Mabila family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
m - redundant category
Sorting
Line 20: Line 20:
[[Badness]] (Sintel): 5.45
[[Badness]] (Sintel): 5.45


== Semabila ==
== Amavil ==
{{See also| No-threes subgroup temperaments #Mabilic }}
Named by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, amavil tempers out [[225/224]] and may be described as the {{nowrap| 34d & 43 }} temperament.
 
Semabila is so named because it is a semaphore temperament.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 49/48, 28672/28125
[[Comma list]]: 225/224, 17496/16807


{{Mapping|legend=1| 1 -4 4 0 | 0 10 -3 5 }}
{{Mapping|legend=1| 1 -4 4 -5 | 0 10 -3 14 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.9854{{c}}, ~112/75 = 670.8838{{c}}
* [[WE]]: ~2 = 1198.8499{{c}}, ~35/24 = 669.3786{{c}}
: [[error map]]: {{val| +0.985 +2.941 +4.977 -14.407 }}
: [[error map]]: {{val| -1.150 -3.569 +0.950 +8.224 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~112/75 = 670.3712{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~35/24 = 669.9710{{c}}
: error map: {{val| 0.000 +1.757 +2.573 -16.970 }}
: error map: {{val| 0.000 -2.245 +3.773 +10.768 }}


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


[[Badness]] (Sintel): 3.38
[[Badness]] (Sintel): 2.77


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 49/48, 56/55, 1350/1331
Comma list: 99/98, 176/175, 864/847


Mapping: {{mapping| 1 -4 4 0 1 | 0 10 -3 5 8 }}
Mapping: {{mapping| 1 -4 4 -5 -1 | 0 10 -3 14 8 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1200.2248{{c}}, ~22/15 = 670.3965{{c}}
* WE: ~2 = 1198.5522{{c}}, ~22/15 = 669.2176{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2804{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9619{{c}}


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


Badness (Sintel): 2.03
Badness (Sintel): 1.41


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 49/48, 56/55, 91/90, 847/845
Comma list: 78/77, 99/98, 144/143, 176/175


Mapping: {{mapping| 1 -4 4 0 1 -3 | 0 10 -3 5 8 12 }}
Mapping: {{mapping| 1 -4 4 -5 -1 -3 | 0 10 -3 14 8 12 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1200.1265{{c}}, ~22/15 = 670.3078{{c}}
* WE: ~2 = 1198.7386{{c}}, ~22/15 = 669.3449{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2429{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9903{{c}}


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


Badness (Sintel): 1.54
Badness (Sintel): 1.07


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 49/48, 56/55, 91/90, 154/153, 375/374
Comma list: 78/77, 99/98, 120/119, 144/143, 176/175


Mapping: {{mapping| 1 -4 4 0 1 -3 8 | 0 10 -3 5 8 12 -7 }}
Mapping: {{mapping| 1 -4 4 -5 -1 -3 8 | 0 10 -3 14 8 12 -7 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.8798{{c}}, ~22/15 = 670.2382{{c}}
* WE: ~2 = 1198.7648{{c}}, ~22/15 = 669.3533{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.3021{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.0080{{c}}


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


Badness (Sintel): 1.62
Badness (Sintel): 1.13


=== 19-limit ===
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187
Comma list: 78/77, 96/95, 99/98, 120/119, 135/133, 144/143


Mapping: {{mapping| 1 -4 4 0 1 -3 8 2 | 0 10 -3 5 8 12 -7 4 }}
Mapping: {{mapping| 1 -4 4 -5 -1 -3 8 -3 | 0 10 -3 14 8 12 -7 13 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1200.4164{{c}}, ~22/15 = 670.4966{{c}}
* WE: ~2 = 1198.5939{{c}}, ~22/15 = 669.2282{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2749{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9712{{c}}
 
{{Optimal ET sequence|legend=0| 9, 34dh, 43, 77deh }}


{{Optimal ET sequence|legend=0| 9, 25e, 34 }}
Badness (Sintel): 1.09


Badness (Sintel): 1.64
== Semabila ==
{{See also| No-threes subgroup temperaments #Mabilic }}


== Amavil ==
Semabila is so named because it is a semaphore temperament.
Named by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, amavil tempers out [[225/224]] and may be described as the {{nowrap| 34d & 43 }} temperament.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 17496/16807
[[Comma list]]: 49/48, 28672/28125


{{Mapping|legend=1| 1 -4 4 -5 | 0 10 -3 14 }}
{{Mapping|legend=1| 1 -4 4 0 | 0 10 -3 5 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1198.8499{{c}}, ~35/24 = 669.3786{{c}}
* [[WE]]: ~2 = 1200.9854{{c}}, ~112/75 = 670.8838{{c}}
: [[error map]]: {{val| -1.150 -3.569 +0.950 +8.224 }}
: [[error map]]: {{val| +0.985 +2.941 +4.977 -14.407 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~35/24 = 669.9710{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~112/75 = 670.3712{{c}}
: error map: {{val| 0.000 -2.245 +3.773 +10.768 }}
: error map: {{val| 0.000 +1.757 +2.573 -16.970 }}


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


[[Badness]] (Sintel): 2.77
[[Badness]] (Sintel): 3.38


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 99/98, 176/175, 864/847
Comma list: 49/48, 56/55, 1350/1331


Mapping: {{mapping| 1 -4 4 -5 -1 | 0 10 -3 14 8 }}
Mapping: {{mapping| 1 -4 4 0 1 | 0 10 -3 5 8 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1198.5522{{c}}, ~22/15 = 669.2176{{c}}
* WE: ~2 = 1200.2248{{c}}, ~22/15 = 670.3965{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9619{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2804{{c}}


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


Badness (Sintel): 1.41
Badness (Sintel): 2.03


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 78/77, 99/98, 144/143, 176/175
Comma list: 49/48, 56/55, 91/90, 847/845


Mapping: {{mapping| 1 -4 4 -5 -1 -3 | 0 10 -3 14 8 12 }}
Mapping: {{mapping| 1 -4 4 0 1 -3 | 0 10 -3 5 8 12 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1198.7386{{c}}, ~22/15 = 669.3449{{c}}
* WE: ~2 = 1200.1265{{c}}, ~22/15 = 670.3078{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9903{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2429{{c}}


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


Badness (Sintel): 1.07
Badness (Sintel): 1.54


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 78/77, 99/98, 120/119, 144/143, 176/175
Comma list: 49/48, 56/55, 91/90, 154/153, 375/374


Mapping: {{mapping| 1 -4 4 -5 -1 -3 8 | 0 10 -3 14 8 12 -7 }}
Mapping: {{mapping| 1 -4 4 0 1 -3 8 | 0 10 -3 5 8 12 -7 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1198.7648{{c}}, ~22/15 = 669.3533{{c}}
* WE: ~2 = 1199.8798{{c}}, ~22/15 = 670.2382{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.0080{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.3021{{c}}


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


Badness (Sintel): 1.13
Badness (Sintel): 1.62


=== 19-limit ===
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 78/77, 96/95, 99/98, 120/119, 135/133, 144/143
Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187


Mapping: {{mapping| 1 -4 4 -5 -1 -3 8 -3 | 0 10 -3 14 8 12 -7 13 }}
Mapping: {{mapping| 1 -4 4 0 1 -3 8 2 | 0 10 -3 5 8 12 -7 4 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1198.5939{{c}}, ~22/15 = 669.2282{{c}}
* WE: ~2 = 1200.4164{{c}}, ~22/15 = 670.4966{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9712{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2749{{c}}


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


Badness (Sintel): 1.09
Badness (Sintel): 1.64


== Tuskaloosa ==
== Tuskaloosa ==
Line 334: Line 334:
Badness (Sintel): 1.44
Badness (Sintel): 1.44


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


[[Comma list]]: 6144/6125, 117649/116640
[[Comma list]]: 3136/3125, 65536/64827


{{Mapping|legend=1| 1 -14 7 -12 | 0 20 -6 19 }}
{{Mapping|legend=1| 1 -4 4 7 | 0 20 -6 -15 }}
: mapping generators: ~2, ~12/7
: mapping generators: ~2, ~128/105


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.5170{{c}}, ~12/7 = 934.7983{{c}}
* [[WE]]: ~2 = 1199.1476{{c}}, ~128/105 = 334.9440{{c}}
: [[error map]]: {{val| -0.483 +0.773 +1.516 -1.862 }}
: [[error map]]: {{val| -0.852 +0.335 +0.613 +1.047 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~12/7 = 935.1643{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 335.1779{{c}}
: error map: {{val| 0.000 +1.330 +2.701 -0.705 }}
: error map: {{val| 0.000 +1.603 +2.619 +3.505 }}


{{Optimal ET sequence|legend=1| 9, …, 59, 68, 77, 145 }}
{{Optimal ET sequence|legend=1| 25, 43, 68, 111, 179, 290cd, 469bccdd }}


[[Badness]] (Sintel): 2.81
[[Badness]] (Sintel): 3.23


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 121/120, 176/175, 67228/66825
Comma list: 176/175, 1375/1372, 16384/16335


Mapping: {{mapping| 1 -14 7 -12 -2 | 0 20 -6 19 7 }}
Mapping: {{mapping| 1 -4 4 7 11 | 0 20 -6 -15 -27 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.9930{{c}}, ~12/7 = 935.1459{{c}}
* WE: ~2 = 1199.3670{{c}}, ~40/33 = 334.9711{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1512{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/33 = 335.1492{{c}}


{{Optimal ET sequence|legend=0| 9, 59, 68, 77, 145e }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness (Sintel): 2.03
Badness (Sintel): 2.12


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 121/120, 176/175, 196/195, 676/675
Comma list: 176/175, 640/637, 676/675, 1375/1372


Mapping: {{mapping| 1 -14 7 -12 -2 -15 | 0 20 -6 19 7 24 }}
Mapping: {{mapping| 1 -4 4 7 11 -3 | 0 20 -6 -15 -27 24 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.9061{{c}}, ~12/7 = 935.0656{{c}}
* WE: ~2 = 1199.3383{{c}}, ~40/33 = 334.9594{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1367{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/33 = 335.1431{{c}}


{{Optimal ET sequence|legend=0| 9, 59f, 68, 77 }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness (Sintel): 1.43
Badness (Sintel): 1.47


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 121/120, 154/153, 176/175, 196/195, 676/675
Comma list: 176/175, 256/255, 442/441, 640/637, 715/714


Mapping: {{mapping| 1 -14 7 -12 -2 -15 15 | 0 20 -6 19 7 24 -14 }}
Mapping: {{mapping| 1 -4 4 7 11 -3 8 | 0 20 -6 -15 -27 24 -14 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.7422{{c}}, ~12/7 = 934.9596{{c}}
* WE: ~2 = 1199.3269{{c}}, ~17/14 = 334.9571{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1572{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/14 = 335.1451{{c}}


{{Optimal ET sequence|legend=0| 9, 59f, 68, 77 }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness (Sintel): 1.42
Badness (Sintel): 1.16


=== 19-limit ===
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 121/120, 154/153, 176/175, 196/195, 209/208, 361/360
Comma list: 176/175, 256/255, 286/285, 363/361, 442/441, 476/475


Mapping: {{mapping| 1 -14 7 -12 -2 -15 15 -9 | 0 20 -6 19 7 24 -14 17 }}
Mapping: {{mapping| 1 -4 4 7 11 -3 8 9 | 0 20 -6 -15 -27 24 -14 -17 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.7650{{c}}, ~12/7 = 934.9782{{c}}
* WE: ~2 = 1199.2658{{c}}, ~17/14 = 334.9455{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1581{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/14 = 335.1516{{c}}


{{Optimal ET sequence|legend=0| 9, 59f, 68, 77 }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness (Sintel): 1.22
Badness (Sintel): 1.06


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


[[Comma list]]: 3136/3125, 65536/64827
[[Comma list]]: 6144/6125, 117649/116640


{{Mapping|legend=1| 1 -4 4 7 | 0 20 -6 -15 }}
{{Mapping|legend=1| 1 -14 7 -12 | 0 20 -6 19 }}
: mapping generators: ~2, ~128/105
: mapping generators: ~2, ~12/7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.1476{{c}}, ~128/105 = 334.9440{{c}}
* [[WE]]: ~2 = 1199.5170{{c}}, ~12/7 = 934.7983{{c}}
: [[error map]]: {{val| -0.852 +0.335 +0.613 +1.047 }}
: [[error map]]: {{val| -0.483 +0.773 +1.516 -1.862 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 335.1779{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~12/7 = 935.1643{{c}}
: error map: {{val| 0.000 +1.603 +2.619 +3.505 }}
: error map: {{val| 0.000 +1.330 +2.701 -0.705 }}


{{Optimal ET sequence|legend=1| 25, 43, 68, 111, 179, 290cd, 469bccdd }}
{{Optimal ET sequence|legend=1| 9, …, 59, 68, 77, 145 }}


[[Badness]] (Sintel): 3.23
[[Badness]] (Sintel): 2.81


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 176/175, 1375/1372, 16384/16335
Comma list: 121/120, 176/175, 67228/66825


Mapping: {{mapping| 1 -4 4 7 11 | 0 20 -6 -15 -27 }}
Mapping: {{mapping| 1 -14 7 -12 -2 | 0 20 -6 19 7 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.3670{{c}}, ~40/33 = 334.9711{{c}}
* WE: ~2 = 1199.9930{{c}}, ~12/7 = 935.1459{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/33 = 335.1492{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1512{{c}}


{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=0| 9, 59, 68, 77, 145e }}


Badness (Sintel): 2.12
Badness (Sintel): 2.03


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 176/175, 640/637, 676/675, 1375/1372
Comma list: 121/120, 176/175, 196/195, 676/675


Mapping: {{mapping| 1 -4 4 7 11 -3 | 0 20 -6 -15 -27 24 }}
Mapping: {{mapping| 1 -14 7 -12 -2 -15 | 0 20 -6 19 7 24 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.3383{{c}}, ~40/33 = 334.9594{{c}}
* WE: ~2 = 1199.9061{{c}}, ~12/7 = 935.0656{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/33 = 335.1431{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1367{{c}}


{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=0| 9, 59f, 68, 77 }}


Badness (Sintel): 1.47
Badness (Sintel): 1.43


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 176/175, 256/255, 442/441, 640/637, 715/714
Comma list: 121/120, 154/153, 176/175, 196/195, 676/675


Mapping: {{mapping| 1 -4 4 7 11 -3 8 | 0 20 -6 -15 -27 24 -14 }}
Mapping: {{mapping| 1 -14 7 -12 -2 -15 15 | 0 20 -6 19 7 24 -14 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.3269{{c}}, ~17/14 = 334.9571{{c}}
* WE: ~2 = 1199.7422{{c}}, ~12/7 = 934.9596{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/14 = 335.1451{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1572{{c}}


{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=0| 9, 59f, 68, 77 }}


Badness (Sintel): 1.16
Badness (Sintel): 1.42


=== 19-limit ===
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 176/175, 256/255, 286/285, 363/361, 442/441, 476/475
Comma list: 121/120, 154/153, 176/175, 196/195, 209/208, 361/360


Mapping: {{mapping| 1 -4 4 7 11 -3 8 9 | 0 20 -6 -15 -27 24 -14 -17 }}
Mapping: {{mapping| 1 -14 7 -12 -2 -15 15 -9 | 0 20 -6 19 7 24 -14 17 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.2658{{c}}, ~17/14 = 334.9455{{c}}
* WE: ~2 = 1199.7650{{c}}, ~12/7 = 934.9782{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/14 = 335.1516{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1581{{c}}


{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=0| 9, 59f, 68, 77 }}


Badness (Sintel): 1.06
Badness (Sintel): 1.22


== Trimabila ==
== Trimabila ==

Revision as of 11:35, 26 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 -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: ⟨-0.646 +0.173 +1.240]

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

Badness (Sintel): 5.45

Amavil

Named by Petr Pařízek in 2011[1], amavil tempers out 225/224 and may be described as the 34d & 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 is so named because it is 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

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

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

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

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
Retrieved from "https://en.xen.wiki/index.php?title=Mabila_family&oldid=224810"