No-elevens subgroup temperaments

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This is a collection of subgroup temperaments which omit the prime harmonic of 11.

Ultrapyth

For full 13-limit extensions, see Archytas clan #Ultrapyth.

Subgroup: 2.3.5.7.13

Comma list: 64/63, 91/90, 4394/4375

Gencom: [2 4/3; 64/63 91/90 4394/4375]

Gencom mapping: [⟨1 2 8 2 0 11], ⟨0 -1 -14 2 0 -18]]

Sval mapping: [⟨1 2 8 2 11], ⟨0 -1 -14 2 -18]]

POL2 generator: ~4/3 = 486.255

Optimal ET sequence: 5, 32, 37

RMS error: 2.318 cents

Meanpop

For full 13-limit extensions, see Meantone family #Septimal meantone.

Subgroup: 2.3.5.7.13

Comma list: 81/80, 105/104, 126/125

Gencom: [2 4/3; 81/80 105/104 126/125]

Gencom mapping: [⟨1 2 4 7 0 10], ⟨0 -1 -4 -10 0 -15]]

Sval mapping: [⟨1 2 4 7 10], ⟨0 -1 -4 -10 -15]]

POL2 generator: ~3/2 = 695.988

Optimal ET sequence: 12f, 19, 31, 50

RMS error: 1.421 cents

Sensi (aka sensation)

For full 13-limit extensions, see Sensipent family or Sensi extensions.

Subgroup: 2.3.5.7.13

Comma list: 91/90, 126/125, 169/168

Gencom: [2 9/7; 91/90 126/125 169/168]

Gencom mapping: [⟨1 6 8 11 0 10], ⟨0 -7 -9 -13 0 -10]]

Sval mapping: [⟨1 6 8 11 10], ⟨0 -7 -9 -13 -10]]

POL2 generator: ~9/7 = 443.322

Optimal ET sequence: 19, 27, 46, 111de, 157de

RMS error: 1.321 cents

Decic

For full 13- and 17-limit extensions, see Cloudy clan #Decic.

Subgroup: 2.3.5.7.13

Comma list: 105/104, 196/195, 8281/8192

Gencom: [2 49/48; 105/104 196/195 8281/8192]

Gencom mapping: [⟨10 16 23 28 0 37], ⟨0 -1 1 0 0 0]]

Sval mapping: [⟨10 16 23 28 37], ⟨0 -1 1 0 0]]

POL2 generator: ~49/48 = 21.1859

Optimal ET sequence: 10, 30b, 40, 50, 60, 110d, 170cdd

RMS error: 1.122 cents

2.3.5.7.13.17

Subgroup: 2.3.5.7.13.17

Comma list: 105/104, 170/169, 196/195, 289/288

Gencom: [2 49/48; 105/104 170/169 196/195 289/288]

Gencom mapping: [⟨10 16 23 28 0 37 41], ⟨0 -1 1 0 0 0 -1]]

Sval mapping: [⟨10 16 23 28 37 41], ⟨0 -1 1 0 0 -1]]

POL2 generator: ~49/48 = 21.1836

Optimal ET sequence: 10, 30bg, 40, 50, 60, 110dg, 170cddg

RMS error: 1.038 cents

Quartonic

For full 13-limit extensions, see Orwellismic temperaments #Quartonic.

Subgroup: 2.3.5.7.13

Comma list: 169/168, 325/324, 640/637

Gencom: [2 36/35; 169/168 325/324 640/637]

Gencom mapping: [⟨1 2 3 3 0 4], ⟨0 -11 -18 -5 0 -8]]

Sval mapping: [⟨1 2 3 3 4], ⟨0 -11 -18 -5 -8]]

POL2 generator: ~36/35 = 45.1821

Optimal ET sequence: 26, 27, 53

RMS error: 0.7439 cents

Unicorn

For full 13-limit extensions, see Unicorn family.

Subgroup: 2.3.5.7.13

Comma list: 126/125, 196/195, 676/675

Gencom: [2 28/27; 126/125, 196/195, 676/675]

Gencom mapping: [⟨1 2 3 4 0 5], ⟨0 -8 -13 -23 0 -25]]

Sval mapping: [⟨1 2 3 4 5], ⟨0 -8 -13 -23 -25]]

POL2 generator: ~28/27 = 62.294

Optimal ET sequence: 19, 39df, 58, 77

RMS error: 0.7092 cents

Septidiasemi

For full 13- and 17-limit extensions, see Breedsmic temperaments #Septidiasemi.

Subgroup: 2.3.5.7.13

Comma list: 2205/2197, 2401/2400, 4096/4095

Gencom: [2 15/14; 2205/2197 2401/2400 4096/4095]

Gencom mapping: [⟨1 -1 6 4 0 4], ⟨0 26 -37 -12 0 -3]]

Sval mapping: [⟨1 -1 6 4 4], ⟨0 26 -37 -12 -3]]

POL2 generator: ~15/14 = 119.297

Optimal ET sequence: 10, 151, 161, 171

RMS error: 0.2002 cents

2.3.5.7.13.17

Subgroup: 2.3.5.7.13.17

Comma list: 833/832, 1275/1274, 2025/2023, 2205/2197

Gencom: [2 15/14; 833/832 1275/1274 2025/2023 2205/2197]

Gencom mapping: [⟨1 -1 6 4 0 4 2], ⟨0 26 -37 -12 0 -3 21]]

Sval mapping: [⟨1 -1 6 4 4 2], ⟨0 26 -37 -12 -3 21]]

POL2 generator: ~15/14 = 119.297

Optimal ET sequence: 10, 151, 161, 171

RMS error: 0.1867 cents

Pontiac

For full 13- and 17-limit extensions, see Schismatic family #Pontiac.

Subgroup: 2.3.5.7.13

Comma list: 625/624, 729/728, 4096/4095

Gencom: [2 4/3; 625/624 729/728 4096/4095]

Gencom mapping: [⟨1 2 -1 19 0 -10], ⟨0 -1 8 -39 0 33]]

Sval mapping: [⟨1 2 -1 19 -10], ⟨0 -1 8 -39 33]]

POL2 generator: ~3/2 = 701.773

Optimal ET sequence: 53, 118, 171, 224, 395

RMS error: 0.1525 cents

2.3.5.7.13.17

Subgroup: 2.3.5.7.13.17

Comma list: 625/624, 729/728, 1225/1224, 2880/2873

Gencom: [2 4/3; 625/624 729/728 1225/1224 2880/2873]

Gencom mapping: [⟨1 2 -1 19 0 -10 29], ⟨0 -1 8 -39 0 33 -60]]

Sval mapping: [⟨1 2 -1 19 -10 29], ⟨0 -1 8 -39 33 -60]]

POL2 generator: ~3/2 = 701.764

Optimal ET sequence: 53, 118, 171, 395, 566…

RMS error: 0.1696 cents

Mitonic

For full 13- and 17-limit extensions, see Minortonic family #Mitonic.

Subgroup: 2.3.5.7.13

Comma list: 4096/4095, 4375/4374, 13720/13689

Gencom: [2 10/9; 4096/4095 4375/4374 13720/13689]

Gencom mapping: [⟨1 -1 -3 6 0 11], ⟨0 17 35 -21 0 -48]]

Sval mapping: [⟨1 -1 -3 6 11], ⟨0 17 35 -21 -48]]

POL2 generator: ~10/9 = 182.471

Optimal ET sequence: 46, 125, 171, 388

RMS error: 0.1442 cents

2.3.5.7.13.17

Subgroup: 2.3.5.7.13.17

Comma list: 833/832, 1225/1224, 1701/1700, 4096/4095

Gencom: [2 10/9; 833/832 1225/1224 1701/1700 4096/4095]

Gencom mapping: [⟨1 -1 -3 6 0 11 5], ⟨0 17 35 -21 0 -48 -6]]

Sval mapping: [⟨1 -1 -3 6 11 5], ⟨0 17 35 -21 -48 -6]]

POL2 generator: ~10/9 = 182.471

Optimal ET sequence: 46, 125, 171, 388

RMS error: 0.1341 cents

Tertiaseptal

For full 13- and 17-limit extensions, see Breedsmic temperaments #Tertiaseptal.

Subgroup: 2.3.5.7.13

Comma list: 625/624, 2401/2400, 4096/4095

Gencom: [2 117/112; 625/624 2401/2400 4096/4095]

Gencom mapping: [⟨1 3 2 3 0 1], ⟨0 -22 5 -3 0 42]]

Sval mapping: [⟨1 3 2 3 1], ⟨0 -22 5 -3 42]]

POL2 generator: ~117/112 = 77.173

Optimal ET sequence: 31, 109, 140, 171, 311

RMS error: 0.1383 cents

2.3.5.7.13.17

Subgroup: 2.3.5.7.13.17

Comma list: 625/624, 833/832, 1225/1224, 4096/4095

Gencom: [2 68/65; 625/624 833/832 1225/1224 4096/4095]

Gencom mapping: [⟨1 3 2 3 0 1 1], ⟨0 -22 5 -3 0 42 48]]

Sval mapping: [⟨1 3 2 3 1 1], ⟨0 -22 5 -3 42 48]]

POL2 generator: ~68/65 = 77.177

Optimal ET sequence: 31, 109f, 140, 171, 311

RMS error: 0.1367 cents

Oquatonic

For full 13-limit extensions, see Horwell temperaments #Oquatonic.

Subgroup: 2.3.5.7.13

Comma list: 625/624, 4096/4095, 10985/10976

Gencom: [40/39 105/104; 625/624 4096/4095 10985/10976]

Gencom mapping: [⟨28 44 65 79 0 104], ⟨0 1 0 -1 0 -1]]

Sval mapping: [⟨28 44 65 79 104], ⟨0 1 0 -1 -1]]

POL2 generator: ~105/104 = 16.4240

Optimal ET sequence: 28, 56, 84, 140, 224, 364

RMS error: 0.1347 cents

Cotoneum

For full 19-limit extensions, see Hemimage temperaments #Cotoneum.

Subgroup: 2.3.5.7.19

Comma list: 343/342, 1216/1215, 48013/48000

Gencom: [2 4/3; 343/342 1216/1215 48013/48000]

Gencom mapping: [⟨1 2 -18 -3 0 0 0 -14], ⟨0 -1 49 14 0 0 0 44]]

Sval mapping: [⟨1 2 -18 -3 -14], ⟨0 -1 49 14 44]]

POL2 generator: ~3/2 = 702.319

Optimal ET sequence: 41, 176, 217

RMS error: 0.1852 cents

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