Xenharmonic Wiki

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.

Mabila

"Mabila" redirects here. For the temperaments that used to go by this name, see Semabila and Mabilic.

Mabila has 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 is part of the diaschismic–gothmic equivalence continuum with n = 5.

Subgroup: 2.3.5

Comma list: 268435456/263671875

Mapping: [⟨1 -4 4], ⟨0 10 -3]]

mapping generators: ~2, ~375/256

Optimal tunings:

  • WE: ~2 = 1199.3545 ¢, ~375/256 = 669.9545 ¢
error map: ⟨-0.646 +0.173 +1.240]
  • CWE: ~2 = 1200.0000 ¢, ~375/256 = 670.2921 ¢
error map: ⟨0.000 +0.966 +2.810]

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

Badness (Sintel): 5.45

Overview to extensions

The second comma in the comma list defines which 7-limit family member we are looking at. Amavil (9 & 43) adds 225/224, semabila (9 & 25) adds 49/48, tuscaloosa (77 & 111) adds 19683/19600, muscogee (43 & 77) adds 126/125. These all use the same generators as mabila.

Cohemimabila (25 & 43) tempers out 3136/3125, splitting the subfifth in two. Hemimabila (9 & 68) tempers out 6144/6125, splitting the subtwelfth in two. Trimabila (9 & 111) tempers out 1728/1715, with a 1/3-octave period.

Amavil

Named by Petr Pařízek in 2011[1], amavil tempers out 225/224 and may be described as the 9 & 43 temperament.

Subgroup: 2.3.5.7

Comma list: 225/224, 17496/16807

Mapping: [⟨1 -4 4 -5], ⟨0 10 -3 14]]

Optimal tunings:

  • WE: ~2 = 1198.8499 ¢, ~35/24 = 669.3786 ¢
error map: ⟨-1.150 -3.569 +0.950 +8.224]
  • CWE: ~2 = 1200.0000 ¢, ~35/24 = 669.9710 ¢
error map: ⟨0.000 -2.245 +3.773 +10.768]

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

Badness (Sintel): 2.77

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 -4 4 -5 -1], ⟨0 10 -3 14 8]]

Optimal tunings:

  • WE: ~2 = 1198.5522 ¢, ~22/15 = 669.2176 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 669.9619 ¢

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

Badness (Sintel): 1.41

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 -4 4 -5 -1 -3], ⟨0 10 -3 14 8 12]]

Optimal tunings:

  • WE: ~2 = 1198.7386 ¢, ~22/15 = 669.3449 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 669.9903 ¢

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

Badness (Sintel): 1.07

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 -4 4 -5 -1 -3 8], ⟨0 10 -3 14 8 12 -7]]

Optimal tunings:

  • WE: ~2 = 1198.7648 ¢, ~22/15 = 669.3533 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 670.0080 ¢

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

Badness (Sintel): 1.13

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 -4 4 -5 -1 -3 8 -3], ⟨0 10 -3 14 8 12 -7 13]]

Optimal tunings:

  • WE: ~2 = 1198.5939 ¢, ~22/15 = 669.2282 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 669.9712 ¢

Optimal ET sequence: 9, 34dh, 43, 77deh

Badness (Sintel): 1.09

Semabila

See also: No-threes subgroup temperaments § Mabilic

Semabila tempers out 49/48 and may be described as the 9 & 25 temperament.

This temperament used to known as septimal mabila. Semabila, by Lériendil in 2024, was so named because it was a semaphore temperament.

Subgroup: 2.3.5.7

Comma list: 49/48, 28672/28125

Mapping: [⟨1 -4 4 0], ⟨0 10 -3 5]]

Optimal tunings:

  • WE: ~2 = 1200.9854 ¢, ~112/75 = 670.8838 ¢
error map: ⟨+0.985 +2.941 +4.977 -14.407]
  • CWE: ~2 = 1200.0000 ¢, ~112/75 = 670.3712 ¢
error map: ⟨0.000 +1.757 +2.573 -16.970]

Optimal ET sequence: 9, 25, 34

Badness (Sintel): 3.38

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 -4 4 0 1], ⟨0 10 -3 5 8]]

Optimal tunings:

  • WE: ~2 = 1200.2248 ¢, ~22/15 = 670.3965 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 670.2804 ¢

Optimal ET sequence: 9, 25e, 34

Badness (Sintel): 2.03

13-limit

Subgroup: 2.3.5.7.11.13

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

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

Optimal tunings:

  • WE: ~2 = 1200.1265 ¢, ~22/15 = 670.3078 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 670.2429 ¢

Optimal ET sequence: 9, 25e, 34

Badness (Sintel): 1.54

17-limit

Subgroup: 2.3.5.7.11.13.17

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

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

Optimal tunings:

  • WE: ~2 = 1199.8798 ¢, ~22/15 = 670.2382 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 670.3021 ¢

Optimal ET sequence: 9, 25e, 34

Badness (Sintel): 1.62

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 -4 4 0 1 -3 8 2], ⟨0 10 -3 5 8 12 -7 4]]

Optimal tunings:

  • WE: ~2 = 1200.4164 ¢, ~22/15 = 670.4966 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 670.2749 ¢

Optimal ET sequence: 9, 25e, 34

Badness (Sintel): 1.64

Tuskaloosa

Named by Xenllium in 2022, tuskaloosa tempers out 19683/19600 and may be described as the 34d & 77 temperament.

Subgroup: 2.3.5.7

Comma list: 19683/19600, 110592/109375

Mapping: [⟨1 -4 4 -24], ⟨0 10 -3 48]]

Optimal tunings:

  • WE: ~2 = 1199.4378 ¢, ~375/256 = 669.9137 ¢
error map: ⟨-0.562 -0.569 +1.696 +0.524]
  • CWE: ~2 = 1200.0000 ¢, ~375/256 = 670.2172 ¢
error map: ⟨0.000 +0.217 +3.035 +1.597]

Optimal ET sequence: 34d, 77, 111, 188, 299cd, 487ccd

Badness (Sintel): 3.67

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 -4 4 -24 -20], ⟨0 10 -3 48 42]]

Optimal tunings:

  • WE: ~2 = 1199.4934 ¢, ~165/112 = 669.9677 ¢
  • CWE: ~2 = 1200.0000 ¢, ~165/112 = 670.2405 ¢

Optimal ET sequence: 34d, 77, 111

Badness (Sintel): 2.04

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 -4 4 -24 -20 -3], ⟨0 10 -3 48 42 12]]

Optimal tunings:

  • WE: ~2 = 1199.4539 ¢, ~96/65 = 669.9476 ¢
  • CWE: ~2 = 1200.0000 ¢, ~96/65 = 670.2425 ¢

Optimal ET sequence: 34d, 77, 111

Badness (Sintel): 1.30

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 -4 4 -24 -20 -3 8], ⟨0 10 -3 48 42 12 -7]]

Optimal tunings:

  • WE: ~2 = 1199.3885 ¢, ~25/17 = 669.9167 ¢
  • CWE: ~2 = 1200.0000 ¢, ~25/17 = 670.2500 ¢

Optimal ET sequence: 34d, 77, 111

Badness (Sintel): 1.16

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 -4 4 -24 -20 -3 8 -22], ⟨0 10 -3 48 42 12 -7 47]]

Optimal tunings:

  • WE: ~2 = 1199.3711 ¢, ~25/17 = 669.8997 ¢
  • CWE: ~2 = 1200.0000 ¢, ~25/17 = 670.2422 ¢

Optimal ET sequence: 34dh, 77, 111

Badness (Sintel): 1.09

Muscogee

Named by Xenllium in 2022, muscogee tempers out 126/125 and may be described as the 43 & 77 temperament.

Subgroup: 2.3.5.7

Comma list: 126/125, 33756345/33554432

Mapping: [⟨1 -4 4 19], ⟨0 10 -3 -29]]

Optimal tunings:

  • WE: ~2 = 1199.9275 ¢, ~375/256 = 670.0525 ¢
error map: ⟨-0.073 -1.140 +3.239 -1.726]
  • CWE: ~2 = 1200.0000 ¢, ~375/256 = 670.0935 ¢
error map: ⟨0.000 -1.020 +3.406 -1.539]

Optimal ET sequence: 34, 43, 77

Badness (Sintel): 4.10

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 -4 4 19 23], ⟨0 10 -3 -29 -35]]

Optimal tunings:

  • WE: ~2 = 1200.0559 ¢, ~165/112 = 670.0760 ¢
  • CWE: ~2 = 1200.0000 ¢, ~165/112 = 670.0441 ¢

Optimal ET sequence: 34e, 43, 77, 120

Badness (Sintel): 2.56

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 -4 4 19 23 -3], ⟨0 10 -3 -29 -35 12]]

Optimal tunings:

  • WE: ~2 = 1200.0428 ¢, ~96/65 = 670.0673 ¢
  • CWE: ~2 = 1200.0000 ¢, ~96/65 = 670.0431 ¢

Optimal ET sequence: 34e, 43, 77, 120

Badness (Sintel): 1.79

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 -4 4 19 23 -3 8], ⟨0 10 -3 -29 -35 12 -7]]

Optimal tunings:

  • WE: ~2 = 1199.8666 ¢, ~25/17 = 669.9675 ¢
  • CWE: ~2 = 1200.0000 ¢, ~25/17 = 670.0429 ¢

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

Badness (Sintel): 1.59

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 -4 4 19 23 -3 8 21], ⟨0 10 -3 -29 -35 12 -7 -30]]

Optimal tunings:

  • WE: ~2 = 1199.8538 ¢, ~25/17 = 669.9631 ¢
  • CWE: ~2 = 1200.0000 ¢, ~25/17 = 670.0460 ¢

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

Badness (Sintel): 1.44

Cohemimabila

Named by Xenllium in 2022, cohemimabila tempers out 3136/3125 as well as 65536/64827 and may be described as the 43 & 68 temperament.

Subgroup: 2.3.5.7

Comma list: 3136/3125, 65536/64827

Mapping: [⟨1 -4 4 7], ⟨0 20 -6 -15]]

mapping generators: ~2, ~128/105

Optimal tunings:

  • WE: ~2 = 1199.1476 ¢, ~128/105 = 334.9440 ¢
error map: ⟨-0.852 +0.335 +0.613 +1.047]
  • CWE: ~2 = 1200.0000 ¢, ~128/105 = 335.1779 ¢
error map: ⟨0.000 +1.603 +2.619 +3.505]

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

Badness (Sintel): 3.23

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 tunings:

  • WE: ~2 = 1199.3670 ¢, ~40/33 = 334.9711 ¢
  • CWE: ~2 = 1200.0000 ¢, ~40/33 = 335.1492 ¢

Optimal ET sequence: 25, 43, 68, 111

Badness (Sintel): 2.12

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 tunings:

  • WE: ~2 = 1199.3383 ¢, ~40/33 = 334.9594 ¢
  • CWE: ~2 = 1200.0000 ¢, ~40/33 = 335.1431 ¢

Optimal ET sequence: 25, 43, 68, 111

Badness (Sintel): 1.47

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 tunings:

  • WE: ~2 = 1199.3269 ¢, ~17/14 = 334.9571 ¢
  • CWE: ~2 = 1200.0000 ¢, ~17/14 = 335.1451 ¢

Optimal ET sequence: 25, 43, 68, 111

Badness (Sintel): 1.16

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 tunings:

  • WE: ~2 = 1199.2658 ¢, ~17/14 = 334.9455 ¢
  • CWE: ~2 = 1200.0000 ¢, ~17/14 = 335.1516 ¢

Optimal ET sequence: 25, 43, 68, 111

Badness (Sintel): 1.06

Hemimabila

Subgroup: 2.3.5.7

Comma list: 6144/6125, 117649/116640

Mapping: [⟨1 -14 7 -12], ⟨0 20 -6 19]]

mapping generators: ~2, ~12/7

Optimal tunings:

  • WE: ~2 = 1199.5170 ¢, ~12/7 = 934.7983 ¢
error map: ⟨-0.483 +0.773 +1.516 -1.862]
  • CWE: ~2 = 1200.0000 ¢, ~12/7 = 935.1643 ¢
error map: ⟨0.000 +1.330 +2.701 -0.705]

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

Badness (Sintel): 2.81

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 -14 7 -12 -2], ⟨0 20 -6 19 7]]

Optimal tunings:

  • WE: ~2 = 1199.9930 ¢, ~12/7 = 935.1459 ¢
  • CWE: ~2 = 1200.0000 ¢, ~12/7 = 935.1512 ¢

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

Badness (Sintel): 2.03

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 -14 7 -12 -2 -15], ⟨0 20 -6 19 7 24]]

Optimal tunings:

  • WE: ~2 = 1199.9061 ¢, ~12/7 = 935.0656 ¢
  • CWE: ~2 = 1200.0000 ¢, ~12/7 = 935.1367 ¢

Optimal ET sequence: 9, 59f, 68, 77

Badness (Sintel): 1.43

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 -14 7 -12 -2 -15 15], ⟨0 20 -6 19 7 24 -14]]

Optimal tunings:

  • WE: ~2 = 1199.7422 ¢, ~12/7 = 934.9596 ¢
  • CWE: ~2 = 1200.0000 ¢, ~12/7 = 935.1572 ¢

Optimal ET sequence: 9, 59f, 68, 77

Badness (Sintel): 1.42

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 -14 7 -12 -2 -15 15 -9], ⟨0 20 -6 19 7 24 -14 17]]

Optimal tunings:

  • WE: ~2 = 1199.7650 ¢, ~12/7 = 934.9782 ¢
  • CWE: ~2 = 1200.0000 ¢, ~12/7 = 935.1581 ¢

Optimal ET sequence: 9, 59f, 68, 77

Badness (Sintel): 1.22

Trimabila

Named by Xenllium in 2022, trimabila tempers out 1728/1715 and may be described as the 9 & 111 temperament.

Subgroup: 2.3.5.7

Comma list: 1728/1715, 268435456/263671875

Mapping: [⟨3 -2 9 1], ⟨0 10 -3 11]]

mapping generators: ~1125/896, ~7/6

Optimal tunings:

  • WE: ~1125/896 = 399.7349 ¢, ~7/6 = 270.0900 ¢
error map: ⟨-0.795 -0.525 +1.030 +1.899]
  • CWE: ~1125/896 = 400.0000 ¢, ~7/6 = 270.2343 ¢
error map: ⟨0.000 +0.388 +2.983 +3.752]

Optimal ET sequence: 9, …, 102d, 111

Badness (Sintel): 6.76

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨3 -2 9 1 7], ⟨0 10 -3 11 5]]

Optimal tunings:

  • WE: ~495/392 = 399.7963 ¢, ~7/6 = 270.1183 ¢
  • CWE: ~495/392 = 400.0000 ¢, ~7/6 = 270.2301 ¢

Optimal ET sequence: 9, …, 102d, 111

Badness (Sintel): 2.71

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨3 -2 9 1 7 3], ⟨0 10 -3 11 5 12]]

Optimal tunings:

  • WE: ~495/392 = 399.7935 ¢, ~7/6 = 270.1144 ¢
  • CWE: ~495/392 = 400.0000 ¢, ~7/6 = 270.2258 ¢

Optimal ET sequence: 9, …, 102df, 111

Badness (Sintel): 1.66

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨3 -2 9 1 7 3 17], ⟨0 10 -3 11 5 12 -7]]

Optimal tunings:

  • WE: ~495/392 = 399.7781 ¢, ~7/6 = 270.1159 ¢
  • CWE: ~495/392 = 400.0000 ¢, ~7/6 = 270.2476 ¢

Optimal ET sequence: 9, 102df, 111

Badness (Sintel): 1.56

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 -2 9 1 7 3 17 6], ⟨0 10 -3 11 5 12 -7 10]]

Optimal tunings:

  • WE: ~208/165 = 399.7588 ¢, ~7/6 = 270.0969 ¢
  • CWE: ~208/165 = 400.0000 ¢, ~7/6 = 270.2391 ¢

Optimal ET sequence: 9, 102dfh, 111

Badness (Sintel): 1.39

References

  1. ↑ Yahoo! Tuning Group | Suggested names for the unclasified temperaments
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