Jubilismic clan

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The jubilismic clan tempers out the jubilisma, 50/49, which means 7/5 and 10/7 are both equated to the 600-cent tritone and the octave is divided in two.

Jubilic

The head of this clan, jubilic, is generated by ~5/4. That and a semioctave gives ~7/4.

Subgroup: 2.5.7

Comma list: 50/49

Sval mapping[2 0 1], 0 1 1]]

sval mapping generators: ~7/5, ~5

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

Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 380.840

Optimal ET sequence2, 4, 6, 16, 22, 60d, 82d, 104dd

Overview to extensions

Lemba finds the perfect fifth three steps away by tempering out 1029/1024. Astrology, five steps away by tempering out 3125/3072. Decimal, two steps away by tempering out 25/24 and 49/48. Walid merges ~5/4 and ~4/3 by tempering out 16/15.

Diminished splits the ~7/5 period into a further two. Pajara slices the ~7/4 into two, with antikythera being every other step thereof. Injera slices the ~5/1 into four. Hedgehog slices the ~7/1 into five.

Lemba, astrology, and doublewide are discussed below; others in the clan are

which are discussed elsewhere.

Lemba

Main article: Lemba

Lemba tempers out 1029/1024, the gamelisma, and a stack of three ~8/7 generators gives an approximate perfect fifth.

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

Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 232.089

Optimal ET sequence10, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.974

Optimal ET sequence10, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.966

Optimal ET sequence10, 16, 26

Badness: 0.025477

Astrology

Astrology tempers out 3125/3072, the magic comma, and a stack of five ~5/4 generators gives an approximate harmonic 3.

Subgroup: 2.3.5.7

Comma list: 50/49, 3125/3072

Mapping[2 0 4 5], 0 5 1 1]]

mapping geenerators: ~7/5, ~5/4

Wedgie⟨⟨10 2 2 -20 -25 -1]]

Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 380.578

Optimal ET sequence6, 16, 22, 60d, 82d

Badness: 0.082673

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 121/120, 176/175

Mapping: [2 0 4 5 5], 0 5 1 1 3]]

Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 380.530

Optimal ET sequence6, 16, 22, 60de, 82de

Badness: 0.039151

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 65/64, 78/77, 121/120

Mapping: [2 0 4 5 5 8], 0 5 1 1 3 -1]]

Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 379.787

Optimal ET sequence6, 16, 22, 38f

Badness: 0.034376

Music

Horoscope

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 66/65, 105/104, 121/120

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

Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 379.837

Optimal ET sequence16, 22f, 38

Badness: 0.035284

Walid

Subgroup: 2.3.5.7

Comma list: 16/15, 50/49

Mapping[2 0 8 9], 0 1 -1 -1]]

mapping generators: ~7/5, ~3

Wedgie⟨⟨2 -2 -2 -8 -9 1]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 749.415

Optimal ET sequence2, 6, 8d

Badness: 0.048978

11-limit

Subgroup: 2.3.5.7.11

Comma list: 16/15, 22/21, 50/49

Mapping: [2 0 8 9 7], 0 1 -1 -1 0]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 749.756

Optimal ET sequence2, 6, 8d

Badness: 0.029193

Antikythera

Named by Gene Ward Smith in 2011[1], antikythera is every other step of pajara.

Subgroup: 2.9.5.7

Comma list: 50/49, 64/63

Sval mapping[2 0 11 12], 0 1 -1 -1]]

mapping generators: ~7/5, ~9

Gencom mapping[2 3 5 6], 0 1/2 -1 -1]]

gencom: [7/5 8/7; 50/49 64/63]

Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 214.095

Optimal ET sequence4, 6, 16, 22, 28

Badness: 0.00501

Doublewide

Subgroup: 2.3.5.7

Comma list: 50/49, 875/864

Mapping[2 1 3 4], 0 4 3 3]]

Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 325.719

Optimal ET sequence4, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 325.545

Optimal ET sequence4, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.038

Optimal ET sequence4e, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.841

Optimal ET sequence4ef, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.427

Optimal ET sequence22e, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.396

Optimal ET sequence22ef, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~45/32 = 553.721

Optimal ET sequence2, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.882

Optimal ET sequence2, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.892

Optimal ET sequence2f, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~27/25 = 140.349

Optimal ET sequence8d, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.587

Optimal ET sequence8d, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.554

Optimal ET sequence8d, 26, 34d, 60d

Badness: 0.024368

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 50/49, 78/77, 85/84, 99/98, 144/143

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

Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.405

Optimal ET sequence8d, 26, 34d, 60d

Badness: 0.018567

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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 54.699

Optimal ET sequence20cd, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 55.184

Optimal ET sequence20cde, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 54.435

Optimal ET sequence22

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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.437

Optimal ET sequence10cd, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.310

Optimal ET sequence10cd, 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]]

Optimal tuning (POTE): ~128/125 = 1\16, ~3/2 = 700.554

Optimal ET sequence16, 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]]

Optimal tuning (POTE): ~22/21 = 1\16, ~3/2 = 700.331

Optimal ET sequence16, 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]]

Optimal tuning (POTE): ~16/15 = 1\12, ~11/8 = 565.023

Optimal ET sequence12, 24d, 36d

Badness: 0.030536