Orwellismic temperaments

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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 GPV sequence26, 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 GPV 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 GPV 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 GPV sequence9, 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 GPV 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 GPV 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 GPV sequence26, 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 GPV sequence26, 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 GPV 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 GPV 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 GPV 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 GPV 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 GPV 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 GPV 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 GPV 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 GPV 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 GPV 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 GPV 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 GPV 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 GPV sequence14, 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 GPV 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 GPV 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 GPV sequence31, 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 GPV 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 GPV 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 GPV sequence14, 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 GPV 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 GPV sequence13d, 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 GPV 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 GPV 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 GPV sequence5, 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 GPV sequence: 5, 75e, 80

Badness: 0.071702