Jubilismic clan

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The jubilismic clan tempers out the jubilisma, 50/49, which means 7/5 and 10/7 are identified and the octave is divided in two.

Doublewide, lemba and diminished are discussed below; others in the clan are pajara, decimal, injera, octokaidecal, hedgehog, bipelog, dubbla, hexe and astrology, which are discussed elsewhere.

No-three jubilismic

Subgroup: 2.5.7

Sval mapping: [⟨2 0 1], ⟨0 1 1]]

Sval mapping generators: ~7/5, ~5

Gencom mapping: [⟨2 0 0 1], ⟨0 0 1 1]]

POTE generator: ~5/4 = 380.840

Optimal GPV sequence: 2, 4, 6, 16, 22, 60d, 82d, 104dd

Lemba

Main article: Lemba

Subgroup: 2.3.5.7

Comma list: 50/49, 525/512

Mapping: [⟨2 2 5 6], ⟨0 3 -1 -1]]

Mapping generators: ~7/5, ~8/7

POTE generator: ~8/7 = 232.089

Optimal GPV sequence: 10, 16, 26, 62c

Badness: 0.062208

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49, 385/384

Mapping: [⟨2 2 5 6 5], ⟨0 3 -1 -1 5]]

POTE generator: ~8/7 = 230.974

Optimal GPV sequence: 10, 16, 26

Badness: 0.041563

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 50/49, 65/64, 78/77

Mapping: [⟨2 2 5 6 5 7], ⟨0 3 -1 -1 5 1]]

POTE generator: ~8/7 = 230.966

Optimal GPV sequence: 10, 16, 26

Badness: 0.025477

Diminished

Deutsch
See also: Dimipent family #Diminished

Subgroup: 2.3.5.7

Comma list: 36/35, 50/49

Mapping: [⟨4 0 3 5], ⟨0 1 1 1]]

Mapping generators: ~6/5, ~3

POTE generator: ~3/2 = 699.523

Optimal GPV sequence: 4, 8d, 12

Badness: 0.022401

Scales: diminished12

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 50/49, 56/55

Mapping: [⟨4 0 3 5 14], ⟨0 1 1 1 0]]

Mapping generators: ~6/5, ~3

POTE generator: ~3/2 = 709.109

Optimal GPV sequence: 4, 8d, 12, 32cddee, 44cddeee

Badness: 0.022132

Scales: diminished12

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 40/39, 50/49, 66/65

Mapping: [⟨4 0 3 5 14 15], ⟨0 1 1 1 0 0]]

Mapping generators: ~6/5, ~3

POTE generator: ~3/2 = 713.773

Optimal GPV sequence: 4, 8d, 12f, 20cdef

Badness: 0.019509

Scales: diminished12

Demolished

Subgroup: 2.3.5.7.11

Comma list: 36/35, 45/44, 50/49

Mapping: [⟨4 0 3 5 -5], ⟨0 1 1 1 3]]

Mapping generators: ~6/5, ~3

POTE generator: ~3/2 = 689.881

Optimal GPV sequence: 12, 28, 40de

Badness: 0.026574

Cohedim

This temperament has been documented in Graham Breed's temperament finder as hemidim, the same name as 11-limit 4e&24 and 13-limit 4ef&24. For 11-limit 8bce&12 temperament, cohedim arguably makes more sense.

Subgroup: 2.3.5.7.11

Comma list: 36/35, 50/49, 125/121

Mapping: [⟨4 1 4 6 6], ⟨0 2 2 2 3]]

Mapping generators: ~6/5, ~11/7

POTE generator: ~12/11 = 101.679

Optimal GPV sequence: 8bce, 12

Badness: 0.054965

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 50/49, 66/65, 125/121

Mapping: [⟨4 1 4 6 6 7], ⟨0 2 2 2 3 3]]

POTE generator: ~12/11 = 102.299

Optimal GPV sequence: 8bcef, 12f

Badness: 0.041707

Doublewide

Subgroup: 2.3.5.7

Comma list: 50/49, 875/864

Mapping: [⟨2 1 3 4], ⟨0 4 3 3]]

POTE generator: ~6/5 = 325.719

Optimal GPV sequence: 4, 14bd, 18, 22, 48, 70c

Badness: 0.043462

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 875/864

Mapping: [⟨2 1 3 4 8], ⟨0 4 3 3 -2]]

POTE generator: ~6/5 = 325.545

Optimal GPV sequence: 4, 14bd, 18, 22, 48, 70c, 118cd

Badness: 0.032058

Fleetwood

Subgroup: 2.3.5.7.11

Comma list: 50/49, 55/54, 176/175

Mapping: [⟨2 1 3 4 2], ⟨0 4 3 3 9]]

POTE generator: ~6/5 = 327.038

Optimal GPV sequence: 4e, 18e, 22

Badness: 0.035202

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 55/54, 65/63, 176/175

Mapping: [⟨2 1 3 4 2 3], ⟨0 4 3 3 9 8]]

POTE generator: ~6/5 = 327.841

Optimal GPV sequence: 4ef, 18e, 22, 84bddf

Badness: 0.031835

Cavalier

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49, 875/864

Mapping: [⟨2 1 3 4 1], ⟨0 4 3 3 11]]

POTE generator: ~6/5 = 323.427

Optimal GPV sequence: 22e, 26

Badness: 0.052899

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 50/49, 78/77, 325/324

Mapping: [⟨2 1 3 4 1 2], ⟨0 4 3 3 11 10]]

POTE generator: ~6/5 = 323.396

Optimal GPV sequence: 22ef, 26

Badness: 0.035040

Elvis

For the 5-limit version of this temperament, see High badness temperaments #Elvis.

Subgroup: 2.3.5.7

Comma list: 50/49, 8505/8192

Mapping: [⟨2 1 10 11], ⟨0 2 -5 -5]]

Wedgie: ⟨⟨4 -10 -10 -25 -27 5]]

POTE generator: ~45/32 = 553.721

Optimal GPV sequence: 2, 24c, 26

Badness: 0.141473

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49, 1344/1331

Mapping: [⟨2 1 10 11 8], ⟨0 2 -5 -5 -1]]

POTE generator: ~11/8 = 553.882

Optimal GPV sequence: 2, 24c, 26

Badness: 0.063212

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 50/49, 78/77, 1053/1024

Mapping: [⟨2 1 10 11 8 16], ⟨0 2 -5 -5 -1 -8]]

POTE generator: ~11/8 = 553.892

Optimal GPV sequence: 2f, 24cf, 26

Badness: 0.043997

Crepuscular

See also: Fifive family #Crepuscular

Subgroup: 2.3.5.7

Comma list: 50/49, 4375/4374

Mapping: [⟨2 2 3 4], ⟨0 5 7 7]]

Wedgie: ⟨⟨10 14 14 -1 -6 -7]]

POTE generator: ~27/25 = 140.349

Optimal GPV sequence: 8d, 26, 34d, 60d

Badness: 0.086669

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 864/847

Mapping: [⟨2 2 3 4 6], ⟨0 5 7 7 4]]

POTE generator: ~12/11 = 140.587

Optimal GPV sequence: 8d, 26, 34d, 60d

Badness: 0.040758

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 78/77, 99/98, 144/143

Mapping: [⟨2 2 3 4 6 6], ⟨0 5 7 7 4 6]]

POTE generator: ~12/11 = 140.554

Optimal GPV sequence: 8d, 26, 34d, 60d

Badness: 0.024368

Comic

For the 5-limit version of this temperament, see High badness temperaments #Comic.

Subgroup: 2.3.5.7

Comma list: 50/49, 2240/2187

Mapping: [⟨2 1 -3 -2], ⟨0 2 7 7]]

Wedgie: ⟨⟨4 14 14 13 11 -7]]

POTE generator: ~81/80 = 54.699

Optimal GPV sequence: 20cd, 22

Badness: 0.084395

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 2662/2625

Mapping: [⟨2 1 -3 -2 -4], ⟨0 2 7 7 10]]

POTE generator: ~81/80 = 55.184

Optimal GPV sequence: 20cde, 22

Badness: 0.045052

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 65/63, 99/98, 968/945

Mapping: [⟨2 1 -3 -2 -4 3], ⟨0 2 7 7 10 4]]

POTE generator: ~81/80 = 54.435

Optimal GPV sequence: 22

Badness: 0.041470

Bipyth

See also: Archytas clan #Superpyth

Subgroup: 2.3.5.7

Comma list: 50/49, 20480/19683

Mapping: [⟨2 0 -24 -23], ⟨0 1 9 9]]

Wedgie: ⟨⟨2 18 18 24 23 -9]]

POTE generator: ~3/2 = 709.437

Optimal GPV sequence: 10cd, 12cd, 22

Badness: 0.165033

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 121/120, 896/891

Mapping: [⟨2 0 -24 -23 -9], ⟨0 1 9 9 5]]

POTE generator: ~3/2 = 709.310

Optimal GPV sequence: 10cd, 12cde, 22

Badness: 0.070910

Sedecic

Subgroup: 2.3.5.7

Comma list: 50/49, 546875/524288

Mapping: [⟨16 0 37 45], ⟨0 1 0 0]]

Wedgie: ⟨⟨16 0 0 -37 -45 0]]

POTE generator: ~3/2 = 700.554

Optimal GPV sequence: 16, 32, 48

Badness: 0.265972

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 385/384, 1331/1323

Mapping: [⟨16 0 37 45 30], ⟨0 1 0 0 1]]

POTE generator: ~3/2 = 700.331

Optimal GPV sequence: 16, 32, 48

Badness: 0.092774

Duodecim

See also: Compton family #Duodecim

Subgroup: 2.3.5.7.11

Comma list: 36/35, 50/49, 64/63

Mapping: [⟨12 19 28 34 0], ⟨0 0 0 0 1]]

POTE generator: ~11/8 = 565.023

Optimal GPV sequence: 12, 24d, 36d

Badness: 0.030536

Vigintiduo

Subgroup: 2.3.5.7.11

Comma list: 50/49, 64/63, 245/243

Mapping: [⟨22 35 51 62 0], ⟨0 0 0 0 1]]

POTE generator: ~11/8 = 557.563

Optimal GPV sequence: 22, 66de, 88bde, 110bd, 198bcdde

Badness: 0.048372

Vigin

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 55/54, 64/63, 99/98

Mapping: [⟨22 35 51 62 76 0], ⟨0 0 0 0 0 1]]

POTE generator: ~13/8 = 844.624

Optimal GPV sequence: 22, 44

Badness: 0.029849

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