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Maquila family: Difference between revisions

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The maquila family tempers out the maquila comma, 562949953421312/556182861328125 = |49 -6 -17>
{{Technical data page}}
The '''maquila family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[maquila comma]] ({{monzo|legend=1| 49 -6 -17 }}, [[ratio]]: 562 949 953 421 312 / 556 182 861 328 125).


=Maquila=
== Maquila ==
Comma: 562949953421312/556182861328125
[[Subgroup]]: 2.3.5


POTE generator: ~375/256 = 664.563
[[Comma list]]: {{monzo| 49 -6 -17 }}


Map: [<1 11 -1|, <0 -17 6|]
{{Mapping|legend=1| 1 -6 5 | 0 17 -6 }}
: mapping generators: ~2, ~512/375


EDOs: 9, 56, 65, 186, 251, 316, 381, 697c
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.7466{{c}}, ~512/375 = 535.3242{{c}}
: [[error map]]: {{val| -0.253 +0.078 +0.474 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~512/375 = 535.4324{{c}}
: error map: {{val| 0.000 +0.396 +1.092 }}


Badness: 0.47251
{{Optimal ET sequence|legend=1| 9, 47b, 56, 65, 186, 251, 316, 381, 697c }}


=Hemimaquila=
[[Badness]] (Sintel): 11.1
Commas: 6144/6125, 184528125/184473632


POTE generator: ~7/6 = 267.716
== Septimal maquila ==
[[Subgroup]]: 2.3.5.7


Map: [<1 -6 5 -5|, <0 34 -12 35|]
[[Comma list]]: 225/224, 30233088/28824005


Wedgie: <<34 -12 35 -98 -40 115||
{{Mapping|legend=1| 1 -6 5 -7 | 0 17 -6 22 }}


EDOs: 9, 121, 130, 251, 381
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.3017{{c}}, ~48/35 = 535.0104{{c}}
: [[error map]]: {{val| -0.698 -2.589 +0.133 +6.290 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~48/35 = 535.3050{{c}}
: error map: {{val| 0.000 -1.770 +1.856 +7.884 }}


Badness: 0.11146
{{Optimal ET sequence|legend=1| 9, 56d, 65d }} *


==11-limit==
<nowiki/>* [[optimal patent val]]: [[74edo|74]]
Commas: 540/539, 5632/5625, 12005/11979


POTE generator: ~7/6 = 267.717
[[Badness]] (Sintel): 5.88


Map: [&lt;1 -6 5 -5 -1|, &lt;0 34 -12 35 20|]
=== 11-limit ===
Subgroup: 2.3.5.7.11


EDOs: 9, 121, 130, 251e, 381e
Comma list: 99/98, 176/175, 73728/73205


Badness: 0.0474
{{Mapping|legend=0| 1 -6 5 -7 -1 | 0 17 -6 22 10 }}


==13-limit==
Optimal tunings:
Commas: 364/363, 540/539, 676/675, 3584/3575
* WE: ~2 = 1199.3341{{c}}, ~15/11 = 535.0238{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 535.3050{{c}}


POTE generator: ~7/6 = 267.719
{{Optimal ET sequence|legend=0| 9, 56d, 65d }} *


Map: [&lt;1 -6 5 -5 -1 -5|, &lt;0 34 -12 35 20 39|]
<nowiki/>* optimal patent val: [[74edo|74]]


EDOs: 9, 121, 130, 251e, 381e
Badness (Sintel): 2.40


Badness: 0.0244
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


[[Category:Theory]]
Comma list: 99/98, 144/143, 176/175, 847/845
[[Category:Temperament family]]
 
[[Category:Maquila]]
{{Mapping|legend=0| 1 -6 5 -7 -1 -7 | 0 17 -6 22 10 24 }}
[[Category:Rank 2]]
 
Optimal tunings:
* WE: ~2 = 1199.2163{{c}}, ~15/11 = 534.9484{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 535.2780{{c}}
 
{{Optimal ET sequence|legend=0| 9, 56df, 65d, 139df }} *
 
<nowiki/>* optimal patent val: [[74edo|74]]
 
Badness (Sintel): 1.74
 
== Maquiloid ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 686/675, 65625/65536
 
{{Mapping|legend=1| 1 -6 5 -3 | 0 17 -6 13 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.3854{{c}}, ~175/128 = 535.6538{{c}}
: [[error map]]: {{val| +0.385 +1.847 +1.691 -6.483 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~175/128 = 535.4907{{c}}
: error map: {{val| 0.000 +1.387 +0.742 -7.447 }}
 
{{Optimal ET sequence|legend=1| 9, 47b, 56, 65, 121d }}
 
[[Badness]] (Sintel): 4.78
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 245/242, 385/384, 686/675
 
{{Mapping|legend=0| 1 -6 5 -3 -1 | 0 17 -6 13 10 }}
 
Optimal tunings:
* WE: ~2 = 1200.0926{{c}}, ~15/11 = 535.5265{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 535.4873{{c}}
 
{{Optimal ET sequence|legend=0| 9, 47b, 56, 65 }}
 
Badness (Sintel): 2.19
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 91/90, 169/168, 245/242, 385/384
 
{{Mapping|legend=0| 1 -6 5 -3 -1 -3 | 0 17 -6 13 10 15 }}
 
Optimal tunings:
* WE: ~2 = 1200.3916{{c}}, ~15/11 = 535.6758{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 535.5109{{c}}
 
{{Optimal ET sequence|legend=0| 9, 47b, 56, 65f }}
 
Badness (Sintel): 1.73
 
== Hemimaquila ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 6144/6125, 184528125/184473632
 
{{Mapping|legend=1| 1 -6 5 -5 | 0 34 -12 35 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7108{{c}}, ~7/6 = 267.6515{{c}}
: [[error map]]: {{val| -0.289 -0.069 +0.422 +0.422 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/6 = 267.7125{{c}}
: error map: {{val| 0.000 +0.271 +1.136 +1.112 }}
 
{{Optimal ET sequence|legend=1| 121, 130, 251, 381 }}
 
[[Badness]] (Sintel): 2.82
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 5632/5625, 12005/11979
 
{{Mapping|legend=0| 1 -6 5 -5 -1 | 0 34 -12 35 20 }}
 
Optimal tunings:
* WE: ~2 = 1199.5846{{c}}, ~7/6 = 267.6248{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/6 = 267.7125{{c}}
 
{{Optimal ET sequence|legend=0| 121, 130, 251e, 381e }}
 
Badness (Sintel): 1.57
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 364/363, 540/539, 676/675, 3584/3575
 
{{Mapping|legend=0| 1 -6 5 -5 -1 -5 | 0 34 -12 35 20 39 }}
 
Optimal tunings:
* WE: ~2 = 1199.6184{{c}}, ~7/6 = 267.6343{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/6 = 267.7145{{c}}
 
{{Optimal ET sequence|legend=0| 121, 130, 251e, 381e }}
 
Badness (Sintel): 1.01
 
[[Category:Maquila family| ]] <!-- main article -->
[[Category:Maquila| ]] <!-- key article -->
[[Category:Temperament families]]
[[Category:Catalogs of rank-2 temperaments]]
Retrieved from "https://en.xen.wiki/w/Maquila_family"