Maquila family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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).
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-07-23 12:56:31 UTC</tt>.<br>
: The original revision id was <tt>555663249</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The maquila family tempers out the maquila comma, 562949953421312/556182861328125 = |49 -6 -17&gt;


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


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


Map: [&lt;1 11 -1|, &lt;0 -17 6|]
{{Mapping|legend=1| 1 -6 5 | 0 17 -6 }}
EDOs: 9, 56, 65, 186, 251, 316, 381, 697c
: mapping generators: ~2, ~512/375
Badness: 0.47251
 
</pre></div>
[[Optimal tuning]]s:
<h4>Original HTML content:</h4>
* [[WE]]: ~2 = 1199.7466{{c}}, ~512/375 = 535.3242{{c}}
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Maquila family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The maquila family tempers out the maquila comma, 562949953421312/556182861328125 = |49 -6 -17&amp;gt;&lt;br /&gt;
: [[error map]]: {{val| -0.253 +0.078 +0.474 }}
&lt;br /&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~512/375 = 535.4324{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Maquila"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Maquila&lt;/h1&gt;
: error map: {{val| 0.000 +0.396 +1.092 }}
Comma: 562949953421312/556182861328125&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 9, 47b, 56, 65, 186, 251, 316, 381, 697c }}
POTE generator: ~375/256 = 664.563&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 11.1
Map: [&amp;lt;1 11 -1|, &amp;lt;0 -17 6|]&lt;br /&gt;
 
EDOs: 9, 56, 65, 186, 251, 316, 381, 697c&lt;br /&gt;
== Septimal maquila ==
Badness: 0.47251&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 30233088/28824005
 
{{Mapping|legend=1| 1 -6 5 -7 | 0 17 -6 22 }}
 
[[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 }} *
 
<nowiki/>* [[optimal patent val]]: [[74edo|74]]
 
[[Badness]] (Sintel): 5.88
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 99/98, 176/175, 73728/73205
 
{{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 }} *
 
<nowiki/>* optimal patent val: [[74edo|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|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}}
 
{{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]]

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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