Mabila family
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The mabila family of temperaments tempers out the mabila comma (monzo: [28 -3 -10⟩, ratio: 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 and minor chords.
Mabila
Subgroup: 2.3.5
Comma list: 268435456/263671875
Mapping: [⟨1 6 1], ⟨0 -10 3]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~512/375 = 529.685 ¢
Optimal ET sequence: 9, 25, 34, 77, 111, 145, 256c
Badness (Smith): 0.232481
Semabila
Semabila is so named because it is a semaphore temperament.
Subgroup: 2.3.5.7
Comma list: 49/48, 28672/28125
Mapping: [⟨1 6 1 5], ⟨0 -10 3 -5]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~75/56 = 529.667 ¢
Optimal ET sequence: 9, 25, 34
Badness (Smith): 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 = 1200.000 ¢, ~15/11 = 529.729 ¢
Optimal ET sequence: 9, 25e, 34
Badness (Smith): 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 = 1200.000 ¢, ~15/11 = 529.763 ¢
Optimal ET sequence: 9, 25e, 34
Badness (Smith): 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 = 1200.000 ¢, ~15/11 = 529.695 ¢
Optimal ET sequence: 9, 25e, 34
Badness (Smith): 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 = 1200.000 ¢, ~15/11 = 529.736 ¢
Optimal ET sequence: 9, 25e, 34
Badness (Smith): 0.026981
Amavil
Subgroup: 2.3.5.7
Comma list: 225/224, 17496/16807
Mapping: [⟨1 6 1 9], ⟨0 -10 3 -14]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~48/35 = 529.979 ¢
Optimal ET sequence: 9, 25d, 34d, 43, 77d, 120dd
Badness (Smith): 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 = 1200.000 ¢, ~15/11 = 529.974 ¢
Optimal ET sequence: 9, 25de, 34d, 43, 77de, 120dde
Badness (Smith): 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 = 1200.000 ¢, ~15/11 = 529.951 ¢
Optimal ET sequence: 9, 25de, 34d, 43, 77de, 120dde
Badness (Smith): 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 = 1200.000 ¢, ~15/11 = 529.957 ¢
Optimal ET sequence: 9, 25de, 34d, 43, 77de, 120ddeg
Badness (Smith): 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 = 1200.000 ¢, ~15/11 = 529.987 ¢
Optimal ET sequence: 9, 25deh, 34dh, 43, 77deh, 120ddeghh
Badness (Smith): 0.017955
Tuskaloosa
Subgroup: 2.3.5.7
Comma list: 19683/19600, 110592/109375
Mapping: [⟨1 6 1 24], ⟨0 -10 3 -48]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~512/375 = 529.772 ¢
Optimal ET sequence: 34d, 77, 111, 188, 299cd
Badness (Smith): 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 = 1200.000 ¢, ~224/165 = 529.749 ¢
Optimal ET sequence: 34d, 77, 111, 299cd, 410ccd, 521ccdd
Badness (Smith): 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 = 1200.000 ¢, ~65/48 = 529.747 ¢
Optimal ET sequence: 34d, 77, 111, 410ccdf, 521ccddff
Badness (Smith): 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 = 1200.000 ¢, ~34/25 = 529.742 ¢
Optimal ET sequence: 34d, 77, 111
Badness (Smith): 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 = 1200.000 ¢, ~19/14 = 529.749 ¢
Optimal ET sequence: 34dh, 77, 111
Badness (Smith): 0.017924
Muscogee
Subgroup: 2.3.5.7
Comma list: 126/125, 33756345/33554432
Mapping: [⟨1 6 1 -10], ⟨0 -10 3 29]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~512/375 = 529.907 ¢
Optimal ET sequence: 34, 43, 77, 274c, 351cc, 428ccd
Badness (Smith): 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 = 1200.000 ¢, ~224/165 = 529.955 ¢
Optimal ET sequence: 34e, 43, 77, 120, 197ce
Badness (Smith): 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 = 1200.000 ¢, ~65/48 = 529.957 ¢
Optimal ET sequence: 34e, 43, 77, 120, 197ce
Badness (Smith): 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 = 1200.000 ¢, ~34/25 = 529.958 ¢
Optimal ET sequence: 34e, 43, 77, 120g, 197ceg
Badness (Smith): 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 = 1200.000 ¢, ~19/14 = 529.955 ¢
Optimal ET sequence: 34e, 43, 77, 120g, 197ceg
Badness (Smith): 0.023670
Hemimabila
Subgroup: 2.3.5.7
Comma list: 6144/6125, 117649/116640
Mapping: [⟨1 6 1 7], ⟨0 -20 6 -19]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/6 = 264.825 ¢
Optimal ET sequence: 9, 59, 68, 77, 145
Badness (Smith): 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 = 1200.000 ¢, ~7/6 = 264.849 ¢
Optimal ET sequence: 9, 59, 68, 77, 145e
Badness (Smith): 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 = 1200.000 ¢, ~7/6 = 264.861 ¢
Optimal ET sequence: 9, 59f, 68, 77, 145e, 222cef
Badness (Smith): 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 = 1200.000 ¢, ~7/6 = 264.839 ¢
Optimal ET sequence: 9, 59f, 68, 77, 145e
Badness (Smith): 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 = 1200.000 ¢, ~7/6 = 264.839 ¢
Optimal ET sequence: 9, 59f, 68, 77, 145e
Badness (Smith): 0.020053
Cohemimabila
Subgroup: 2.3.5.7
Comma list: 3136/3125, 65536/64827
Mapping: [⟨1 -4 4 7], ⟨0 20 -6 -15]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~128/105 = 335.182 ¢
Optimal ET sequence: 25, 43, 68, 111, 179, 290cd, 469bccdd
Badness (Smith): 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 = 1200.000 ¢, ~40/33 = 335.148 ¢
Optimal ET sequence: 25, 43, 68, 111
Badness (Smith): 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 = 1200.000 ¢, ~40/33 = 335.144 ¢
Optimal ET sequence: 25, 43, 68, 111
Badness (Smith): 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 = 1200.000 ¢, ~17/14 = 335.145 ¢
Optimal ET sequence: 25, 43, 68, 111
Badness (Smith): 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 = 1200.000 ¢, ~17/14 = 335.151 ¢
Optimal ET sequence: 25, 43, 68, 111
Badness (Smith): 0.017450
Trimabila
Subgroup: 2.3.5.7
Comma list: 1728/1715, 268435456/263671875
Mapping: [⟨3 8 6 12], ⟨0 -10 3 -11]]
Optimal tuning (POTE): ~1125/896 = 400.000 ¢, ~7/6 = 270.269 ¢
Optimal ET sequence: 9, 102d, 111
Badness (Smith): 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 = 400.000 ¢, ~7/6 = 270.256 ¢
Optimal ET sequence: 9, 102d, 111
Badness (Smith): 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 = 400.000 ¢, ~7/6 = 270.254 ¢ (or ~14/13 = 129.746 ¢)
Optimal ET sequence: 9, 102df, 111
Badness (Smith): 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 = 400.000 ¢, ~7/6 = 270.266 ¢ (or ~14/13 = 129.734 ¢)
Optimal ET sequence: 9, 102df, 111
Badness (Smith): 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 = 400.000 ¢, ~7/6 = 270.260 ¢ (or ~14/13 = 129.740 ¢)
Optimal ET sequence: 9, 102dfh, 111
Badness (Smith): 0.022851