Mabila family

The mabila family of rank-2 temperaments tempers out [28 -3 -10⟩ = 268435456/263671875 in the 5-limit. This gives a temperament structure superficially similar to mavila, with extremely sharp fourths/flat fifths, three of which make a major third. However, unlike mavila, 10 of these bad fifths reach a more in tune one, which is useful for creating resolutions when using a large enough gamut, such as the 9L 7s mos which has 3 good major & minor chords.

Mabila

Subgroup: 2.3.5

Comma list: 268435456/263671875

Mapping: [⟨1 6 1], ⟨0 -10 3]]

Optimal tuning (POTE): ~2 = 1\1, ~512/375 = 529.685

Optimal ET sequence: 9, 25, 34, 77, 111, 145, 256c

Badness: 0.232481

Semabila

See also: Semaphoresmic clan § Semabila

See also: No-threes subgroup temperaments § Mabilic

Subgroup: 2.3.5.7

Comma list: 49/48, 28672/28125

Mapping: [⟨1 6 1 5], ⟨0 -10 3 -5]]

Wedgie: ⟨⟨ 10 -3 5 -28 -20 20 ]]

Optimal tuning (POTE): ~2 = 1\1, ~75/56 = 529.667

Optimal ET sequence: 9, 25, 34

Badness: 0.133638

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 56/55, 1350/1331

Mapping: [⟨1 6 1 5 7], ⟨0 -10 3 -5 -8]]

Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.729

Optimal ET sequence: 9, 25e, 34

Badness: 0.061501

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 56/55, 91/90, 847/845

Mapping: [⟨1 6 1 5 7 9], ⟨0 -10 3 -5 -8 -12]]

Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.763

Optimal ET sequence: 9, 25e, 34

Badness: 0.037270

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 49/48, 56/55, 91/90, 154/153, 375/374

Mapping: [⟨1 6 1 5 7 9 1], ⟨0 -10 3 -5 -8 -12 7]]

Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.695

Optimal ET sequence: 9, 25e, 34

Badness: 0.031888

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187

Mapping: [⟨1 6 1 5 7 9 1 6], ⟨0 -10 3 -5 -8 -12 7 -4]]

Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.736

Optimal ET sequence: 9, 25e, 34

Badness: 0.026981

Amavil

Subgroup: 2.3.5.7

Comma list: 225/224, 17496/16807

Mapping: [⟨1 6 1 9], ⟨0 -10 3 -14]]

Wedgie: ⟨⟨ 10 -3 14 -28 -6 41 ]]

Optimal tuning (POTE): ~2 = 1\1, ~48/35 = 529.979

Optimal ET sequence: 9, 25d, 34d, 43, 77d, 120dd

Badness: 0.109625

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 864/847

Mapping: [⟨1 6 1 9 7], ⟨0 -10 3 -14 -8]]

Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.974

Optimal ET sequence: 9, 25de, 34d, 43, 77de, 120dde

Badness: 0.042649

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 78/77, 99/98, 144/143, 176/175

Mapping: [⟨1 6 1 9 7 9], ⟨0 -10 3 -14 -8 -12]]

Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.951

Optimal ET sequence: 9, 25de, 34d, 43, 77de, 120dde

Badness: 0.025791

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 78/77, 99/98, 120/119, 144/143, 176/175

Mapping: [⟨1 6 1 9 7 9 1], ⟨0 -10 3 -14 -8 -12 7]]

Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.957

Optimal ET sequence: 9, 25de, 34d, 43, 77de, 120ddeg

Badness: 0.022092

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 78/77, 96/95, 99/98, 120/119, 135/133, 144/143

Mapping: [⟨1 6 1 9 7 9 1 10], ⟨0 -10 3 -14 -8 -12 7 -13]]

Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.987

Optimal ET sequence: 9, 25deh, 34dh, 43, 77deh, 120ddeghh

Badness: 0.017955

Tuskaloosa

Subgroup: 2.3.5.7

Comma list: 19683/19600, 110592/109375

Mapping: [⟨1 6 1 24], ⟨0 -10 3 -48]]

Wedgie: ⟨⟨ 10 -3 48 -28 48 120 ]]

Optimal tuning (POTE): ~2 = 1\1, ~512/375 = 529.772

Optimal ET sequence: 34d, 77, 111, 188, 299cd

Badness: 0.145058

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 1331/1323, 19683/19600

Mapping: [⟨1 6 1 24 22], ⟨0 -10 3 -48 -42]]

Optimal tuning (POTE): ~2 = 1\1, ~224/165 = 529.749

Optimal ET sequence: 34d, 77, 111, 299cd, 410ccd, 521ccdd

Badness: 0.061773

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 351/350, 676/675, 1331/1323

Mapping: [⟨1 6 1 24 22 9], ⟨0 -10 3 -48 -42 -12]]

Optimal tuning (POTE): ~2 = 1\1, ~65/48 = 529.747

Optimal ET sequence: 34d, 77, 111, 410ccdf, 521ccddff

Badness: 0.031480

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 176/175, 256/255, 351/350, 676/675, 715/714

Mapping: [⟨1 6 1 24 22 9 1], ⟨0 -10 3 -48 -42 -12 7]]

Optimal tuning (POTE): ~2 = 1\1, ~34/25 = 529.742

Optimal ET sequence: 34d, 77, 111

Badness: 0.022765

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 176/175, 256/255, 286/285, 351/350, 363/361, 476/475

Mapping: [⟨1 6 1 24 22 9 1 25], ⟨0 -10 3 -48 -42 -12 7 -47]]

Optimal tuning (POTE): ~2 = 1\1, ~19/14 = 529.749

Optimal ET sequence: 34dh, 77, 111

Badness: 0.017924

Muscogee

Subgroup: 2.3.5.7

Comma list: 126/125, 33756345/33554432

Mapping: [⟨1 6 1 -10], ⟨0 -10 3 29]]

Wedgie: ⟨⟨ 10 -3 -29 -28 -74 -59 ]]

Optimal tuning (POTE): ~2 = 1\1, ~512/375 = 529.907

Optimal ET sequence: 34, 43, 77, 274c, 351cc, 428ccd

Badness: 0.162021

11-limit

Subgroup: 2.3.5.7.11

Comma list: 126/125, 176/175, 264627/262144

Mapping: [⟨1 6 1 -10 -12], ⟨0 -10 3 29 35]]

Optimal tuning (POTE): ~2 = 1\1, ~224/165 = 529.955

Optimal ET sequence: 34e, 43, 77, 120, 197ce

Badness: 0.077552

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 176/175, 676/675, 1287/1280

Mapping: [⟨1 6 1 -10 -12 9], ⟨0 -10 3 29 35 -12]]

Optimal tuning (POTE): ~2 = 1\1, ~65/48 = 529.957

Optimal ET sequence: 34e, 43, 77, 120, 197ce

Badness: 0.043352

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 126/125, 176/175, 256/255, 273/272, 676/675

Mapping: [⟨1 6 1 -10 -12 9 1], ⟨0 -10 3 29 35 -12 7]]

Optimal tuning (POTE): ~2 = 1\1, ~34/25 = 529.958

Optimal ET sequence: 34e, 43, 77, 120g, 197ceg

Badness: 0.031217

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 126/125, 171/170, 176/175, 256/255, 273/272, 363/361

Mapping: [⟨1 6 1 -10 -12 9 1 -9], ⟨0 -10 3 29 35 -12 7 30]]

Optimal tuning (POTE): ~2 = 1\1, ~19/14 = 529.955

Optimal ET sequence: 34e, 43, 77, 120g, 197ceg

Badness: 0.023670

Hemimabila

Subgroup: 2.3.5.7

Comma list: 6144/6125, 117649/116640

Mapping: [⟨1 6 1 7], ⟨0 -20 6 -19]]

Wedgie: ⟨⟨ 20 -6 19 -56 -26 61 ]]

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 264.825

Optimal ET sequence: 9, 59, 68, 77, 145

Badness: 0.111130

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 67228/66825

Mapping: [⟨1 6 1 7 5], ⟨0 -20 6 -19 -7]]

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 264.849

Optimal ET sequence: 9, 59, 68, 77, 145e

Badness: 0.061426

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 176/175, 196/195, 676/675

Mapping: [⟨1 6 1 7 5 9], ⟨0 -20 6 -19 -7 -24]]

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 264.861

Optimal ET sequence: 9, 59f, 68, 77, 145e, 222cef

Badness: 0.034531

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 121/120, 154/153, 176/175, 196/195, 676/675

Mapping: [⟨1 6 1 7 5 9 1], ⟨0 -20 6 -19 -7 -24 14]]

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 264.839

Optimal ET sequence: 9, 59f, 68, 77, 145e

Badness: 0.027851

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 121/120, 154/153, 176/175, 196/195, 209/208, 361/360

Mapping: [⟨1 6 1 7 5 9 1 8], ⟨0 -20 6 -19 -7 -24 14 -17]]

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 264.839

Optimal ET sequence: 9, 59f, 68, 77, 145e

Badness: 0.020053

Cohemimabila

Subgroup: 2.3.5.7

Comma list: 3136/3125, 65536/64827

Mapping: [⟨1 -4 4 7], ⟨0 20 -6 -15]]

Wedgie: ⟨⟨ 20 -6 -15 -56 -80 -18 ]]

Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 335.182

Optimal ET sequence: 25, 43, 68, 111, 179, 290cd, 469bccdd

Badness: 0.127451

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 1375/1372, 16384/16335

Mapping: [⟨1 -4 4 7 11], ⟨0 20 -6 -15 -27]]

Optimal tuning (POTE): ~2 = 1\1, ~40/33 = 335.148

Optimal ET sequence: 25, 43, 68, 111

Badness: 0.064164

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 640/637, 676/675, 1375/1372

Mapping: [⟨1 -4 4 7 11 -3], ⟨0 20 -6 -15 -27 24]]

Optimal tuning (POTE): ~2 = 1\1, ~40/33 = 335.144

Optimal ET sequence: 25, 43, 68, 111

Badness: 0.035463

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 176/175, 256/255, 442/441, 640/637, 715/714

Mapping: [⟨1 -4 4 7 11 -3 8], ⟨0 20 -6 -15 -27 24 -14]]

Optimal tuning (POTE): ~2 = 1\1, ~17/14 = 335.145

Optimal ET sequence: 25, 43, 68, 111

Badness: 0.022728

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 176/175, 256/255, 286/285, 363/361, 442/441, 476/475

Mapping: [⟨1 -4 4 7 11 -3 8 9], ⟨0 20 -6 -15 -27 24 -14 -17]]

Optimal tuning (POTE): ~2 = 1\1, ~17/14 = 335.151

Optimal ET sequence: 25, 43, 68, 111

Badness: 0.017450

Trimabila

Subgroup: 2.3.5.7

Comma list: 1728/1715, 268435456/263671875

Mapping: [⟨3 8 6 12], ⟨0 -10 3 -11]]

Wedgie: ⟨⟨ 30 -9 33 -84 -32 102 ]]

Optimal tuning (POTE): ~1125/896 = 1\3, ~7/6 = 270.269

Optimal ET sequence: 9, 102d, 111

Badness: 0.267168

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 540/539, 805255/802816

Mapping: [⟨3 8 6 12 12], ⟨0 -10 3 -11 -5]]

Optimal tuning (POTE): ~495/392 = 1\3, ~7/6 = 270.256

Optimal ET sequence: 9, 102d, 111

Badness: 0.081946

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 540/539, 676/675, 1573/1568

Mapping: [⟨3 8 6 12 12 15], ⟨0 -10 3 -11 -5 -12]]

Optimal tuning (POTE): ~495/392 = 1\3, ~7/6 = 270.254 (or ~14/13 = 129.746)

Optimal ET sequence: 9, 102df, 111

Badness: 0.040102

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 176/175, 256/255, 540/539, 676/675, 715/714

Mapping: [⟨3 8 6 12 12 15 10], ⟨0 -10 3 -11 -5 -12 7]]

Optimal tuning (POTE): ~495/392 = 1\3, ~7/6 = 270.266 (or ~14/13 = 129.734)

Optimal ET sequence: 9, 102df, 111

Badness: 0.030657

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 176/175, 256/255, 286/285, 363/361, 476/475, 540/539

Mapping: [⟨3 8 6 12 12 15 10 16], ⟨0 -10 3 -11 -5 -12 7 -10]]

Optimal tuning (POTE): ~208/165 = 1\3, ~7/6 = 270.260 (or ~14/13 = 129.740)

Optimal ET sequence: 9, 102dfh, 111

Badness: 0.022851