Jubilismic clan

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.

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 sequence: 2, 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. Diminished splits the ~7/5 period into a further two. Pajara slices the ~7/4 into two. 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

• Diminished → Dimipent family
• Pajara → Diaschismic family
• Decimal → Dicot family
• Injera → Meantone family
• Octokaidecal → Trienstonic clan
• Hedgehog → Porcupine family
• Bipelog → Pelogic family
• Dubbla → Wesley family
• Hexe → Augmented family

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 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]]

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

Optimal ET 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]]

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

Optimal ET sequence: 10, 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 sequence: 6, 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 sequence: 6, 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 sequence: 6, 16, 22, 38f

Badness: 0.034376

Music

• Astrology Percussion Quintet No 1^{[dead link]} play^{[dead link]} by Joel Taylor

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 sequence: 16, 22f, 38

Badness: 0.035284

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 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]]

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

Optimal ET 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]]

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

Optimal ET 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]]

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

Optimal ET 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]]

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

Optimal ET 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]]

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

Optimal ET 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 ]]

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

Optimal ET 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]]

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

Optimal ET 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]]

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

Optimal ET 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 ]]

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

Optimal ET 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]]

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

Optimal ET 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]]

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

Optimal ET 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 ]]

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

Optimal ET 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]]

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

Optimal ET 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]]

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

Optimal ET 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 ]]

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

Optimal ET 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]]

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

Optimal ET 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 ]]

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

Optimal ET 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]]

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

Optimal ET 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]]

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

Optimal ET 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]]

Optimal tuning (POTE): ~36/35 = 1\22, ~11/8 = 557.563

Optimal ET 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]]

Optimal tuning (POTE): ~33/32 = 1\22, ~13/8 = 844.624

Optimal ET sequence: 22, 44

Badness: 0.029849