: {{val list| 75e, 80 }}
Vals: {{val list| 5, 75e, 80 }}


Badness: 0.071702
Badness: 0.071702

Revision as of 21:03, 26 April 2021

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

Temperaments not discussed here include:

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

Subgroup: 2.3.5

Comma list: 8968066875/8589934592

Mapping: [⟨1 3 -3], ⟨0 -4 15]]

POTE generator: ~512/405 = 425.474

Template:Val list

Badness: 0.723413

7-limit

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

Subgroup: 2.3.5

Comma list: 10460353203/9765625000

Mapping: [⟨1 2 3], ⟨0 -13 -21]]

POTE generator: ~6561/6250 = 38.571

Template:Val list

Badness: 1.344681

7-limit

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

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

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