Maquila family: Difference between revisions

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m Units & misc. cleanup
Switch to Sintel's badness, WE & CWE tunings
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{{Mapping|legend=1| 1 -6 5 | 0 17 -6 }}
{{Mapping|legend=1| 1 -6 5 | 0 17 -6 }}
: mapping generators: ~2, ~512/375


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~512/375 = 535.437{{c}}
[[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 }}


{{Optimal ET sequence|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]] (Smith): 0.472510
[[Badness]] (Sintel): 11.1


== Septimal maquila ==
== Septimal maquila ==
Line 22: Line 27:
{{Mapping|legend=1| 1 -6 5 -7 | 0 17 -6 22 }}
{{Mapping|legend=1| 1 -6 5 -7 | 0 17 -6 22 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~48/35 = 535.322{{c}}
[[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 }}


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


[[Badness]] (Smith): 0.232430
<nowiki/>* [[optimal patent val]]: [[74edo|74]]
 
[[Badness]] (Sintel): 5.88


=== 11-limit ===
=== 11-limit ===
Line 35: Line 46:
Mapping: {{mapping| 1 -6 5 -7 -1 | 0 17 -6 22 10 }}
Mapping: {{mapping| 1 -6 5 -7 -1 | 0 17 -6 22 10 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 535.321{{c}}
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 }}
{{Optimal ET sequence|legend=0| 9, 56d, 65d }} *


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


=== 13-limit ===
=== 13-limit ===
Line 48: Line 63:
Mapping: {{mapping| 1 -6 5 -7 -1 -7 | 0 17 -6 22 10 24 }}
Mapping: {{mapping| 1 -6 5 -7 -1 -7 | 0 17 -6 22 10 24 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 535.298{{c}}
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 }} *


{{Optimal ET sequence|legend=0| 9, 56df, 65d, 139df, 204ddff }}
<nowiki/>* optimal patent val: [[74edo|74]]


Badness (Smith): 0.042198
Badness (Sintel): 1.74


== Maquiloid ==
== Maquiloid ==
Line 61: Line 80:
{{Mapping|legend=1| 1 -6 5 -3 | 0 17 -6 13 }}
{{Mapping|legend=1| 1 -6 5 -3 | 0 17 -6 13 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~175/128 = 535.482{{c}}
[[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, 38b, 47b, 56, 65, 121d, 186dd }}
{{Optimal ET sequence|legend=1| 9, 47b, 56, 65, 121d }}


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


=== 11-limit ===
=== 11-limit ===
Line 74: Line 97:
Mapping: {{mapping| 1 -6 5 -3 -1 | 0 17 -6 13 10 }}
Mapping: {{mapping| 1 -6 5 -3 -1 | 0 17 -6 13 10 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 535.485{{c}}
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, 38be, 47b, 56, 65, 121d, 186dde }}
{{Optimal ET sequence|legend=0| 9, 47b, 56, 65 }}


Badness (Smith): 0.066234
Badness (Sintel): 2.19


=== 13-limit ===
=== 13-limit ===
Line 87: Line 112:
Mapping: {{mapping| 1 -6 5 -3 -1 -3 | 0 17 -6 13 10 15 }}
Mapping: {{mapping| 1 -6 5 -3 -1 -3 | 0 17 -6 13 10 15 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 535.501{{c}}
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, 38be, 47b, 56, 65f, 121df, 186ddeff }}
{{Optimal ET sequence|legend=0| 9, 47b, 56, 65f }}


Badness (Smith): 0.041850
Badness (Sintel): 1.73


== Hemimaquila ==
== Hemimaquila ==
Line 100: Line 127:
{{Mapping|legend=1| 1 -6 5 -5 | 0 34 -12 35 }}
{{Mapping|legend=1| 1 -6 5 -5 | 0 34 -12 35 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/6 = 267.716{{c}}
[[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| 9, 121, 130, 251, 381 }}
{{Optimal ET sequence|legend=1| 121, 130, 251, 381 }}


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


=== 11-limit ===
=== 11-limit ===
Line 113: Line 144:
Mapping: {{mapping| 1 -6 5 -5 -1 | 0 34 -12 35 20 }}
Mapping: {{mapping| 1 -6 5 -5 -1 | 0 34 -12 35 20 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 267.717{{c}}
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| 9, 121, 130, 251e, 381e }}
{{Optimal ET sequence|legend=0| 121, 130, 251e, 381e }}


Badness (Smith): 0.047440
Badness (Sintel): 1.57


=== 13-limit ===
=== 13-limit ===
Line 126: Line 159:
Mapping: {{mapping| 1 -6 5 -5 -1 -5 | 0 34 -12 35 20 39 }}
Mapping: {{mapping| 1 -6 5 -5 -1 -5 | 0 34 -12 35 20 39 }}


Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 267.719{{c}}
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| 9, 121, 130, 251e, 381e }}
{{Optimal ET sequence|legend=0| 121, 130, 251e, 381e }}


Badness (Smith): 0.024445
Badness (Sintel): 1.01


[[Category:Maquila family| ]] <!-- main article -->
[[Category:Maquila family| ]] <!-- main article -->

Revision as of 09:00, 21 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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