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Maquila family: Difference between revisions

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The maquila family tempers out the [[maquila comma]], 562949953421312/556182861328125 = {{monzo|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


[[Mapping]]: [{{val|1 -6 5}}, {{val|0 17 -6}}]
[[Comma list]]: {{monzo| 49 -6 -17 }}


[[POTE generator]]: ~512/375 = 535.437
{{Mapping|legend=1| 1 -6 5 | 0 17 -6 }}
: mapping generators: ~2, ~512/375


{{Val list|legend=1| 9, 38b, 47b, 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]]: 0.472510
{{Optimal ET sequence|legend=1| 9, 47b, 56, 65, 186, 251, 316, 381, 697c }}
 
[[Badness]] (Sintel): 11.1
 
== Septimal maquila ==
[[Subgroup]]: 2.3.5.7


=== 7-limit  ===
[[Comma list]]: 225/224, 30233088/28824005
[[Comma list]]: 225/224, 30233088/28824005


[[Mapping]]: [{{val|1 -6 5 -7}}, {{val|0 17 -6 22}}]
{{Mapping|legend=1| 1 -6 5 -7 | 0 17 -6 22 }}


{{Multival|legend=1|17 -6 22 -49 -13 68}}
[[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 }}


[[POTE generator]]: ~48/35 = 535.322
{{Optimal ET sequence|legend=1| 9, 56d, 65d }} *


{{Val list|legend=1| 9, 56d, 65d }}
<nowiki/>* [[optimal patent val]]: [[74edo|74]]


[[Badness]]: 0.232430
[[Badness]] (Sintel): 5.88
 
=== 11-limit ===
Subgroup: 2.3.5.7.11


=== 11-limit  ===
Comma list: 99/98, 176/175, 73728/73205
Comma list: 99/98, 176/175, 73728/73205


Mapping: [{{val|1 -6 5 -7 -1}}, {{val|0 17 -6 22 10}}]
{{Mapping|legend=0| 1 -6 5 -7 -1 | 0 17 -6 22 10 }}
 
Optimal tunings:
* WE: ~2 = 1199.3341{{c}}, ~15/11 = 535.0238{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 535.3050{{c}}
 
{{Optimal ET sequence|legend=0| 9, 56d, 65d }} *


POTE generator: ~15/11 = 535.321
<nowiki/>* optimal patent val: [[74edo|74]]


Vals: {{Val list| 9, 56d, 65d }}
Badness (Sintel): 2.40


Badness: 0.072550
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=== 13-limit  ===
Comma list: 99/98, 144/143, 176/175, 847/845
Comma list: 99/98, 144/143, 176/175, 847/845


Mapping: [{{val|1 -6 5 -7 -1 -7}}, {{val|0 17 -6 22 10 24}}]
{{Mapping|legend=0| 1 -6 5 -7 -1 -7 | 0 17 -6 22 10 24 }}
 
Optimal tunings:
* WE: ~2 = 1199.2163{{c}}, ~15/11 = 534.9484{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 535.2780{{c}}


POTE generator: ~15/11 = 535.298
{{Optimal ET sequence|legend=0| 9, 56df, 65d, 139df }} *


Vals: {{Val list| 9, 56df, 65d, 139df, 204ddff }}
<nowiki/>* optimal patent val: [[74edo|74]]


Badness: 0.042198
Badness (Sintel): 1.74
 
== Maquiloid ==
[[Subgroup]]: 2.3.5.7


== Maquiloid  ==
[[Comma list]]: 686/675, 65625/65536
[[Comma list]]: 686/675, 65625/65536


[[Mapping]]: [{{val|1 -6 5 -3}}, {{val|0 17 -6 13}}]
{{Mapping|legend=1| 1 -6 5 -3 | 0 17 -6 13 }}


{{Multival|legend=1|17 -6 13 -49 -27 47}}
[[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 }}


[[POTE generator]]: ~175/128 = 535.482
{{Optimal ET sequence|legend=1| 9, 47b, 56, 65, 121d }}


{{Val list|legend=1| 9, 38b, 47b, 56, 65, 121d, 186dd }}
[[Badness]] (Sintel): 4.78


[[Badness]]: 0.188977
=== 11-limit ===
Subgroup: 2.3.5.7.11


=== 11-limit  ===
Comma list: 245/242, 385/384, 686/675
Comma list: 245/242, 385/384, 686/675


Mapping: [{{val|1 -6 5 -3 -1}}, {{val|0 17 -6 13 10}}]
{{Mapping|legend=0| 1 -6 5 -3 -1 | 0 17 -6 13 10 }}


POTE generator: ~15/11 = 535.485
Optimal tunings:  
* WE: ~2 = 1200.0926{{c}}, ~15/11 = 535.5265{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 535.4873{{c}}


Vals: {{Val list| 9, 38be, 47b, 56, 65, 121d, 186dde }}
{{Optimal ET sequence|legend=0| 9, 47b, 56, 65 }}


Badness: 0.066234
Badness (Sintel): 2.19
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=== 13-limit  ===
Comma list: 91/90, 169/168, 245/242, 385/384
Comma list: 91/90, 169/168, 245/242, 385/384


Mapping: [{{val|1 -6 5 -3 -1 -3}}, {{val|0 17 -6 13 10 15}}]
{{Mapping|legend=0| 1 -6 5 -3 -1 -3 | 0 17 -6 13 10 15 }}


POTE generator: ~15/11 = 535.501
Optimal tunings:  
* WE: ~2 = 1200.3916{{c}}, ~15/11 = 535.6758{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 535.5109{{c}}


Vals: {{Val list| 9, 38be, 47b, 56, 65f, 121df, 186ddeff }}
{{Optimal ET sequence|legend=0| 9, 47b, 56, 65f }}


Badness: 0.041850
Badness (Sintel): 1.73
 
== Hemimaquila ==
[[Subgroup]]: 2.3.5.7


== Hemimaquila  ==
[[Comma list]]: 6144/6125, 184528125/184473632
[[Comma list]]: 6144/6125, 184528125/184473632


[[Mapping]]: [{{val|1 -6 5 -5}}, {{val|0 34 -12 35}}]
{{Mapping|legend=1| 1 -6 5 -5 | 0 34 -12 35 }}


{{Multival|legend=1|34 -12 35 -98 -40 115}}
[[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 }}


[[POTE generator]]: ~7/6 = 267.716
{{Optimal ET sequence|legend=1| 121, 130, 251, 381 }}


{{Val list|legend=1| 9, 121, 130, 251, 381 }}
[[Badness]] (Sintel): 2.82


[[Badness]]: 0.111465
=== 11-limit ===
Subgroup: 2.3.5.7.11


=== 11-limit  ===
Comma list: 540/539, 5632/5625, 12005/11979
Comma list: 540/539, 5632/5625, 12005/11979


Mapping: [{{val|1 -6 5 -5 -1}}, {{val|0 34 -12 35 20}}]
{{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}}


POTE generator: ~7/6 = 267.717
{{Optimal ET sequence|legend=0| 121, 130, 251e, 381e }}


Vals: {{Val list| 9, 121, 130, 251e, 381e }}
Badness (Sintel): 1.57


Badness: 0.047440
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=== 13-limit  ===
Comma list: 364/363, 540/539, 676/675, 3584/3575
Comma list: 364/363, 540/539, 676/675, 3584/3575


Mapping: [{{val|1 -6 5 -5 -1 -5}}, {{val|0 34 -12 35 20 39}}]
{{Mapping|legend=0| 1 -6 5 -5 -1 -5 | 0 34 -12 35 20 39 }}


POTE generator: ~7/6 = 267.719
Optimal tunings:  
* WE: ~2 = 1199.6184{{c}}, ~7/6 = 267.6343{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/6 = 267.7145{{c}}


Vals: {{Val list| 9, 121, 130, 251e, 381e }}
{{Optimal ET sequence|legend=0| 121, 130, 251e, 381e }}


Badness: 0.024445
Badness (Sintel): 1.01


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