Mabila family: Difference between revisions

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The '''mabila family''' tempers out {{monzo|28 -3 -10}} = 268435456/263671875 in the 5-limit. This gives it's temperaments a structure superficially similar to [[Mavila_temperament|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.  
{{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.  


== Mabila ==
== Mabila ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma]]: 268435456/263671875
[[Comma list]]: 268435456/263671875


[[Mapping]]: [{{Val| 1 6 1 }}, {{Val| 0 -10 3 }}]
{{Mapping|legend=1| 1 6 1 | 0 -10 3 }}


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


{{Val list|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]]: 0.232481


== Septimal mabila ==
== Semabila ==
{{see also| Slendro clan #Mabila }}
{{See also| No-threes subgroup temperaments #Mabilic }}


Subgroup: 2.3.5.7
Semabila is so named because it is a semaphore temperament.
 
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 49/48, 28672/28125
[[Comma list]]: 49/48, 28672/28125


[[Mapping]]: [{{val| 1 6 1 5 }}, {{val| 0 -10 3 -5 }}]
{{Mapping|legend=1| 1 6 1 5 | 0 -10 3 -5 }}
 
{{Multival|legend=1| 10 -3 5 -28 -20 20 }}


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


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


[[Badness]]: 0.133638
[[Badness]]: 0.133638
Line 36: Line 37:
Comma list: 49/48, 56/55, 1350/1331
Comma list: 49/48, 56/55, 1350/1331


Mapping: [{{val| 1 6 1 5 7 }}, {{val| 0 -10 3 -5 -8 }}]
Mapping: {{mapping| 1 6 1 5 7 | 0 -10 3 -5 -8 }}


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


Optimal GPV sequence: {{Val list| 9, 25e, 34 }}
{{Optimal ET sequence|legend=1| 9, 25e, 34 }}


Badness: 0.061501
Badness: 0.061501
Line 49: Line 50:
Comma list: 49/48, 56/55, 91/90, 847/845
Comma list: 49/48, 56/55, 91/90, 847/845


Mapping: [{{val| 1 6 1 5 7 9 }}, {{val| 0 -10 3 -5 -8 -12 }}]
Mapping: {{mapping| 1 6 1 5 7 9 | 0 -10 3 -5 -8 -12 }}


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


Optimal GPV sequence: {{Val list| 9, 25e, 34 }}
{{Optimal ET sequence|legend=1| 9, 25e, 34 }}


Badness: 0.037270
Badness: 0.037270
Line 62: Line 63:
Comma list: 49/48, 56/55, 91/90, 154/153, 375/374
Comma list: 49/48, 56/55, 91/90, 154/153, 375/374


Mapping: [{{val| 1 6 1 5 7 9 1 }}, {{val| 0 -10 3 -5 -8 -12 7 }}]
Mapping: {{mapping| 1 6 1 5 7 9 1 | 0 -10 3 -5 -8 -12 7 }}


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


Optimal GPV sequence: {{Val list| 9, 25e, 34 }}
{{Optimal ET sequence|legend=1| 9, 25e, 34 }}


Badness: 0.031888
Badness: 0.031888
Line 75: Line 76:
Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187
Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187


Mapping: [{{val| 1 6 1 5 7 9 1 6 }}, {{val| 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 }}


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


Optimal GPV sequence: {{Val list| 9, 25e, 34 }}
{{Optimal ET sequence|legend=1| 9, 25e, 34 }}


Badness: 0.026981
Badness: 0.026981


== Amavil ==
== Amavil ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 17496/16807
[[Comma list]]: 225/224, 17496/16807


[[Mapping]]: [{{val| 1 6 1 9 }}, {{val| 0 -10 3 -14 }}]
{{Mapping|legend=1| 1 6 1 9 | 0 -10 3 -14 }}
 
{{Multival|legend=1| 10 -3 14 -28 -6 41 }}


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


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


[[Badness]]: 0.109625
[[Badness]]: 0.109625
Line 103: Line 102:
Comma list: 99/98, 176/175, 864/847
Comma list: 99/98, 176/175, 864/847


Mapping: [{{val| 1 6 1 9 7 }}, {{val| 0 -10 3 -14 -8 }}]
Mapping: {{mapping| 1 6 1 9 7 | 0 -10 3 -14 -8 }}


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


Optimal GPV sequence: {{Val list| 9, 25de, 34d, 43, 77de, 120dde }}
{{Optimal ET sequence|legend=1| 9, 25de, 34d, 43, 77de, 120dde }}


Badness: 0.042649
Badness: 0.042649
Line 116: Line 115:
Comma list: 78/77, 99/98, 144/143, 176/175
Comma list: 78/77, 99/98, 144/143, 176/175


Mapping: [{{val| 1 6 1 9 7 9 }}, {{val| 0 -10 3 -14 -8 -12 }}]
Mapping: {{mapping| 1 6 1 9 7 9 | 0 -10 3 -14 -8 -12 }}


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


Optimal GPV sequence: {{Val list| 9, 25de, 34d, 43, 77de, 120dde }}
{{Optimal ET sequence|legend=1| 9, 25de, 34d, 43, 77de, 120dde }}


Badness: 0.025791
Badness: 0.025791
Line 129: Line 128:
Comma list: 78/77, 99/98, 120/119, 144/143, 176/175
Comma list: 78/77, 99/98, 120/119, 144/143, 176/175


Mapping: [{{val| 1 6 1 9 7 9 1 }}, {{val| 0 -10 3 -14 -8 -12 7 }}]
Mapping: {{mapping| 1 6 1 9 7 9 1 | 0 -10 3 -14 -8 -12 7 }}


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


Optimal GPV sequence: {{Val list| 9, 25de, 34d, 43, 77de, 120ddeg }}
{{Optimal ET sequence|legend=1| 9, 25de, 34d, 43, 77de, 120ddeg }}


Badness: 0.022092
Badness: 0.022092
Line 142: Line 141:
Comma list: 78/77, 96/95, 99/98, 120/119, 135/133, 144/143
Comma list: 78/77, 96/95, 99/98, 120/119, 135/133, 144/143


Mapping: [{{val| 1 6 1 9 7 9 1 10 }}, {{val| 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 }}


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


Optimal GPV sequence: {{Val list| 9, 25deh, 34dh, 43, 77deh, 120ddeghh }}
{{Optimal ET sequence|legend=1| 9, 25deh, 34dh, 43, 77deh, 120ddeghh }}


Badness: 0.017955
Badness: 0.017955


== Tuskaloosa ==
== Tuskaloosa ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 19683/19600, 110592/109375
[[Comma list]]: 19683/19600, 110592/109375


[[Mapping]]: [{{val|1 6 1 24}}, {{val|0 -10 3 -48}}]
{{Mapping|legend=1| 1 6 1 24 | 0 -10 3 -48 }}
 
{{Multival|legend=1| 10 -3 48 -28 48 120 }}


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


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


[[Badness]]: 0.145058
[[Badness]]: 0.145058
Line 170: Line 167:
Comma list: 176/175, 1331/1323, 19683/19600
Comma list: 176/175, 1331/1323, 19683/19600


Mapping: [{{val|1 6 1 24 22}}, {{val|0 -10 3 -48 -42}}]
Mapping: {{mapping| 1 6 1 24 22 | 0 -10 3 -48 -42 }}


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


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


Badness: 0.061773
Badness: 0.061773
Line 183: Line 180:
Comma list: 176/175, 351/350, 676/675, 1331/1323
Comma list: 176/175, 351/350, 676/675, 1331/1323


Mapping: [{{val|1 6 1 24 22 9}}, {{val|0 -10 3 -48 -42 -12}}]
Mapping: {{mapping| 1 6 1 24 22 9 | 0 -10 3 -48 -42 -12 }}


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


Optimal GPV sequence: {{Val list| 34d, 77, 111, 410ccdf, 521ccddff }}
{{Optimal ET sequence|legend=1| 34d, 77, 111, 410ccdf, 521ccddff }}


Badness: 0.031480
Badness: 0.031480
Line 196: Line 193:
Comma list: 176/175, 256/255, 351/350, 676/675, 715/714
Comma list: 176/175, 256/255, 351/350, 676/675, 715/714


Mapping: [{{val|1 6 1 24 22 9 1}}, {{val|0 -10 3 -48 -42 -12 7}}]
Mapping: {{mapping| 1 6 1 24 22 9 1 | 0 -10 3 -48 -42 -12 7 }}


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


Optimal GPV sequence: {{Val list| 34d, 77, 111 }}
{{Optimal ET sequence|legend=1| 34d, 77, 111 }}


Badness: 0.022765
Badness: 0.022765
Line 209: Line 206:
Comma list: 176/175, 256/255, 286/285, 351/350, 363/361, 476/475
Comma list: 176/175, 256/255, 286/285, 351/350, 363/361, 476/475


Mapping: [{{val|1 6 1 24 22 9 1 25}}, {{val|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 }}


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


Optimal GPV sequence: {{Val list| 34dh, 77, 111 }}
{{Optimal ET sequence|legend=1| 34dh, 77, 111 }}


Badness: 0.017924
Badness: 0.017924


== Muscogee ==
== Muscogee ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 126/125, 33756345/33554432
[[Comma list]]: 126/125, 33756345/33554432


[[Mapping]]: [{{val|1 6 1 -10}}, {{val|0 -10 3 29}}]
{{Mapping|legend=1| 1 6 1 -10 | 0 -10 3 29 }}
 
{{Multival|legend=1| 10 -3 -29 -28 -74 -59 }}


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


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


[[Badness]]: 0.162021
[[Badness]]: 0.162021
Line 237: Line 232:
Comma list: 126/125, 176/175, 264627/262144
Comma list: 126/125, 176/175, 264627/262144


Mapping: [{{val|1 6 1 -10 -12}}, {{val|0 -10 3 29 35}}]
Mapping: {{mapping| 1 6 1 -10 -12 | 0 -10 3 29 35 }}


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


Optimal GPV sequence: {{Val list| 34e, 43, 77, 120, 197ce }}
{{Optimal ET sequence|legend=1| 34e, 43, 77, 120, 197ce }}


Badness: 0.077552
Badness: 0.077552
Line 250: Line 245:
Comma list: 126/125, 176/175, 676/675, 1287/1280
Comma list: 126/125, 176/175, 676/675, 1287/1280


Mapping: [{{val|1 6 1 -10 -12 9}}, {{val|0 -10 3 29 35 -12}}]
Mapping: {{mapping| 1 6 1 -10 -12 9 | 0 -10 3 29 35 -12 }}


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


Optimal GPV sequence: {{Val list| 34e, 43, 77, 120, 197ce }}
{{Optimal ET sequence|legend=1| 34e, 43, 77, 120, 197ce }}


Badness: 0.043352
Badness: 0.043352
Line 263: Line 258:
Comma list: 126/125, 176/175, 256/255, 273/272, 676/675
Comma list: 126/125, 176/175, 256/255, 273/272, 676/675


Mapping: [{{val|1 6 1 -10 -12 9 1}}, {{val|0 -10 3 29 35 -12 7}}]
Mapping: {{mapping| 1 6 1 -10 -12 9 1 | 0 -10 3 29 35 -12 7 }}


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


Optimal GPV sequence: {{Val list| 34e, 43, 77, 120g, 197ceg }}
{{Optimal ET sequence|legend=1| 34e, 43, 77, 120g, 197ceg }}


Badness: 0.031217
Badness: 0.031217
Line 276: Line 271:
Comma list: 126/125, 171/170, 176/175, 256/255, 273/272, 363/361
Comma list: 126/125, 171/170, 176/175, 256/255, 273/272, 363/361


Mapping: [{{val|1 6 1 -10 -12 9 1 -9}}, {{val|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 }}


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


Optimal GPV sequence: {{Val list| 34e, 43, 77, 120g, 197ceg }}
{{Optimal ET sequence|legend=1| 34e, 43, 77, 120g, 197ceg }}


Badness: 0.023670
Badness: 0.023670


== Hemimabila ==
== Hemimabila ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 6144/6125, 117649/116640
[[Comma list]]: 6144/6125, 117649/116640


[[Mapping]]: [{{val|1 6 1 7}}, {{val|0 -20 6 -19}}]
{{Mapping|legend=1| 1 6 1 7 | 0 -20 6 -19 }}
 
{{Multival|legend=1| 20 -6 19 -56 -26 61 }}


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


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


[[Badness]]: 0.111130
[[Badness]]: 0.111130
Line 304: Line 297:
Comma list: 121/120, 176/175, 67228/66825
Comma list: 121/120, 176/175, 67228/66825


Mapping: [{{val|1 6 1 7 5}}, {{val|0 -20 6 -19 -7}}]
Mapping: {{mapping| 1 6 1 7 5 | 0 -20 6 -19 -7 }}


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


Optimal GPV sequence: {{Val list| 9, 59, 68, 77, 145e }}
{{Optimal ET sequence|legend=1| 9, 59, 68, 77, 145e }}


Badness: 0.061426
Badness: 0.061426
Line 317: Line 310:
Comma list: 121/120, 176/175, 196/195, 676/675
Comma list: 121/120, 176/175, 196/195, 676/675


Mapping: [{{val|1 6 1 7 5 9}}, {{val|0 -20 6 -19 -7 -24}}]
Mapping: {{mapping| 1 6 1 7 5 9 | 0 -20 6 -19 -7 -24 }}


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


Optimal GPV sequence: {{Val list| 9, 59f, 68, 77, 145e, 222cef }}
{{Optimal ET sequence|legend=1| 9, 59f, 68, 77, 145e, 222cef }}


Badness: 0.034531
Badness: 0.034531
Line 330: Line 323:
Comma list: 121/120, 154/153, 176/175, 196/195, 676/675
Comma list: 121/120, 154/153, 176/175, 196/195, 676/675


Mapping: [{{val|1 6 1 7 5 9 1}}, {{val|0 -20 6 -19 -7 -24 14}}]
Mapping: {{mapping| 1 6 1 7 5 9 1 | 0 -20 6 -19 -7 -24 14 }}


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


Optimal GPV sequence: {{Val list| 9, 59f, 68, 77, 145e }}
{{Optimal ET sequence|legend=1| 9, 59f, 68, 77, 145e }}


Badness: 0.027851
Badness: 0.027851
Line 343: Line 336:
Comma list: 121/120, 154/153, 176/175, 196/195, 209/208, 361/360
Comma list: 121/120, 154/153, 176/175, 196/195, 209/208, 361/360


Mapping: [{{val|1 6 1 7 5 9 1 8}}, {{val|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 }}


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


Optimal GPV sequence: {{Val list| 9, 59f, 68, 77, 145e }}
{{Optimal ET sequence|legend=1| 9, 59f, 68, 77, 145e }}


Badness: 0.020053
Badness: 0.020053


== Cohemimabila ==
== Cohemimabila ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 3136/3125, 65536/64827
[[Comma list]]: 3136/3125, 65536/64827


[[Mapping]]: [{{val|1 -4 4 7}}, {{val|0 20 -6 -15}}]
{{Mapping|legend=1| 1 -4 4 7 | 0 20 -6 -15 }}
 
{{Multival|legend=1| 20 -6 -15 -56 -80 -18 }}


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


{{Val list|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]]: 0.127451
Line 371: Line 362:
Comma list: 176/175, 1375/1372, 16384/16335
Comma list: 176/175, 1375/1372, 16384/16335


Mapping: [{{val|1 -4 4 7 11}}, {{val|0 20 -6 -15 -27}}]
Mapping: {{mapping| 1 -4 4 7 11 | 0 20 -6 -15 -27 }}


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


Optimal GPV sequence: {{Val list| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=1| 25, 43, 68, 111 }}


Badness: 0.064164
Badness: 0.064164
Line 384: Line 375:
Comma list: 176/175, 640/637, 676/675, 1375/1372
Comma list: 176/175, 640/637, 676/675, 1375/1372


Mapping: [{{val|1 -4 4 7 11 -3}}, {{val|0 20 -6 -15 -27 24}}]
Mapping: {{mapping| 1 -4 4 7 11 -3 | 0 20 -6 -15 -27 24 }}


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


Optimal GPV sequence: {{Val list| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=1| 25, 43, 68, 111 }}


Badness: 0.035463
Badness: 0.035463
Line 397: Line 388:
Comma list: 176/175, 256/255, 442/441, 640/637, 715/714
Comma list: 176/175, 256/255, 442/441, 640/637, 715/714


Mapping: [{{val|1 -4 4 7 11 -3 8}}, {{val|0 20 -6 -15 -27 24 -14}}]
Mapping: {{mapping| 1 -4 4 7 11 -3 8 | 0 20 -6 -15 -27 24 -14 }}


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


Optimal GPV sequence: {{Val list| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=1| 25, 43, 68, 111 }}


Badness: 0.022728
Badness: 0.022728
Line 410: Line 401:
Comma list: 176/175, 256/255, 286/285, 363/361, 442/441, 476/475
Comma list: 176/175, 256/255, 286/285, 363/361, 442/441, 476/475


Mapping: [{{val|1 -4 4 7 11 -3 8 9}}, {{val|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 }}


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


Optimal GPV sequence: {{Val list| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=1| 25, 43, 68, 111 }}


Badness: 0.017450
Badness: 0.017450


== Trimabila ==
== Trimabila ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1728/1715, 268435456/263671875
[[Comma list]]: 1728/1715, 268435456/263671875


[[Mapping]]: [{{val|3 8 6 12}}, {{val|0 -10 3 -11}}]
{{Mapping|legend=1| 3 8 6 12 | 0 -10 3 -11 }}
 
{{Multival|legend=1| 30 -9 33 -84 -32 102 }}


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


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


[[Badness]]: 0.267168
[[Badness]]: 0.267168
Line 438: Line 427:
Comma list: 176/175, 540/539, 805255/802816
Comma list: 176/175, 540/539, 805255/802816


Mapping: [{{val|3 8 6 12 12}}, {{val|0 -10 3 -11 -5}}]
Mapping: {{mapping| 3 8 6 12 12 | 0 -10 3 -11 -5 }}


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


Optimal GPV sequence: {{Val list| 9, 102d, 111 }}
{{Optimal ET sequence|legend=1| 9, 102d, 111 }}


Badness: 0.081946
Badness: 0.081946
Line 451: Line 440:
Comma list: 176/175, 540/539, 676/675, 1573/1568
Comma list: 176/175, 540/539, 676/675, 1573/1568


Mapping: [{{val|3 8 6 12 12 15}}, {{val|0 -10 3 -11 -5 -12}}]
Mapping: {{mapping| 3 8 6 12 12 15 | 0 -10 3 -11 -5 -12 }}


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


Optimal GPV sequence: {{Val list| 9, 102df, 111 }}
{{Optimal ET sequence|legend=1| 9, 102df, 111 }}


Badness: 0.040102
Badness: 0.040102
Line 464: Line 453:
Comma list: 176/175, 256/255, 540/539, 676/675, 715/714
Comma list: 176/175, 256/255, 540/539, 676/675, 715/714


Mapping: [{{val|3 8 6 12 12 15 10}}, {{val|0 -10 3 -11 -5 -12 7}}]
Mapping: {{mapping| 3 8 6 12 12 15 10 | 0 -10 3 -11 -5 -12 7 }}


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


Optimal GPV sequence: {{Val list| 9, 102df, 111 }}
{{Optimal ET sequence|legend=1| 9, 102df, 111 }}


Badness: 0.030657
Badness: 0.030657
Line 477: Line 466:
Comma list: 176/175, 256/255, 286/285, 363/361, 476/475, 540/539
Comma list: 176/175, 256/255, 286/285, 363/361, 476/475, 540/539


Mapping: [{{val|3 8 6 12 12 15 10 16}}, {{val|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 }}


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


Optimal GPV sequence: {{Val list| 9, 102dfh, 111 }}
{{Optimal ET sequence|legend=1| 9, 102dfh, 111 }}


Badness: 0.022851
Badness: 0.022851


[[Category:Regular temperament theory]]
[[Category:Temperament families]]
[[Category:Temperament family]]
[[Category:Pages with mostly numerical content]]
[[Category:Mabila family| ]] <!-- main article -->
[[Category:Mabila family| ]] <!-- main article -->
[[Category:Mabila| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Latest revision as of 07:33, 30 July 2025

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 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: 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 = 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]]

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]]

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]]

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]]

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]]

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]]

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

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