Mabila family: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
The '''mabila family''' of [[Rank-2 temperament|rank-2]] [[temperament]]s [[Tempering out|tempers out]] {{monzo| 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.  
The '''mabila family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[mabila comma]] ({{monzo|legend=1| 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 ==
== Mabila ==
Line 9: Line 9:
{{Mapping|legend=1| 1 6 1 | 0 -10 3 }}
{{Mapping|legend=1| 1 6 1 | 0 -10 3 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~512/375 = 529.685
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~512/375 = 529.685{{c}}


{{Optimal ET sequence|legend=1| 9, 25, 34, 77, 111, 145, 256c }}
{{Optimal ET sequence|legend=1| 9, 25, 34, 77, 111, 145, 256c }}


[[Badness]]: 0.232481
[[Badness]] (Smith): 0.232481


== Semabila ==
== Semabila ==
Line 26: Line 26:
{{Mapping|legend=1| 1 6 1 5 | 0 -10 3 -5 }}
{{Mapping|legend=1| 1 6 1 5 | 0 -10 3 -5 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~75/56 = 529.667
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~75/56 = 529.667{{c}}


{{Optimal ET sequence|legend=1| 9, 25, 34 }}
{{Optimal ET sequence|legend=1| 9, 25, 34 }}


[[Badness]]: 0.133638
[[Badness]] (Smith): 0.133638


=== 11-limit ===
=== 11-limit ===
Line 39: Line 39:
Mapping: {{mapping| 1 6 1 5 7 | 0 -10 3 -5 -8 }}
Mapping: {{mapping| 1 6 1 5 7 | 0 -10 3 -5 -8 }}


Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.729
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.729{{c}}


{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
{{Optimal ET sequence|legend=0| 9, 25e, 34 }}


Badness: 0.061501
Badness (Smith): 0.061501


=== 13-limit ===
=== 13-limit ===
Line 52: Line 52:
Mapping: {{mapping| 1 6 1 5 7 9 | 0 -10 3 -5 -8 -12 }}
Mapping: {{mapping| 1 6 1 5 7 9 | 0 -10 3 -5 -8 -12 }}


Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.763
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.763{{c}}


{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
{{Optimal ET sequence|legend=0| 9, 25e, 34 }}


Badness: 0.037270
Badness (Smith): 0.037270


=== 17-limit ===
=== 17-limit ===
Line 65: Line 65:
Mapping: {{mapping| 1 6 1 5 7 9 1 | 0 -10 3 -5 -8 -12 7 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.695{{c}}


{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
{{Optimal ET sequence|legend=0| 9, 25e, 34 }}


Badness: 0.031888
Badness (Smith): 0.031888


=== 19-limit ===
=== 19-limit ===
Line 78: Line 78:
Mapping: {{mapping| 1 6 1 5 7 9 1 6 | 0 -10 3 -5 -8 -12 7 -4 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.736{{c}}


{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
{{Optimal ET sequence|legend=0| 9, 25e, 34 }}


Badness: 0.026981
Badness (Smith): 0.026981


== Amavil ==
== Amavil ==
Line 91: Line 91:
{{Mapping|legend=1| 1 6 1 9 | 0 -10 3 -14 }}
{{Mapping|legend=1| 1 6 1 9 | 0 -10 3 -14 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~48/35 = 529.979
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~48/35 = 529.979{{c}}


{{Optimal ET sequence|legend=1| 9, 25d, 34d, 43, 77d, 120dd }}
{{Optimal ET sequence|legend=1| 9, 25d, 34d, 43, 77d, 120dd }}


[[Badness]]: 0.109625
[[Badness]] (Smith): 0.109625


=== 11-limit ===
=== 11-limit ===
Line 104: Line 104:
Mapping: {{mapping| 1 6 1 9 7 | 0 -10 3 -14 -8 }}
Mapping: {{mapping| 1 6 1 9 7 | 0 -10 3 -14 -8 }}


Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.974
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.974{{c}}


{{Optimal ET sequence|legend=1| 9, 25de, 34d, 43, 77de, 120dde }}
{{Optimal ET sequence|legend=0| 9, 25de, 34d, 43, 77de, 120dde }}


Badness: 0.042649
Badness (Smith): 0.042649


=== 13-limit ===
=== 13-limit ===
Line 117: Line 117:
Mapping: {{mapping| 1 6 1 9 7 9 | 0 -10 3 -14 -8 -12 }}
Mapping: {{mapping| 1 6 1 9 7 9 | 0 -10 3 -14 -8 -12 }}


Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.951
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.951{{c}}


{{Optimal ET sequence|legend=1| 9, 25de, 34d, 43, 77de, 120dde }}
{{Optimal ET sequence|legend=0| 9, 25de, 34d, 43, 77de, 120dde }}


Badness: 0.025791
Badness (Smith): 0.025791


=== 17-limit ===
=== 17-limit ===
Line 130: Line 130:
Mapping: {{mapping| 1 6 1 9 7 9 1 | 0 -10 3 -14 -8 -12 7 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.957{{c}}


{{Optimal ET sequence|legend=1| 9, 25de, 34d, 43, 77de, 120ddeg }}
{{Optimal ET sequence|legend=0| 9, 25de, 34d, 43, 77de, 120ddeg }}


Badness: 0.022092
Badness (Smith): 0.022092


=== 19-limit ===
=== 19-limit ===
Line 143: Line 143:
Mapping: {{mapping| 1 6 1 9 7 9 1 10 | 0 -10 3 -14 -8 -12 7 -13 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.987{{c}}


{{Optimal ET sequence|legend=1| 9, 25deh, 34dh, 43, 77deh, 120ddeghh }}
{{Optimal ET sequence|legend=0| 9, 25deh, 34dh, 43, 77deh, 120ddeghh }}


Badness: 0.017955
Badness (Smith): 0.017955


== Tuskaloosa ==
== Tuskaloosa ==
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{{Mapping|legend=1| 1 6 1 24 | 0 -10 3 -48 }}
{{Mapping|legend=1| 1 6 1 24 | 0 -10 3 -48 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~512/375 = 529.772
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~512/375 = 529.772{{c}}


{{Optimal ET sequence|legend=1| 34d, 77, 111, 188, 299cd }}
{{Optimal ET sequence|legend=1| 34d, 77, 111, 188, 299cd }}


[[Badness]]: 0.145058
[[Badness]] (Smith): 0.145058


=== 11-limit ===
=== 11-limit ===
Line 169: Line 169:
Mapping: {{mapping| 1 6 1 24 22 | 0 -10 3 -48 -42 }}
Mapping: {{mapping| 1 6 1 24 22 | 0 -10 3 -48 -42 }}


Optimal tuning (POTE): ~2 = 1\1, ~224/165 = 529.749
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~224/165 = 529.749{{c}}


{{Optimal ET sequence|legend=1| 34d, 77, 111, 299cd, 410ccd, 521ccdd }}
{{Optimal ET sequence|legend=0| 34d, 77, 111, 299cd, 410ccd, 521ccdd }}


Badness: 0.061773
Badness (Smith): 0.061773


=== 13-limit ===
=== 13-limit ===
Line 182: Line 182:
Mapping: {{mapping| 1 6 1 24 22 9 | 0 -10 3 -48 -42 -12 }}
Mapping: {{mapping| 1 6 1 24 22 9 | 0 -10 3 -48 -42 -12 }}


Optimal tuning (POTE): ~2 = 1\1, ~65/48 = 529.747
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~65/48 = 529.747{{c}}


{{Optimal ET sequence|legend=1| 34d, 77, 111, 410ccdf, 521ccddff }}
{{Optimal ET sequence|legend=0| 34d, 77, 111, 410ccdf, 521ccddff }}


Badness: 0.031480
Badness (Smith): 0.031480


=== 17-limit ===
=== 17-limit ===
Line 195: Line 195:
Mapping: {{mapping| 1 6 1 24 22 9 1 | 0 -10 3 -48 -42 -12 7 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.000{{c}}, ~34/25 = 529.742{{c}}


{{Optimal ET sequence|legend=1| 34d, 77, 111 }}
{{Optimal ET sequence|legend=0| 34d, 77, 111 }}


Badness: 0.022765
Badness (Smith): 0.022765


=== 19-limit ===
=== 19-limit ===
Line 208: Line 208:
Mapping: {{mapping| 1 6 1 24 22 9 1 25 | 0 -10 3 -48 -42 -12 7 -47 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.000{{c}}, ~19/14 = 529.749{{c}}


{{Optimal ET sequence|legend=1| 34dh, 77, 111 }}
{{Optimal ET sequence|legend=0| 34dh, 77, 111 }}


Badness: 0.017924
Badness (Smith): 0.017924


== Muscogee ==
== Muscogee ==
Line 221: Line 221:
{{Mapping|legend=1| 1 6 1 -10 | 0 -10 3 29 }}
{{Mapping|legend=1| 1 6 1 -10 | 0 -10 3 29 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~512/375 = 529.907
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~512/375 = 529.907{{c}}


{{Optimal ET sequence|legend=1| 34, 43, 77, 274c, 351cc, 428ccd }}
{{Optimal ET sequence|legend=1| 34, 43, 77, 274c, 351cc, 428ccd }}


[[Badness]]: 0.162021
[[Badness]] (Smith): 0.162021


=== 11-limit ===
=== 11-limit ===
Line 234: Line 234:
Mapping: {{mapping| 1 6 1 -10 -12 | 0 -10 3 29 35 }}
Mapping: {{mapping| 1 6 1 -10 -12 | 0 -10 3 29 35 }}


Optimal tuning (POTE): ~2 = 1\1, ~224/165 = 529.955
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~224/165 = 529.955{{c}}


{{Optimal ET sequence|legend=1| 34e, 43, 77, 120, 197ce }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120, 197ce }}


Badness: 0.077552
Badness (Smith): 0.077552


=== 13-limit ===
=== 13-limit ===
Line 247: Line 247:
Mapping: {{mapping| 1 6 1 -10 -12 9 | 0 -10 3 29 35 -12 }}
Mapping: {{mapping| 1 6 1 -10 -12 9 | 0 -10 3 29 35 -12 }}


Optimal tuning (POTE): ~2 = 1\1, ~65/48 = 529.957
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~65/48 = 529.957{{c}}


{{Optimal ET sequence|legend=1| 34e, 43, 77, 120, 197ce }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120, 197ce }}


Badness: 0.043352
Badness (Smith): 0.043352


=== 17-limit ===
=== 17-limit ===
Line 260: Line 260:
Mapping: {{mapping| 1 6 1 -10 -12 9 1 | 0 -10 3 29 35 -12 7 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.000{{c}}, ~34/25 = 529.958{{c}}


{{Optimal ET sequence|legend=1| 34e, 43, 77, 120g, 197ceg }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120g, 197ceg }}


Badness: 0.031217
Badness (Smith): 0.031217


=== 19-limit ===
=== 19-limit ===
Line 273: Line 273:
Mapping: {{mapping| 1 6 1 -10 -12 9 1 -9 | 0 -10 3 29 35 -12 7 30 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.000{{c}}, ~19/14 = 529.955{{c}}


{{Optimal ET sequence|legend=1| 34e, 43, 77, 120g, 197ceg }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120g, 197ceg }}


Badness: 0.023670
Badness (Smith): 0.023670


== Hemimabila ==
== Hemimabila ==
Line 286: Line 286:
{{Mapping|legend=1| 1 6 1 7 | 0 -20 6 -19 }}
{{Mapping|legend=1| 1 6 1 7 | 0 -20 6 -19 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 264.825
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/6 = 264.825{{c}}


{{Optimal ET sequence|legend=1| 9, 59, 68, 77, 145 }}
{{Optimal ET sequence|legend=1| 9, 59, 68, 77, 145 }}


[[Badness]]: 0.111130
[[Badness]] (Smith): 0.111130


=== 11-limit ===
=== 11-limit ===
Line 299: Line 299:
Mapping: {{mapping| 1 6 1 7 5 | 0 -20 6 -19 -7 }}
Mapping: {{mapping| 1 6 1 7 5 | 0 -20 6 -19 -7 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 264.849
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 264.849{{c}}


{{Optimal ET sequence|legend=1| 9, 59, 68, 77, 145e }}
{{Optimal ET sequence|legend=0| 9, 59, 68, 77, 145e }}


Badness: 0.061426
Badness (Smith): 0.061426


=== 13-limit ===
=== 13-limit ===
Line 312: Line 312:
Mapping: {{mapping| 1 6 1 7 5 9 | 0 -20 6 -19 -7 -24 }}
Mapping: {{mapping| 1 6 1 7 5 9 | 0 -20 6 -19 -7 -24 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 264.861
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 264.861{{c}}


{{Optimal ET sequence|legend=1| 9, 59f, 68, 77, 145e, 222cef }}
{{Optimal ET sequence|legend=0| 9, 59f, 68, 77, 145e, 222cef }}


Badness: 0.034531
Badness (Smith): 0.034531


=== 17-limit ===
=== 17-limit ===
Line 325: Line 325:
Mapping: {{mapping| 1 6 1 7 5 9 1 | 0 -20 6 -19 -7 -24 14 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 264.839{{c}}


{{Optimal ET sequence|legend=1| 9, 59f, 68, 77, 145e }}
{{Optimal ET sequence|legend=0| 9, 59f, 68, 77, 145e }}


Badness: 0.027851
Badness (Smith): 0.027851


=== 19-limit ===
=== 19-limit ===
Line 338: Line 338:
Mapping: {{mapping| 1 6 1 7 5 9 1 8 | 0 -20 6 -19 -7 -24 14 -17 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 264.839{{c}}


{{Optimal ET sequence|legend=1| 9, 59f, 68, 77, 145e }}
{{Optimal ET sequence|legend=0| 9, 59f, 68, 77, 145e }}


Badness: 0.020053
Badness (Smith): 0.020053


== Cohemimabila ==
== Cohemimabila ==
Line 351: Line 351:
{{Mapping|legend=1| 1 -4 4 7 | 0 20 -6 -15 }}
{{Mapping|legend=1| 1 -4 4 7 | 0 20 -6 -15 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~128/105 = 335.182
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~128/105 = 335.182{{c}}


{{Optimal ET sequence|legend=1| 25, 43, 68, 111, 179, 290cd, 469bccdd }}
{{Optimal ET sequence|legend=1| 25, 43, 68, 111, 179, 290cd, 469bccdd }}


[[Badness]]: 0.127451
[[Badness]] (Smith): 0.127451


=== 11-limit ===
=== 11-limit ===
Line 364: Line 364:
Mapping: {{mapping| 1 -4 4 7 11 | 0 20 -6 -15 -27 }}
Mapping: {{mapping| 1 -4 4 7 11 | 0 20 -6 -15 -27 }}


Optimal tuning (POTE): ~2 = 1\1, ~40/33 = 335.148
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~40/33 = 335.148{{c}}


{{Optimal ET sequence|legend=1| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness: 0.064164
Badness (Smith): 0.064164


=== 13-limit ===
=== 13-limit ===
Line 377: Line 377:
Mapping: {{mapping| 1 -4 4 7 11 -3 | 0 20 -6 -15 -27 24 }}
Mapping: {{mapping| 1 -4 4 7 11 -3 | 0 20 -6 -15 -27 24 }}


Optimal tuning (POTE): ~2 = 1\1, ~40/33 = 335.144
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~40/33 = 335.144{{c}}


{{Optimal ET sequence|legend=1| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness: 0.035463
Badness (Smith): 0.035463


=== 17-limit ===
=== 17-limit ===
Line 390: Line 390:
Mapping: {{mapping| 1 -4 4 7 11 -3 8 | 0 20 -6 -15 -27 24 -14 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.000{{c}}, ~17/14 = 335.145{{c}}


{{Optimal ET sequence|legend=1| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness: 0.022728
Badness (Smith): 0.022728


=== 19-limit ===
=== 19-limit ===
Line 403: Line 403:
Mapping: {{mapping| 1 -4 4 7 11 -3 8 9 | 0 20 -6 -15 -27 24 -14 -17 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.000{{c}}, ~17/14 = 335.151{{c}}


{{Optimal ET sequence|legend=1| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness: 0.017450
Badness (Smith): 0.017450


== Trimabila ==
== Trimabila ==
Line 416: Line 416:
{{Mapping|legend=1| 3 8 6 12 | 0 -10 3 -11 }}
{{Mapping|legend=1| 3 8 6 12 | 0 -10 3 -11 }}


[[Optimal tuning]] ([[POTE]]): ~1125/896 = 1\3, ~7/6 = 270.269
[[Optimal tuning]] ([[POTE]]): ~1125/896 = 400.000{{c}}, ~7/6 = 270.269{{c}}


{{Optimal ET sequence|legend=1| 9, 102d, 111 }}
{{Optimal ET sequence|legend=1| 9, 102d, 111 }}


[[Badness]]: 0.267168
[[Badness]] (Smith): 0.267168


=== 11-limit ===
=== 11-limit ===
Line 429: Line 429:
Mapping: {{mapping| 3 8 6 12 12 | 0 -10 3 -11 -5 }}
Mapping: {{mapping| 3 8 6 12 12 | 0 -10 3 -11 -5 }}


Optimal tuning (POTE): ~495/392 = 1\3, ~7/6 = 270.256
Optimal tuning (POTE): ~495/392 = 400.000{{c}}, ~7/6 = 270.256{{c}}


{{Optimal ET sequence|legend=1| 9, 102d, 111 }}
{{Optimal ET sequence|legend=0| 9, 102d, 111 }}


Badness: 0.081946
Badness (Smith): 0.081946


=== 13-limit ===
=== 13-limit ===
Line 442: Line 442:
Mapping: {{mapping| 3 8 6 12 12 15 | 0 -10 3 -11 -5 -12 }}
Mapping: {{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 tuning (POTE): ~495/392 = 400.000{{c}}, ~7/6 = 270.254{{c}} (or ~14/13 = 129.746{{c}})


{{Optimal ET sequence|legend=1| 9, 102df, 111 }}
{{Optimal ET sequence|legend=0| 9, 102df, 111 }}


Badness: 0.040102
Badness (Smith): 0.040102


=== 17-limit ===
=== 17-limit ===
Line 455: Line 455:
Mapping: {{mapping| 3 8 6 12 12 15 10 | 0 -10 3 -11 -5 -12 7 }}
Mapping: {{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 tuning (POTE): ~495/392 = 400.000{{c}}, ~7/6 = 270.266{{c}} (or ~14/13 = 129.734{{c}})


{{Optimal ET sequence|legend=1| 9, 102df, 111 }}
{{Optimal ET sequence|legend=0| 9, 102df, 111 }}


Badness: 0.030657
Badness (Smith): 0.030657


=== 19-limit ===
=== 19-limit ===
Line 468: Line 468:
Mapping: {{mapping| 3 8 6 12 12 15 10 16 | 0 -10 3 -11 -5 -12 7 -10 }}
Mapping: {{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 tuning (POTE): ~208/165 = 400.000{{c}}, ~7/6 = 270.260{{c}} (or ~14/13 = 129.740{{c}})


{{Optimal ET sequence|legend=1| 9, 102dfh, 111 }}
{{Optimal ET sequence|legend=0| 9, 102dfh, 111 }}


Badness: 0.022851
Badness (Smith): 0.022851


[[Category:Temperament families]]
[[Category:Temperament families]]

Revision as of 10:54, 23 February 2026

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

See also: No-threes subgroup temperaments § Mabilic

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

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