Orwellismic temperaments: Difference between revisions

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Line 35: Line 35:
POTE genertor: ~10/9 = 185.962
POTE genertor: ~10/9 = 185.962


Vals: {{val list| 26, 58, 142e, 200cdee }}
Optimal GPV sequence: {{val list| 26, 58, 142e, 200cdee }}


Badness: 0.046373
Badness: 0.046373
Line 48: Line 48:
POTE generator: ~10/9 = 185.955
POTE generator: ~10/9 = 185.955


Vals: {{val list| 26, 58, 84, 142ef }}
Optimal GPV sequence: {{val list| 26, 58, 84, 142ef }}


Badness: 0.025035
Badness: 0.025035
Line 76: Line 76:
POTE generator: ~7/6 = 269.036
POTE generator: ~7/6 = 269.036


Vals: {{val list| 9, 49, 58, 165cdee }}
Optimal GPV sequence: {{val list| 9, 49, 58, 165cdee }}


Badness: 0.040721
Badness: 0.040721
Line 89: Line 89:
POTE generator: ~7/6 = 269.021
POTE generator: ~7/6 = 269.021


Vals: {{val list| 9, 49f, 58 }}
Optimal GPV sequence: {{val list| 9, 49f, 58 }}


Badness: 0.023683
Badness: 0.023683
Line 132: Line 132:
POTE generator: ~36/35 = 45.041
POTE generator: ~36/35 = 45.041


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


Badness: 0.034031
Badness: 0.034031
Line 145: Line 145:
POTE generator: ~36/35 = 45.080
POTE generator: ~36/35 = 45.080


Vals: {{val list| 26e, 27e, 53, 80, 133d, 213d}}
Optimal GPV sequence: {{val list| 26e, 27e, 53, 80, 133d, 213d}}


Badness: 0.023875
Badness: 0.023875
Line 158: Line 158:
POTE generator: ~36/35 = 45.132
POTE generator: ~36/35 = 45.132


Vals: {{val list| 26, 27e, 53e, 80e }}
Optimal GPV sequence: {{val list| 26, 27e, 53e, 80e }}


Badness: 0.041786
Badness: 0.041786
Line 171: Line 171:
POTE generator: ~36/35 = 45.205
POTE generator: ~36/35 = 45.205


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


Badness: 0.027692
Badness: 0.027692
Line 184: Line 184:
POTE generator: ~36/35 = 45.385
POTE generator: ~36/35 = 45.385


Vals: {{val list| 26, 53 }}
Optimal GPV sequence: {{val list| 26, 53 }}


Badness: 0.053285
Badness: 0.053285
Line 197: Line 197:
POTE generator: ~36/35 = 45.387
POTE generator: ~36/35 = 45.387


Vals: {{val list| 26, 53, 132e, 185cdef, 238cdef}}
Optimal GPV sequence: {{val list| 26, 53, 132e, 185cdef, 238cdef}}


Badness: 0.028818
Badness: 0.028818
Line 210: Line 210:
POTE generator: ~36/35 = 45.129
POTE generator: ~36/35 = 45.129


Vals: {{Val list| 26, 54c, 80, 186de, 266dde }}
Optimal GPV sequence: {{Val list| 26, 54c, 80, 186de, 266dde }}


Badness: 0.060737
Badness: 0.060737
Line 223: Line 223:
POTE generator: ~36/35 = 45.153
POTE generator: ~36/35 = 45.153


Vals: {{Val list| 26, 54c, 80, 106, 186de }}
Optimal GPV sequence: {{Val list| 26, 54c, 80, 106, 186de }}


Badness: 0.039891
Badness: 0.039891
Line 253: Line 253:
POTE generator: ~9/7 = 425.550
POTE generator: ~9/7 = 425.550


Vals: {{val list| 14, 17, 31, 79, 110e, 141e }}
Optimal GPV sequence: {{val list| 14, 17, 31, 79, 110e, 141e }}


Badness: 0.039595
Badness: 0.039595
Line 266: Line 266:
POTE generator: ~9/7 = 425.501
POTE generator: ~9/7 = 425.501


Vals: {{val list| 14, 17, 31, 79f, 110ef, 141ef }}
Optimal GPV sequence: {{val list| 14, 17, 31, 79f, 110ef, 141ef }}


Badness: 0.037408
Badness: 0.037408
Line 296: Line 296:
POTE generator: ~36/35 = 38.565
POTE generator: ~36/35 = 38.565


Vals: {{val list| 31, 156ce, 187ce, 218bcee, 249bcee }}
Optimal GPV sequence: {{val list| 31, 156ce, 187ce, 218bcee, 249bcee }}


Badness: 0.044186
Badness: 0.044186
Line 309: Line 309:
POTE generator: ~36/35 = 38.444
POTE generator: ~36/35 = 38.444


Vals: {{val list| 31, 94cff, 125cff }}
Optimal GPV sequence: {{val list| 31, 94cff, 125cff }}


Badness: 0.038116
Badness: 0.038116
Line 339: Line 339:
POTE generator: ~3/2 = 691.040
POTE generator: ~3/2 = 691.040


Vals: {{Val list| 14, 26, 40, 66b }}
Optimal GPV sequence: {{Val list| 14, 26, 40, 66b }}


Badness: 0.095777
Badness: 0.095777
Line 369: Line 369:
POTE generator: ~3/2 = 696.296
POTE generator: ~3/2 = 696.296


Vals: {{Val list| 13d, 26, 91cd }}
Optimal GPV sequence: {{Val list| 13d, 26, 91cd }}


Badness: 0.098847
Badness: 0.098847
Line 382: Line 382:
POTE generator: ~3/2 = 695.879
POTE generator: ~3/2 = 695.879


Vals: {{Val list| 13d, 26, 91cdf }}
Optimal GPV sequence: {{Val list| 13d, 26, 91cdf }}


Badness: 0.059216
Badness: 0.059216
Line 408: Line 408:
POTE generator: ~7/4 = 975.1212
POTE generator: ~7/4 = 975.1212


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


Badness: 0.071702
Badness: 0.071702

Revision as of 06:32, 8 January 2022

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

Temperaments discussed elsewhere 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list

Badness: 0.023683

Quartonic

Quartonic tempers out saleyo 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]]

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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list

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]]

POTE generator: ~36/35 = 45.129

Optimal GPV sequence: Template:Val list

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]]

POTE generator: ~36/35 = 45.153

Optimal GPV sequence: Template:Val list

Badness: 0.039891

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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list

Badness: 0.071702

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