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Mabila family: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
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.  
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]].  


== Mabila ==
== 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 {{nowrap| ''n'' {{=}} 5 }}.
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


Line 14: Line 20:
: [[error map]]: {{val| -0.646 +0.173 +1.240 }}
: [[error map]]: {{val| -0.646 +0.173 +1.240 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.2921{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.2921{{c}}
: error map: {{val| -0.646 +0.173 +1.240 }}
: error map: {{val| 0.000 +0.966 +2.810 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~375/256 = 670.315{{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 }}
Line 21: Line 26:
[[Badness]] (Sintel): 5.45
[[Badness]] (Sintel): 5.45


== Semabila ==
=== Overview to extensions ===
{{See also| No-threes subgroup temperaments #Mabilic }}
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.


Semabila is so named because it is a semaphore temperament.
== Amavil ==
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| 9 & 43 }} 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 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~112/75 = 670.333{{c}} -->


{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.271{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.237{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.305{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.264{{c}} -->
 
{{Optimal ET sequence|legend=0| 9, 34dh, 43, 77deh }}
 
Badness (Sintel): 1.09


{{Optimal ET sequence|legend=0| 9, 25e, 34 }}
== Semabila ==
{{See also| No-threes subgroup temperaments #Mabilic }}


Badness (Sintel): 1.64
Semabila tempers out [[49/48]] and may be described as the {{nowrap| 9 & 25 }} temperament.  


== Amavil ==
This temperament used to known as ''septimal mabila''. Semabila, by [[Lériendil]] in 2024, was so named because it was 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 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~35/24 = 670.021{{c}} -->


{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.026{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.049{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.043{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.013{{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 ==
Named by [[Xenllium]] in 2022, tuskaloosa tempers out [[19683/19600]] and may be described as the {{nowrap| 34d & 77 }} temperament.
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 203: Line 207:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.2172{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.2172{{c}}
: error map: {{val| 0.000 +0.217 +3.035 +1.597 }}
: error map: {{val| 0.000 +0.217 +3.035 +1.597 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~375/256 = 670.228{{c}} -->


{{Optimal ET sequence|legend=1| 34d, 77, 111, 188, 299cd, 487ccd }}
{{Optimal ET sequence|legend=1| 34d, 77, 111, 188, 299cd, 487ccd }}
Line 219: Line 222:
* WE: ~2 = 1199.4934{{c}}, ~165/112 = 669.9677{{c}}
* WE: ~2 = 1199.4934{{c}}, ~165/112 = 669.9677{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~165/112 = 670.2405{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~165/112 = 670.2405{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~165/112 = 670.251{{c}} -->


{{Optimal ET sequence|legend=0| 34d, 77, 111 }}
{{Optimal ET sequence|legend=0| 34d, 77, 111 }}
Line 235: Line 237:
* WE: ~2 = 1199.4539{{c}}, ~96/65 = 669.9476{{c}}
* WE: ~2 = 1199.4539{{c}}, ~96/65 = 669.9476{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~96/65 = 670.2425{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~96/65 = 670.2425{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~96/65 = 670.253{{c}} -->


{{Optimal ET sequence|legend=0| 34d, 77, 111 }}
{{Optimal ET sequence|legend=0| 34d, 77, 111 }}
Line 251: Line 252:
* WE: ~2 = 1199.3885{{c}}, ~25/17 = 669.9167{{c}}
* WE: ~2 = 1199.3885{{c}}, ~25/17 = 669.9167{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.2500{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.2500{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~25/17 = 670.258{{c}} -->


{{Optimal ET sequence|legend=0| 34d, 77, 111 }}
{{Optimal ET sequence|legend=0| 34d, 77, 111 }}
Line 267: Line 267:
* WE: ~2 = 1199.3711{{c}}, ~25/17 = 669.8997{{c}}
* WE: ~2 = 1199.3711{{c}}, ~25/17 = 669.8997{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.2422{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.2422{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~25/17 = 670.251{{c}} -->


{{Optimal ET sequence|legend=0| 34dh, 77, 111 }}
{{Optimal ET sequence|legend=0| 34dh, 77, 111 }}
Line 274: Line 273:


== Muscogee ==
== Muscogee ==
Named by [[Xenllium]] in 2022, muscogee tempers out [[126/125]] and may be described as the {{nowrap| 43 & 77 }} temperament.
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 285: Line 286:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.0935{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.0935{{c}}
: error map: {{val| 0.000 -1.020 +3.406 -1.539 }}
: error map: {{val| 0.000 -1.020 +3.406 -1.539 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~375/256 = 670.093{{c}} -->


{{Optimal ET sequence|legend=1| 34, 43, 77 }}
{{Optimal ET sequence|legend=1| 34, 43, 77 }}
Line 301: Line 301:
* WE: ~2 = 1200.0559{{c}}, ~165/112 = 670.0760{{c}}
* WE: ~2 = 1200.0559{{c}}, ~165/112 = 670.0760{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~165/112 = 670.0441{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~165/112 = 670.0441{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~165/112 = 670.045{{c}} -->


{{Optimal ET sequence|legend=0| 34e, 43, 77, 120 }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120 }}
Line 317: Line 316:
* WE: ~2 = 1200.0428{{c}}, ~96/65 = 670.0673{{c}}
* WE: ~2 = 1200.0428{{c}}, ~96/65 = 670.0673{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~96/65 = 670.0431{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~96/65 = 670.0431{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~96/65 = 670.043{{c}} -->


{{Optimal ET sequence|legend=0| 34e, 43, 77, 120 }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120 }}
Line 333: Line 331:
* WE: ~2 = 1199.8666{{c}}, ~25/17 = 669.9675{{c}}
* WE: ~2 = 1199.8666{{c}}, ~25/17 = 669.9675{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.0429{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.0429{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~25/17 = 670.042{{c}} -->


{{Optimal ET sequence|legend=0| 34e, 43, 77, 120g }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120g }}
Line 349: Line 346:
* WE: ~2 = 1199.8538{{c}}, ~25/17 = 669.9631{{c}}
* WE: ~2 = 1199.8538{{c}}, ~25/17 = 669.9631{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.0460{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.0460{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~25/17 = 529.955{{c}} -->


{{Optimal ET sequence|legend=0| 34e, 43, 77, 120g }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120g }}
Line 355: Line 351:
Badness (Sintel): 1.44
Badness (Sintel): 1.44


== Hemimabila ==
== Cohemimabila ==
Named by [[Xenllium]] in 2022, cohemimabila tempers out [[3136/3125]] as well as [[65536/64827]] and may be described as the {{nowrap| 43 & 68 }} temperament.
 
[[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 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~7/6 = 935.175{{c}} -->


{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~12/7 = 935.151{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~12/7 = 935.139{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~12/7 = 935.161{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~7/6 = 264.839{{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 }}
<!-- * [[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| 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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~40/33 = 335.148{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~40/33 = 335.144{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~17/14 = 335.145{{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}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~17/14 = 335.151{{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 ==
Named by [[Xenllium]] in 2022, trimabila tempers out [[1728/1715]] and may be described as the {{nowrap| 9 & 111 }} temperament.
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 534: Line 524:
* [[CWE]]: ~1125/896 = 400.0000{{c}}, ~7/6 = 270.2343{{c}}
* [[CWE]]: ~1125/896 = 400.0000{{c}}, ~7/6 = 270.2343{{c}}
: error map: {{val| 0.000 +0.388 +2.983 +3.752 }}
: error map: {{val| 0.000 +0.388 +2.983 +3.752 }}
<!-- * [[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 }}
Line 550: Line 539:
* WE: ~495/392 = 399.7963{{c}}, ~7/6 = 270.1183{{c}}
* WE: ~495/392 = 399.7963{{c}}, ~7/6 = 270.1183{{c}}
* CWE: ~495/392 = 400.0000{{c}}, ~7/6 = 270.2301{{c}}
* CWE: ~495/392 = 400.0000{{c}}, ~7/6 = 270.2301{{c}}
<!-- * POTE: ~495/392 = 400.000{{c}}, ~7/6 = 270.256{{c}} -->


{{Optimal ET sequence|legend=0| 9, …, 102d, 111 }}
{{Optimal ET sequence|legend=0| 9, …, 102d, 111 }}
Line 566: Line 554:
* WE: ~495/392 = 399.7935{{c}}, ~7/6 = 270.1144{{c}}
* WE: ~495/392 = 399.7935{{c}}, ~7/6 = 270.1144{{c}}
* CWE: ~495/392 = 400.0000{{c}}, ~7/6 = 270.2258{{c}}
* CWE: ~495/392 = 400.0000{{c}}, ~7/6 = 270.2258{{c}}
<!-- * POTE: ~495/392 = 400.000{{c}}, ~7/6 = 270.254{{c}} (or ~14/13 = 129.746{{c}}) -->


{{Optimal ET sequence|legend=0| 9, …, 102df, 111 }}
{{Optimal ET sequence|legend=0| 9, …, 102df, 111 }}
Line 582: Line 569:
* WE: ~495/392 = 399.7781{{c}}, ~7/6 = 270.1159{{c}}
* WE: ~495/392 = 399.7781{{c}}, ~7/6 = 270.1159{{c}}
* CWE: ~495/392 = 400.0000{{c}}, ~7/6 = 270.2476{{c}}
* CWE: ~495/392 = 400.0000{{c}}, ~7/6 = 270.2476{{c}}
<!-- * POTE: ~495/392 = 400.000{{c}}, ~7/6 = 270.266{{c}} (or ~14/13 = 129.734{{c}}) -->


{{Optimal ET sequence|legend=0| 9, 102df, 111 }}
{{Optimal ET sequence|legend=0| 9, 102df, 111 }}
Line 598: Line 584:
* WE: ~208/165 = 399.7588{{c}}, ~7/6 = 270.0969{{c}}
* WE: ~208/165 = 399.7588{{c}}, ~7/6 = 270.0969{{c}}
* CWE: ~208/165 = 400.0000{{c}}, ~7/6 = 270.2391{{c}}
* CWE: ~208/165 = 400.0000{{c}}, ~7/6 = 270.2391{{c}}
<!-- * POTE: ~208/165 = 400.000{{c}}, ~7/6 = 270.260{{c}} (or ~14/13 = 129.740{{c}}) -->


{{Optimal ET sequence|legend=0| 9, 102dfh, 111 }}
{{Optimal ET sequence|legend=0| 9, 102dfh, 111 }}
Line 606: Line 591:
== References ==
== References ==


[[Category:Mabila family| ]] <!-- main article -->
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Mabila family| ]] <!-- main article -->
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Mabila| ]] <!-- key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Mabila_family"