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 ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma]]: 562949953421312/556182861328125
[[Comma list]]: {{monzo| 49 -6 -17 }}


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


[[POTE generator]]: ~512/375 = 535.437
[[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 }}


{{Val list|legend=1| 9, 38b, 47b, 56, 65, 186, 251, 316, 381, 697c }}
{{Optimal ET sequence|legend=1| 9, 47b, 56, 65, 186, 251, 316, 381, 697c }}


[[Badness]]: 0.472510
[[Badness]] (Sintel): 11.1


=== 7-limit ===
== Septimal maquila ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[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 ===
=== 11-limit ===
Line 34: Line 44:
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 }}


POTE generator: ~15/11 = 535.321
Optimal tunings:  
* WE: ~2 = 1199.3341{{c}}, ~15/11 = 535.0238{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 535.3050{{c}}


Optimal GPV sequence: {{Val list| 9, 56d, 65d }}
{{Optimal ET sequence|legend=0| 9, 56d, 65d }} *


Badness: 0.072550
<nowiki/>* optimal patent val: [[74edo|74]]
 
Badness (Sintel): 2.40


=== 13-limit ===
=== 13-limit ===
Line 47: Line 61:
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 }} *


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


Badness: 0.042198
Badness (Sintel): 1.74


== Maquiloid ==
== Maquiloid ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[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}}


[[POTE generator]]: ~175/128 = 535.482
[[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 }}


{{Val list|legend=1| 9, 38b, 47b, 56, 65, 121d, 186dd }}
{{Optimal ET sequence|legend=1| 9, 47b, 56, 65, 121d }}


[[Badness]]: 0.188977
[[Badness]] (Sintel): 4.78


=== 11-limit ===
=== 11-limit ===
Line 75: Line 95:
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}}


Optimal GPV sequence: {{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 ===
=== 13-limit ===
Line 88: Line 110:
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}}


Optimal GPV sequence: {{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 ==
== Hemimaquila ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[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}}


[[POTE generator]]: ~7/6 = 267.716
[[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 }}


{{Val list|legend=1| 9, 121, 130, 251, 381 }}
{{Optimal ET sequence|legend=1| 121, 130, 251, 381 }}


[[Badness]]: 0.111465
[[Badness]] (Sintel): 2.82


=== 11-limit ===
=== 11-limit ===
Line 116: Line 142:
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 }}


POTE generator: ~7/6 = 267.717
Optimal tunings:  
* WE: ~2 = 1199.5846{{c}}, ~7/6 = 267.6248{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/6 = 267.7125{{c}}


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


Badness: 0.047440
Badness (Sintel): 1.57


=== 13-limit ===
=== 13-limit ===
Line 129: Line 157:
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}}


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


Badness: 0.024445
Badness (Sintel): 1.01


[[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]]

Latest revision as of 12:32, 24 September 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 maquila family of temperaments tempers out the maquila comma (monzo: [49 -6 -17⟩, ratio: 562 949 953 421 312 / 556 182 861 328 125).

Maquila

Subgroup: 2.3.5

Comma list: [49 -6 -17⟩

Mapping: [⟨1 -6 5], ⟨0 17 -6]]

mapping generators: ~2, ~512/375

Optimal tunings:

  • WE: ~2 = 1199.7466 ¢, ~512/375 = 535.3242 ¢
error map: ⟨-0.253 +0.078 +0.474]
  • CWE: ~2 = 1200.0000 ¢, ~512/375 = 535.4324 ¢
error map: ⟨0.000 +0.396 +1.092]

Optimal ET sequence: 9, 47b, 56, 65, 186, 251, 316, 381, 697c

Badness (Sintel): 11.1

Septimal maquila

Subgroup: 2.3.5.7

Comma list: 225/224, 30233088/28824005

Mapping: [⟨1 -6 5 -7], ⟨0 17 -6 22]]

Optimal tunings:

  • WE: ~2 = 1199.3017 ¢, ~48/35 = 535.0104 ¢
error map: ⟨-0.698 -2.589 +0.133 +6.290]
  • CWE: ~2 = 1200.0000 ¢, ~48/35 = 535.3050 ¢
error map: ⟨0.000 -1.770 +1.856 +7.884]

Optimal ET sequence: 9, 56d, 65d *

* optimal patent val: 74

Badness (Sintel): 5.88

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 73728/73205

Mapping: [⟨1 -6 5 -7 -1], ⟨0 17 -6 22 10]]

Optimal tunings:

  • WE: ~2 = 1199.3341 ¢, ~15/11 = 535.0238 ¢
  • CWE: ~2 = 1200.0000 ¢, ~15/11 = 535.3050 ¢

Optimal ET sequence: 9, 56d, 65d *

* optimal patent val: 74

Badness (Sintel): 2.40

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 144/143, 176/175, 847/845

Mapping: [⟨1 -6 5 -7 -1 -7], ⟨0 17 -6 22 10 24]]

Optimal tunings:

  • WE: ~2 = 1199.2163 ¢, ~15/11 = 534.9484 ¢
  • CWE: ~2 = 1200.0000 ¢, ~15/11 = 535.2780 ¢

Optimal ET sequence: 9, 56df, 65d, 139df *

* optimal patent val: 74

Badness (Sintel): 1.74

Maquiloid

Subgroup: 2.3.5.7

Comma list: 686/675, 65625/65536

Mapping: [⟨1 -6 5 -3], ⟨0 17 -6 13]]

Optimal tunings:

  • WE: ~2 = 1200.3854 ¢, ~175/128 = 535.6538 ¢
error map: ⟨+0.385 +1.847 +1.691 -6.483]
  • CWE: ~2 = 1200.0000 ¢, ~175/128 = 535.4907 ¢
error map: ⟨0.000 +1.387 +0.742 -7.447]

Optimal ET sequence: 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: [⟨1 -6 5 -3 -1], ⟨0 17 -6 13 10]]

Optimal tunings:

  • WE: ~2 = 1200.0926 ¢, ~15/11 = 535.5265 ¢
  • CWE: ~2 = 1200.0000 ¢, ~15/11 = 535.4873 ¢

Optimal ET sequence: 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: [⟨1 -6 5 -3 -1 -3], ⟨0 17 -6 13 10 15]]

Optimal tunings:

  • WE: ~2 = 1200.3916 ¢, ~15/11 = 535.6758 ¢
  • CWE: ~2 = 1200.0000 ¢, ~15/11 = 535.5109 ¢

Optimal ET sequence: 9, 47b, 56, 65f

Badness (Sintel): 1.73

Hemimaquila

Subgroup: 2.3.5.7

Comma list: 6144/6125, 184528125/184473632

Mapping: [⟨1 -6 5 -5], ⟨0 34 -12 35]]

Optimal tunings:

  • WE: ~2 = 1199.7108 ¢, ~7/6 = 267.6515 ¢
error map: ⟨-0.289 -0.069 +0.422 +0.422]
  • CWE: ~2 = 1200.0000 ¢, ~7/6 = 267.7125 ¢
error map: ⟨0.000 +0.271 +1.136 +1.112]

Optimal ET sequence: 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: [⟨1 -6 5 -5 -1], ⟨0 34 -12 35 20]]

Optimal tunings:

  • WE: ~2 = 1199.5846 ¢, ~7/6 = 267.6248 ¢
  • CWE: ~2 = 1200.0000 ¢, ~7/6 = 267.7125 ¢

Optimal ET sequence: 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: [⟨1 -6 5 -5 -1 -5], ⟨0 34 -12 35 20 39]]

Optimal tunings:

  • WE: ~2 = 1199.6184 ¢, ~7/6 = 267.6343 ¢
  • CWE: ~2 = 1200.0000 ¢, ~7/6 = 267.7145 ¢

Optimal ET sequence: 121, 130, 251e, 381e

Badness (Sintel): 1.01

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