Orwellismic temperaments

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

Temperaments considered below are secant, infraorwell, quartonic, sentinel, diesic, philips, triskaidekic, and pentorwell. Discussed elsewhere are:

Secant

Subgroup: 2.3.5.7

Comma list: 1728/1715, 177147/175000

Mapping[2 1 0 5], 0 7 15 2]]

Mapping generators: ~567/400, ~10/9

Wedgie⟨⟨14 30 4 15 -33 -75]]

Optimal tuning (POTE): ~567/400 = 1\2, ~10/9 = 185.885

Optimal ET 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]]

Optimal tuning (POTE): ~99/70 = 1\2, ~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]]

Optimal tuning (POTE): ~99/70 = 1\2, ~10/9 = 185.955

Optimal ET sequence: 26, 58, 84, 142ef

Badness: 0.025035

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 144/143, 170/169, 221/220, 351/350, 441/440

Mapping: [2 1 0 5 6 4 6], 0 7 15 2 3 11 7]]

Optimal tuning (POTE): ~17/12 = 1\2, ~10/9 = 185.916

Optimal ET sequence: 26, 58, 84, 142ef

Badness: 0.021642

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 144/143, 153/152, 170/169, 210/209, 221/220, 400/399

Mapping: [2 1 0 5 6 4 6 2], 0 7 15 2 3 11 7 21]]

Optimal tuning (POTE): ~17/12 = 1\2, ~10/9 = 185.858

Optimal ET sequence: 26, 58h, 84, 142efh, 226deefgh

Badness: 0.018565

Infraorwell

Subgroup: 2.3.5.7

Comma list: 1728/1715, 28672/28125

Mapping[1 14 0 16], 0 -16 3 -17]]

Mapping generators: ~2, ~12/7

Wedgie⟨⟨16 -3 17 -42 -18 48]]

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.032

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~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]]

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.021

Optimal ET sequence: 9, 49f, 58

Badness: 0.023683

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]]

Mapping generators: ~2, ~9/7

Wedgie⟨⟨4 -15 9 -33 3 63]]

Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.596

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~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]]

Optimal tuning (POTE): ~2 = 1\1, ~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]]

Mapping generators: ~2, ~36/35

Wedgie⟨⟨13 21 6 3 -27 -45]]

Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.567

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~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]]

Optimal tuning (POTE): ~2 = 1\1, ~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]]

Mapping generators: ~81/56, ~3

Wedgie⟨⟨2 -18 8 -33 7 69]]

Optimal tuning (POTE): ~81/56 = 1\2, ~3/2 = 691.174

Optimal ET 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]]

Optimal tuning (POTE): ~63/44 = 1\2, ~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]]

Mapping generators: ~15/14, ~3

Wedgie⟨⟨13 0 13 -30 -16 30]]

Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 694.143

Optimal ET 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]]

Optimal tuning (POTE): ~15/14 = 1\13, ~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]]

Optimal tuning (POTE): ~15/14 = 1\13, ~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 0 -36 22], 0 1 6 -1]]

Optimal tunings:

  • CTE: ~280/243 = 1\5, ~3/2 = 704.3709 (~64/63 = 15.6291)
  • POTE: ~280/243 = 1\5, ~3/2 = 704.9128 (~64/63 = 15.0872)

Optimal ET sequence5, 75, 80

Badness: 0.148665

11-limit

Subgroup: 2.3.5.7.11

Comma list: 896/891, 1728/1715, 2200/2187

Mapping: [5 0 -36 22 57], 0 1 6 -1 -5]]

Optimal tunings:

  • CTE: ~55/48 = 1\5, ~3/2 = 704.8440 (~99/98 = 15.1560)
  • POTE: ~55/48 = 1\5, ~3/2 = 704.8788 (~99/98 = 15.1212)

Optimal ET sequence: 75e, 80, 315bcdddee

Badness: 0.071702

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 352/351, 364/363, 1728/1715

Mapping: [5 0 -36 22 57 82], 0 1 6 -1 -5 -8]]

Optimal tunings:

  • CTE: ~55/48 = 1\5, ~3/2 = 704.7636 (~99/98 = 15.2364)
  • CWE: ~55/48 = 1\5, ~3/2 = 704.7112 (~99/98 = 15.2882)

Optimal ET sequence: 75e, 80, 155de

Badness: 0.0557