Xenharmonic Wiki

Mabila family: Difference between revisions

VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,032 edits
Created page with "The '''mabila family''' tempers out {{monzo|28 -3 -10}} = 268435456/263671875 in the 5-limit. == Mabila == Subgroup: 2.3.5 Comma: 268435456/263671875 Mapping: [{{Va..."
 
m Recategorize
 
(27 intermediate revisions by 8 users not shown)
Line 1: Line 1:
The '''mabila family''' tempers out {{monzo|28 -3 -10}} = 268435456/263671875 in the 5-limit.
{{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]].  


== Mabila ==
== Mabila ==
Subgroup: 2.3.5
: ''"Mabila" redirects here. For the temperaments that used to go by this name, see [[Semabila]] and [[Mabilic]].''


[[Comma]]: 268435456/263671875
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.


[[Mapping]]: [{{Val| 1 6 1 }}, {{Val| 0 -10 3 }}]
Mabila is part of the [[diaschismic–gothmic equivalence continuum]] with {{nowrap| ''n'' {{=}} 5 }}.


[[POTE generator]]: ~512/375 = 529.685
[[Subgroup]]: 2.3.5


{{Val list|legend=1| 9, 25, 34, 77, 111, 145, 256c }}
[[Comma list]]: 268435456/263671875


[[Badness]]: 0.232481
{{Mapping|legend=1| 1 -4 4 | 0 10 -3 }}
: mapping generators: ~2, ~375/256


== Septimal mabila ==
[[Optimal tuning]]s:
{{see also| Slendro clan #Mabila }}
* [[WE]]: ~2 = 1199.3545{{c}}, ~375/256 = 669.9545{{c}}
: [[error map]]: {{val| -0.646 +0.173 +1.240 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.2921{{c}}
: error map: {{val| 0.000 +0.966 +2.810 }}


Subgroup: 2.3.5.7
{{Optimal ET sequence|legend=1| 9, 25, 34, 77, 111, 145, 256c }}


[[Comma list]]: 49/48, 28672/28125
[[Badness]] (Sintel): 5.45
 
=== Overview to extensions ===
The second comma in the comma list defines which 7-limit family member we are looking at. Amavil (9 & 43) adds [[225/224]], semabila (9 & 25) adds [[49/48]], tuscaloosa (77 & 111) adds [[19683/19600]], muscogee (43 & 77) adds [[126/125]]. These all use the same generators as mabila.
 
Cohemimabila (25 & 43) tempers out [[3136/3125]], splitting the subfifth in two. Hemimabila (9 & 68) tempers out [[6144/6125]], splitting the subtwelfth in two. Trimabila (9 & 111) tempers out [[1728/1715]], with a 1/3-octave period.
 
== Amavil ==
Named by [[Petr Pařízek]] in 2011<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.


[[Mapping]]: [{{val| 1 6 1 5 }}, {{val| 0 -10 3 -5 }}]
[[Subgroup]]: 2.3.5.7


{{Multival|legend=1| 10 -3 5 -28 -20 20 }}
[[Comma list]]: 225/224, 17496/16807


[[POTE generator]]: ~75/56 = 529.667
{{Mapping|legend=1| 1 -4 4 -5 | 0 10 -3 14 }}


{{Val list|legend=1| 9, 25, 34 }}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.8499{{c}}, ~35/24 = 669.3786{{c}}
: [[error map]]: {{val| -1.150 -3.569 +0.950 +8.224 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~35/24 = 669.9710{{c}}
: error map: {{val| 0.000 -2.245 +3.773 +10.768 }}


[[Badness]]: 0.133638
{{Optimal ET sequence|legend=1| 9, 25d, 34d, 43, 77d }}
 
[[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: [{{val| 1 6 1 5 7 }}, {{val| 0 -10 3 -5 -8 }}]
Mapping: {{mapping| 1 -4 4 -5 -1 | 0 10 -3 14 8 }}


POTE generator: ~15/11 = 529.729
Optimal tunings:  
* WE: ~2 = 1198.5522{{c}}, ~22/15 = 669.2176{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9619{{c}}


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


Badness: 0.061501
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: [{{val| 1 6 1 5 7 9 }}, {{val| 0 -10 3 -5 -8 -12 }}]
Mapping: {{mapping| 1 -4 4 -5 -1 -3 | 0 10 -3 14 8 12 }}


POTE generator: ~15/11 = 529.763
Optimal tunings:  
* WE: ~2 = 1198.7386{{c}}, ~22/15 = 669.3449{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9903{{c}}


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


Badness: 0.037270
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: [{{val| 1 6 1 5 7 9 1 }}, {{val| 0 -10 3 -5 -8 -12 7 }}]
Mapping: {{mapping| 1 -4 4 -5 -1 -3 8 | 0 10 -3 14 8 12 -7 }}


POTE generator: ~15/11 = 529.695
Optimal tunings:  
* WE: ~2 = 1198.7648{{c}}, ~22/15 = 669.3533{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.0080{{c}}


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


Badness: 0.031888
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 -5 -1 -3 8 -3 | 0 10 -3 14 8 12 -7 13 }}
 
Optimal tunings:
* WE: ~2 = 1198.5939{{c}}, ~22/15 = 669.2282{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9712{{c}}


Mapping: [{{val| 1 6 1 5 7 9 1 6 }}, {{val| 0 -10 3 -5 -8 -12 7 -4 }}]
{{Optimal ET sequence|legend=0| 9, 34dh, 43, 77deh }}


POTE generator: ~15/11 = 529.736
Badness (Sintel): 1.09


Optimal GPV sequence: {{Val list| 9, 25e, 34 }}
== Semabila ==
{{See also| No-threes subgroup temperaments #Mabilic }}


Badness: 0.026981
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.
Subgroup: 2.3.5.7


[[Comma list]]: 225/224, 17496/16807
[[Subgroup]]: 2.3.5.7


[[Mapping]]: [{{val| 1 6 1 9 }}, {{val| 0 -10 3 -14 }}]
[[Comma list]]: 49/48, 28672/28125


{{Multival|legend=1| 10 -3 14 -28 -6 41 }}
{{Mapping|legend=1| 1 -4 4 0 | 0 10 -3 5 }}


[[POTE generator]]: ~48/35 = 529.979
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.9854{{c}}, ~112/75 = 670.8838{{c}}
: [[error map]]: {{val| +0.985 +2.941 +4.977 -14.407 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~112/75 = 670.3712{{c}}
: error map: {{val| 0.000 +1.757 +2.573 -16.970 }}


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


[[Badness]]: 0.109625
[[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: [{{val| 1 6 1 9 7 }}, {{val| 0 -10 3 -14 -8 }}]
Mapping: {{mapping| 1 -4 4 0 1 | 0 10 -3 5 8 }}


POTE generator: ~15/11 = 529.974
Optimal tunings:  
* WE: ~2 = 1200.2248{{c}}, ~22/15 = 670.3965{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2804{{c}}


Optimal GPV sequence: {{Val list| 9, 25de, 34d, 43, 77de, 120dde }}
{{Optimal ET sequence|legend=0| 9, 25e, 34 }}


Badness: 0.042649
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: [{{val| 1 6 1 9 7 9 }}, {{val| 0 -10 3 -14 -8 -12 }}]
Mapping: {{mapping| 1 -4 4 0 1 -3 | 0 10 -3 5 8 12 }}


POTE generator: ~15/11 = 529.951
Optimal tunings:  
* WE: ~2 = 1200.1265{{c}}, ~22/15 = 670.3078{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2429{{c}}


Optimal GPV sequence: {{Val list| 9, 25de, 34d, 43, 77de, 120dde }}
{{Optimal ET sequence|legend=0| 9, 25e, 34 }}


Badness: 0.025791
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: [{{val| 1 6 1 9 7 9 1 }}, {{val| 0 -10 3 -14 -8 -12 7 }}]
Mapping: {{mapping| 1 -4 4 0 1 -3 8 | 0 10 -3 5 8 12 -7 }}


POTE generator: ~15/11 = 529.957
Optimal tunings:  
* WE: ~2 = 1199.8798{{c}}, ~22/15 = 670.2382{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.3021{{c}}


Optimal GPV sequence: {{Val list| 9, 25de, 34d, 43, 77de, 120ddeg }}
{{Optimal ET sequence|legend=0| 9, 25e, 34 }}


Badness: 0.022092
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: [{{val| 1 6 1 9 7 9 1 10 }}, {{val| 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 }}


POTE generator: ~15/11 = 529.987
Optimal tunings:  
* WE: ~2 = 1200.4164{{c}}, ~22/15 = 670.4966{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2749{{c}}


Optimal GPV sequence: {{Val list| 9, 25deh, 34dh, 43, 77deh, 120ddeghh }}
{{Optimal ET sequence|legend=0| 9, 25e, 34 }}


Badness: 0.017955
Badness (Sintel): 1.64


== Tuskaloosa ==
== Tuskaloosa ==
Subgroup: 2.3.5.7
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


[[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 -4 4 -24 | 0 10 -3 48 }}


[[POTE generator]]: ~512/375 = 529.772
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.4378{{c}}, ~375/256 = 669.9137{{c}}
: [[error map]]: {{val| -0.562 -0.569 +1.696 +0.524 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.2172{{c}}
: error map: {{val| 0.000 +0.217 +3.035 +1.597 }}


{{Val list|legend=1| 34d, 77, 111, 188, 299cd }}
{{Optimal ET sequence|legend=1| 34d, 77, 111, 188, 299cd, 487ccd }}


[[Badness]]: 0.145058
[[Badness]] (Sintel): 3.67


=== 11-limit ===
=== 11-limit ===
Line 168: Line 217:
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 -4 4 -24 -20 | 0 10 -3 48 42 }}


POTE generator: ~224/165 = 529.749
Optimal tunings:  
* WE: ~2 = 1199.4934{{c}}, ~165/112 = 669.9677{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~165/112 = 670.2405{{c}}


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


Badness: 0.061773
Badness (Sintel): 2.04


=== 13-limit ===
=== 13-limit ===
Line 181: Line 232:
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 -4 4 -24 -20 -3 | 0 10 -3 48 42 12 }}


POTE generator: ~65/48 = 529.747
Optimal tunings:  
* WE: ~2 = 1199.4539{{c}}, ~96/65 = 669.9476{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~96/65 = 670.2425{{c}}


Optimal GPV sequence: {{Val list| 34d, 77, 111, 410ccdf, 521ccddff }}
{{Optimal ET sequence|legend=0| 34d, 77, 111 }}


Badness: 0.031480
Badness (Sintel): 1.30


=== 17-limit ===
=== 17-limit ===
Line 194: Line 247:
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 -4 4 -24 -20 -3 8 | 0 10 -3 48 42 12 -7 }}


POTE generator: ~34/25 = 529.742
Optimal tunings:  
* WE: ~2 = 1199.3885{{c}}, ~25/17 = 669.9167{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.2500{{c}}


Optimal GPV sequence: {{Val list| 34d, 77, 111 }}
{{Optimal ET sequence|legend=0| 34d, 77, 111 }}


Badness: 0.022765
Badness (Sintel): 1.16


=== 19-limit ===
=== 19-limit ===
Line 207: Line 262:
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 -4 4 -24 -20 -3 8 -22 | 0 10 -3 48 42 12 -7 47 }}


POTE generator: ~19/14 = 529.749
Optimal tunings:  
* WE: ~2 = 1199.3711{{c}}, ~25/17 = 669.8997{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.2422{{c}}


Optimal GPV sequence: {{Val list| 34dh, 77, 111 }}
{{Optimal ET sequence|legend=0| 34dh, 77, 111 }}


Badness: 0.017924
Badness (Sintel): 1.09


== Muscogee ==
== Muscogee ==
Subgroup: 2.3.5.7
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


[[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 -4 4 19 | 0 10 -3 -29 }}


[[POTE generator]]: ~512/375 = 529.907
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.9275{{c}}, ~375/256 = 670.0525{{c}}
: [[error map]]: {{val| -0.073 -1.140 +3.239 -1.726 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.0935{{c}}
: error map: {{val| 0.000 -1.020 +3.406 -1.539 }}


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


[[Badness]]: 0.162021
[[Badness]] (Sintel): 4.10


=== 11-limit ===
=== 11-limit ===
Line 233: Line 296:
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 -4 4 19 23 | 0 10 -3 -29 -35 }}


POTE generator: ~224/165 = 529.955
Optimal tunings:  
* WE: ~2 = 1200.0559{{c}}, ~165/112 = 670.0760{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~165/112 = 670.0441{{c}}


Optimal GPV sequence: {{Val list| 34e, 43, 77, 120, 197ce }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120 }}


Badness: 0.077552
Badness (Sintel): 2.56


=== 13-limit ===
=== 13-limit ===
Line 246: Line 311:
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 -4 4 19 23 -3 | 0 10 -3 -29 -35 12 }}


POTE generator: ~65/48 = 529.957
Optimal tunings:  
* WE: ~2 = 1200.0428{{c}}, ~96/65 = 670.0673{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~96/65 = 670.0431{{c}}


Optimal GPV sequence: {{Val list| 34e, 43, 77, 120, 197ce }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120 }}


Badness: 0.043352
Badness (Sintel): 1.79


=== 17-limit ===
=== 17-limit ===
Line 259: Line 326:
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 -4 4 19 23 -3 8 | 0 10 -3 -29 -35 12 -7 }}


POTE generator: ~34/25 = 529.958
Optimal tunings:  
* WE: ~2 = 1199.8666{{c}}, ~25/17 = 669.9675{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.0429{{c}}


Optimal GPV sequence: {{Val list| 34e, 43, 77, 120g, 197ceg }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120g }}


Badness: 0.031217
Badness (Sintel): 1.59


=== 19-limit ===
=== 19-limit ===
Line 272: Line 341:
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 -4 4 19 23 -3 8 21 | 0 10 -3 -29 -35 12 -7 -30 }}
 
Optimal tunings:
* WE: ~2 = 1199.8538{{c}}, ~25/17 = 669.9631{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.0460{{c}}


POTE generator: ~19/14 = 529.955
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120g }}


Optimal GPV sequence: {{Val list| 34e, 43, 77, 120g, 197ceg }}
Badness (Sintel): 1.44


Badness: 0.023670
== 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.  


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


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


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


[[POTE generator]]: ~7/6 = 264.825
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.1476{{c}}, ~128/105 = 334.9440{{c}}
: [[error map]]: {{val| -0.852 +0.335 +0.613 +1.047 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 335.1779{{c}}
: error map: {{val| 0.000 +1.603 +2.619 +3.505 }}


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


[[Badness]]: 0.111130
[[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: [{{val|1 6 1 7 5}}, {{val|0 -20 6 -19 -7}}]
Mapping: {{mapping| 1 -4 4 7 11 | 0 20 -6 -15 -27 }}


POTE generator: ~7/6 = 264.849
Optimal tunings:  
* WE: ~2 = 1199.3670{{c}}, ~40/33 = 334.9711{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/33 = 335.1492{{c}}


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


Badness: 0.061426
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: [{{val|1 6 1 7 5 9}}, {{val|0 -20 6 -19 -7 -24}}]
Mapping: {{mapping| 1 -4 4 7 11 -3 | 0 20 -6 -15 -27 24 }}


POTE generator: ~7/6 = 264.861
Optimal tunings:  
* WE: ~2 = 1199.3383{{c}}, ~40/33 = 334.9594{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/33 = 335.1431{{c}}


Optimal GPV sequence: {{Val list| 9, 59f, 68, 77, 145e, 222cef }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness: 0.034531
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: [{{val|1 6 1 7 5 9 1}}, {{val|0 -20 6 -19 -7 -24 14}}]
Mapping: {{mapping| 1 -4 4 7 11 -3 8 | 0 20 -6 -15 -27 24 -14 }}


POTE generator: ~7/6 = 264.839
Optimal tunings:  
* WE: ~2 = 1199.3269{{c}}, ~17/14 = 334.9571{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/14 = 335.1451{{c}}


Optimal GPV sequence: {{Val list| 9, 59f, 68, 77, 145e }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness: 0.027851
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: [{{val|1 6 1 7 5 9 1 8}}, {{val|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 }}


POTE generator: ~7/6 = 264.839
Optimal tunings:  
* WE: ~2 = 1199.2658{{c}}, ~17/14 = 334.9455{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/14 = 335.1516{{c}}


Optimal GPV sequence: {{Val list| 9, 59f, 68, 77, 145e }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness: 0.020053
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]]: [{{val|1 -4 4 7}}, {{val|0 20 -6 -15}}]
{{Mapping|legend=1| 1 -14 7 -12 | 0 20 -6 19 }}
: mapping generators: ~2, ~12/7


[[POTE generator]]: ~128/105 = 335.182
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.5170{{c}}, ~12/7 = 934.7983{{c}}
: [[error map]]: {{val| -0.483 +0.773 +1.516 -1.862 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~12/7 = 935.1643{{c}}
: error map: {{val| 0.000 +1.330 +2.701 -0.705 }}


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


[[Badness]]: 0.127451
[[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: [{{val|1 -4 4 7 11}}, {{val|0 20 -6 -15 -27}}]
Mapping: {{mapping| 1 -14 7 -12 -2 | 0 20 -6 19 7 }}


POTE generator: ~40/33 = 335.148
Optimal tunings:  
* WE: ~2 = 1199.9930{{c}}, ~12/7 = 935.1459{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1512{{c}}


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


Badness: 0.064164
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: [{{val|1 -4 4 7 11 -3}}, {{val|0 20 -6 -15 -27 24}}]
Mapping: {{mapping| 1 -14 7 -12 -2 -15 | 0 20 -6 19 7 24 }}


POTE generator: ~40/33 = 335.144
Optimal tunings:  
* WE: ~2 = 1199.9061{{c}}, ~12/7 = 935.0656{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1367{{c}}


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


Badness: 0.035463
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: [{{val|1 -4 4 7 11 -3 8}}, {{val|0 20 -6 -15 -27 24 -14}}]
Mapping: {{mapping| 1 -14 7 -12 -2 -15 15 | 0 20 -6 19 7 24 -14 }}


POTE generator: ~17/14 = 335.145
Optimal tunings:  
* WE: ~2 = 1199.7422{{c}}, ~12/7 = 934.9596{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1572{{c}}


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


Badness: 0.022728
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: [{{val|1 -4 4 7 11 -3 8 9}}, {{val|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 }}


POTE generator: ~17/14 = 335.151
Optimal tunings:  
* WE: ~2 = 1199.7650{{c}}, ~12/7 = 934.9782{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1581{{c}}


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


Badness: 0.017450
Badness (Sintel): 1.22


== Trimabila ==
== Trimabila ==
Subgroup: 2.3.5.7
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


[[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 -2 9 1 | 0 10 -3 11 }}
: mapping generators: ~1125/896, ~7/6


[[POTE generator]]: ~7/6 = 270.269
[[Optimal tuning]]s:
* [[WE]]: ~1125/896 = 399.7349{{c}}, ~7/6 = 270.0900{{c}}
: [[error map]]: {{val| -0.795 -0.525 +1.030 +1.899 }}
* [[CWE]]: ~1125/896 = 400.0000{{c}}, ~7/6 = 270.2343{{c}}
: error map: {{val| 0.000 +0.388 +2.983 +3.752 }}


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


[[Badness]]: 0.267168
[[Badness]] (Sintel): 6.76


=== 11-limit ===
=== 11-limit ===
Line 428: Line 534:
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 -2 9 1 7 | 0 10 -3 11 5 }}
 
Optimal tunings:
* WE: ~495/392 = 399.7963{{c}}, ~7/6 = 270.1183{{c}}
* CWE: ~495/392 = 400.0000{{c}}, ~7/6 = 270.2301{{c}}
 
{{Optimal ET sequence|legend=0| 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: {{mapping| 3 -2 9 1 7 3 | 0 10 -3 11 5 12 }}
 
Optimal tunings:
* WE: ~495/392 = 399.7935{{c}}, ~7/6 = 270.1144{{c}}
* CWE: ~495/392 = 400.0000{{c}}, ~7/6 = 270.2258{{c}}
 
{{Optimal ET sequence|legend=0| 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: {{mapping| 3 -2 9 1 7 3 17 | 0 10 -3 11 5 12 -7 }}
 
Optimal tunings:
* WE: ~495/392 = 399.7781{{c}}, ~7/6 = 270.1159{{c}}
* CWE: ~495/392 = 400.0000{{c}}, ~7/6 = 270.2476{{c}}
 
{{Optimal ET sequence|legend=0| 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: {{mapping| 3 -2 9 1 7 3 17 6 | 0 10 -3 11 5 12 -7 10 }}
 
Optimal tunings:
* WE: ~208/165 = 399.7588{{c}}, ~7/6 = 270.0969{{c}}
* CWE: ~208/165 = 400.0000{{c}}, ~7/6 = 270.2391{{c}}


POTE generator: ~7/6 = 270.256
{{Optimal ET sequence|legend=0| 9, 102dfh, 111 }}


Optimal GPV sequence: {{Val list| 9, 102d, 111 }}
Badness (Sintel): 1.39


Badness: 0.081946
== References ==


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