Orwellismic temperaments: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 24: Line 24:
[[POTE generator]]: ~10/9 = 185.885
[[POTE generator]]: ~10/9 = 185.885


{{Val list|legend=1| 26, 58, 84, 142, 368cd }}
{{Optimal ET sequence|legend=1| 26, 58, 84, 142, 368cd }}


[[Badness]]: 0.095278
[[Badness]]: 0.095278
Line 37: Line 37:
POTE genertor: ~10/9 = 185.962
POTE genertor: ~10/9 = 185.962


Optimal GPV sequence: {{val list| 26, 58, 142e, 200cdee }}
{{Optimal ET sequence|legend=1| 26, 58, 142e, 200cdee }}


Badness: 0.046373
Badness: 0.046373
Line 50: Line 50:
POTE generator: ~10/9 = 185.955
POTE generator: ~10/9 = 185.955


Optimal GPV sequence: {{val list| 26, 58, 84, 142ef }}
{{Optimal ET sequence|legend=1| 26, 58, 84, 142ef }}


Badness: 0.025035
Badness: 0.025035
Line 65: Line 65:
[[POTE generator]]: ~7/6 = 269.032
[[POTE generator]]: ~7/6 = 269.032


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


[[Badness]]: 0.117073
[[Badness]]: 0.117073
Line 78: Line 78:
POTE generator: ~7/6 = 269.036
POTE generator: ~7/6 = 269.036


Optimal GPV sequence: {{val list| 9, 49, 58, 165cdee }}
{{Optimal ET sequence|legend=1| 9, 49, 58, 165cdee }}


Badness: 0.040721
Badness: 0.040721
Line 91: Line 91:
POTE generator: ~7/6 = 269.021
POTE generator: ~7/6 = 269.021


Optimal GPV sequence: {{val list| 9, 49f, 58 }}
{{Optimal ET sequence|legend=1| 9, 49f, 58 }}


Badness: 0.023683
Badness: 0.023683
Line 106: Line 106:
[[POTE generator]]: ~250/243 = 45.233
[[POTE generator]]: ~250/243 = 45.233


{{Val list|legend=1| 26, 27, 53, 239, 292, 345, 398, 451 }}
{{Optimal ET sequence|legend=1| 26, 27, 53, 239, 292, 345, 398, 451 }}


[[Badness]]: 0.117250
[[Badness]]: 0.117250
Line 121: Line 121:
[[POTE generator]]: ~36/35 = 45.139
[[POTE generator]]: ~36/35 = 45.139


{{Val list|legend=1| 26, 27, 53, 80, 133d, 186d, 319d }}
{{Optimal ET sequence|legend=1| 26, 27, 53, 80, 133d, 186d, 319d }}


[[Badness]]: 0.042632
[[Badness]]: 0.042632
Line 134: Line 134:
POTE generator: ~36/35 = 45.041
POTE generator: ~36/35 = 45.041


Optimal GPV sequence: {{val list| 26e, 27e, 53, 80, 213d, 293bcd }}
{{Optimal ET sequence|legend=1| 26e, 27e, 53, 80, 213d, 293bcd }}


Badness: 0.034031
Badness: 0.034031
Line 147: Line 147:
POTE generator: ~36/35 = 45.080
POTE generator: ~36/35 = 45.080


Optimal GPV sequence: {{val list| 26e, 27e, 53, 80, 133d, 213d}}
{{Optimal ET sequence|legend=1| 26e, 27e, 53, 80, 133d, 213d}}


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


Optimal GPV sequence: {{val list| 26, 27e, 53e, 80e }}
{{Optimal ET sequence|legend=1| 26, 27e, 53e, 80e }}


Badness: 0.041786
Badness: 0.041786
Line 173: Line 173:
POTE generator: ~36/35 = 45.205
POTE generator: ~36/35 = 45.205


Optimal GPV sequence: {{val list| 26, 27e, 53e }}
{{Optimal ET sequence|legend=1| 26, 27e, 53e }}


Badness: 0.027692
Badness: 0.027692
Line 186: Line 186:
POTE generator: ~36/35 = 45.385
POTE generator: ~36/35 = 45.385


Optimal GPV sequence: {{val list| 26, 53 }}
{{Optimal ET sequence|legend=1| 26, 53 }}


Badness: 0.053285
Badness: 0.053285
Line 199: Line 199:
POTE generator: ~36/35 = 45.387
POTE generator: ~36/35 = 45.387


Optimal GPV sequence: {{val list| 26, 53, 132e, 185cdef, 238cdef}}
{{Optimal ET sequence|legend=1| 26, 53, 132e, 185cdef, 238cdef}}


Badness: 0.028818
Badness: 0.028818
Line 212: Line 212:
POTE generator: ~36/35 = 45.129
POTE generator: ~36/35 = 45.129


Optimal GPV sequence: {{Val list| 26, 54c, 80, 186de, 266dde }}
{{Optimal ET sequence|legend=1| 26, 54c, 80, 186de, 266dde }}


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


Optimal GPV sequence: {{Val list| 26, 54c, 80, 106, 186de }}
{{Optimal ET sequence|legend=1| 26, 54c, 80, 106, 186de }}


Badness: 0.039891
Badness: 0.039891
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POTE generator: ~100/99 = 15.046
POTE generator: ~100/99 = 15.046


Optimal GPV sequence: {{Val list| 79, 80, 239dd, 319dd }}
{{Optimal ET sequence|legend=1| 79, 80, 239dd, 319dd }}


Badness: 0.099950
Badness: 0.099950
Line 251: Line 251:
POTE generator: ~100/99 = 15.060
POTE generator: ~100/99 = 15.060


Optimal GPV sequence: {{Val list| 79, 80, 159d, 239dd }}
{{Optimal ET sequence|legend=1| 79, 80, 159d, 239dd }}


Badness: 0.061645
Badness: 0.061645
Line 264: Line 264:
POTE generator: ~100/99 = 15.066
POTE generator: ~100/99 = 15.066


Optimal GPV sequence: {{Val list| 79, 80, 159d, 239dd }}
{{Optimal ET sequence|legend=1| 79, 80, 159d, 239dd }}


Badness: 0.046718
Badness: 0.046718
Line 281: Line 281:
[[POTE generator]]: ~9/7 = 425.596
[[POTE generator]]: ~9/7 = 425.596


{{Val list|legend=1| 14, 17, 31, 110, 141, 172b, 375bc }}
{{Optimal ET sequence|legend=1| 14, 17, 31, 110, 141, 172b, 375bc }}


[[Badness]]: 0.093805
[[Badness]]: 0.093805
Line 294: Line 294:
POTE generator: ~9/7 = 425.550
POTE generator: ~9/7 = 425.550


Optimal GPV sequence: {{val list| 14, 17, 31, 79, 110e, 141e }}
{{Optimal ET sequence|legend=1| 14, 17, 31, 79, 110e, 141e }}


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


Optimal GPV sequence: {{val list| 14, 17, 31, 79f, 110ef, 141ef }}
{{Optimal ET sequence|legend=1| 14, 17, 31, 79f, 110ef, 141ef }}


Badness: 0.037408
Badness: 0.037408
Line 324: Line 324:
[[POTE generator]]: ~36/35 = 38.567
[[POTE generator]]: ~36/35 = 38.567


{{Val list|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}


[[Badness]]: 0.107348
[[Badness]]: 0.107348
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POTE generator: ~36/35 = 38.565
POTE generator: ~36/35 = 38.565


Optimal GPV sequence: {{val list| 31, 156ce, 187ce, 218bcee, 249bcee }}
{{Optimal ET sequence|legend=1| 31, 156ce, 187ce, 218bcee, 249bcee }}


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


Optimal GPV sequence: {{val list| 31, 94cff, 125cff }}
{{Optimal ET sequence|legend=1| 31, 94cff, 125cff }}


Badness: 0.038116
Badness: 0.038116
Line 367: Line 367:
[[POTE generator]]: ~3/2 = 691.174
[[POTE generator]]: ~3/2 = 691.174


{{Val list|legend=1| 14, 26, 66b, 92bc }}
{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc }}


[[Badness]]: 0.228602
[[Badness]]: 0.228602
Line 380: Line 380:
POTE generator: ~3/2 = 691.040
POTE generator: ~3/2 = 691.040


Optimal GPV sequence: {{Val list| 14, 26, 40, 66b }}
{{Optimal ET sequence|legend=1| 14, 26, 40, 66b }}


Badness: 0.095777
Badness: 0.095777
Line 397: Line 397:
[[POTE generator]]: ~3/2 = 694.143
[[POTE generator]]: ~3/2 = 694.143


{{Val list|legend=1| 13d, 26 }}
{{Optimal ET sequence|legend=1| 13d, 26 }}


[[Badness]]: 0.219050
[[Badness]]: 0.219050
Line 410: Line 410:
POTE generator: ~3/2 = 696.296
POTE generator: ~3/2 = 696.296


Optimal GPV sequence: {{Val list| 13d, 26, 91cd }}
{{Optimal ET sequence|legend=1| 13d, 26, 91cd }}


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


Optimal GPV sequence: {{Val list| 13d, 26, 91cdf }}
{{Optimal ET sequence|legend=1| 13d, 26, 91cdf }}


Badness: 0.059216
Badness: 0.059216
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[[POTE generator]]: ~7/4 = 975.0872
[[POTE generator]]: ~7/4 = 975.0872


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


[[Badness]]: 0.148665
[[Badness]]: 0.148665
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POTE generator: ~7/4 = 975.1212
POTE generator: ~7/4 = 975.1212


Optimal GPV sequence: {{val list| 5, 75e, 80 }}
{{Optimal ET sequence|legend=1| 5, 75e, 80 }}


Badness: 0.071702
Badness: 0.071702

Revision as of 16:35, 7 May 2023

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

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]]

POTE genertor: ~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]]

POTE generator: ~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]]

Wedgie: ⟨⟨ 16 -3 17 -42 -18 48 ]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~7/6 = 269.021

Optimal ET sequence: 9, 49f, 58

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

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 ]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

Wedgie: ⟨⟨ 4 -15 9 -33 3 63 ]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

Wedgie: ⟨⟨ 13 21 6 3 -27 -45 ]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

Wedgie: ⟨⟨ 2 -18 8 -33 7 69 ]]

POTE generator: ~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]]

POTE generator: ~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]]

Wedgie: ⟨⟨ 13 0 13 -30 -16 30 ]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~7/4 = 975.1212

Optimal ET sequence: 5, 75e, 80

Badness: 0.071702

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