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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>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-07 09:25:24 UTC</tt>.<br>
: The original revision id was <tt>299261208</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">[[toc|flat]]


=Escapade=
<div style="float: right;">
The **escapade family** tempers out the [[escapade comma]], |32 -7 -9&gt;, of size 9.492 [[cent]]s.
[[File:Escapade.png|alt=Escapade.png|thumb|600x560px|An image of the tuning spectrum of 2.3.5.11 escapade, in terms of the generator; [[Edo]] [[patent val]] tunings are marked with vertical lines whose length indicates the edo's tolerance, i.e. half of its step size in either direction of just, and some small edos supporting the temperament are labeled.]]
</div>


[[POTE tuning|POTE generator]]: (~16875/16384) 55.293
The '''escapade family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[escapade comma]], {{monzo| 32 -7 -9 }}, of size 9.492 [[cent]]s. The defining feature of this comma is splitting [[5/3]] into sixteen quartertones of which [[5/4]] makes up seven and [[4/3]] makes up nine; therefore [[16/15]] is two generator steps. It most naturally manifests as a [[2.3.5.11 subgroup|2.3.5.11-subgroup]] temperament, tempering out [[4000/3993]] and [[5632/5625]].


Map: [&lt;1 2 2|, &lt;0 -9 7|]
Extensions of escapade to incorporate prime 7 (and therefore the full [[11-limit]]) include escapist ({{nowrap| 21 & 22 }}), tempering out [[225/224]] and mapping 7 to −4 generators; escaped ({{nowrap| 22 & 87 }}), tempering out [[245/243]] and mapping 7 to −26 generators; alphaquarter ({{nowrap| 65d & 87 }}), tempering out [[5120/5103]] and mapping 7 to 61 generators; septisuperfourth (a.k.a. biscapade) ({{nowrap| 22 & 86 }}), tempering out [[6144/6125]], splitting the octave in half and mapping 7 to −15 generators; and arch ({{nowrap| 43 & 87 }}), tempering out [[3136/3125]] and splitting the generator into two [[64/63]] intervals; all are considered below.
EDOs: [[21edo|21]], [[22edo|22]], [[43edo|43]], [[65edo|65]], 152, 217, 586, 803


==7-limit==
== Escapade ==
Commas: 225/224, 12288/12005
[[Subgroup]]: 2.3.5


[[POTE tuning|POTE temperament]]: (~49/48) 55.327
[[Comma list]]: 4294967296/4271484375


Map: [&lt;1 2 2 3|, &lt;0 -9 7 -4|]
{{Mapping|legend=1| 1 2 2 | 0 -9 7 }}
Wedgie: &lt;&lt;9 -7 4 -32 -19 29||
: mapping generators: ~2, ~16875/16384
EDOs: 21, 22, 43, 65


==11-limit==
[[Optimal tuning]]s:
Commas: 99/98, 176/175, 2560/2541
* [[WE]]: ~2 = 1199.8082{{c}}, ~16875/16384 = 55.2840{{c}}
: [[error map]]: {{val| -0.192 +0.105 +0.291 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16875/16384 = 55.2961{{c}}
: error map: {{val| 0.000 +0.380 +0.759 }}


[[POTE tuning|POTE temperament]]: 55.354
{{Optimal ET sequence|legend=1| 21, 22, 43, 65, 152, 217, 586, 803 }}


Map: [&lt;1 2 2 3 3|, &lt;0 -9 7 -4 10|]
[[Badness]] (Sintel): 1.965
EDOs: 21, 22, 43, 65


=Escaped=
=== 2.3.5.11 subgroup ===
Commas: 245/243, 65625/65536
Since (an ideally slightly flat) 4/3 is split into 9 generators, it makes sense to equate the 3-generator interval to [[11/10]] by tempering out 4000/3993, and therefore the generator to {{nowrap| (11/10)/(16/15) {{=}} [[33/32]] }}; this does minimal damage to the temperament. This structure in 2.3.5.11 occurs in all extensions of escapade to include prime 7, and therefore will be considered the fount of all further extensions.


[[POTE tuning|POTE generator]]: 55.122
Subgroup: 2.3.5.11


Map: [&lt;1 2 2 4|, &lt;0 -9 7 -26|]
Comma list: 4000/3993, 5632/5625
Wedgie: &lt;&lt;9 -7 26 -32 16 80||
EDOs: 22, 65, [[87edo|87]], 196, 283


==11-limit==
{{Mapping|legend=2| 1 2 2 3 | 0 -9 7 10 }}
Commas: 245/243, 385/384, 4000/3993


[[POTE tuning|POTE generator]]: 55.126
Optimal tunings:
* WE: ~2 = 1199.7406{{c}}, ~33/32 = 55.2653{{c}}
: error map: {{val| -0.259 +0.139 +0.024 +0.557 }}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.2770{{c}}
: error map: {{val| 0.000 +0.552 +0.625 +1.452 }}


Map: [&lt;1 2 2 4 3|, &lt;0 -9 7 -26 10|]
{{Optimal ET sequence|legend=0| 21, 22, 43, 65, 87, 152, 369, 521e }}
EDOs: 22, 65, 87, 196, 283


=Biscapade=
Badness (Sintel): 0.335
Commas: 6144/6125, 118098/117649


[[POTE tuning|POTE generator]]: 55.230
=== 2.3.5.11.31 subgroup ===
One may note that the generator represents the square root of [[16/15]] and therefore it would be logical to also temper out [[961/960]] ({{S|31}}) so that the generator is equated to {{nowrap| [[32/31]][[~]][[31/30]] }} in addition to 33/32.


Map: [&lt;2 4 4 7|, &lt;0 -9 7 -15|]
For intervals along the chain of generators in the 2.3.5.11.31 subgroup temperament, out to 22 generators up, see the third column of [[16ed5/3 #Intervals]].
Wedgie: &lt;&lt;18 -14 30 -64 -3 109||
EDOs: 22, [[86edo|86]], 108, 130, 152, 282


==11-limit==
Subgroup: 2.3.5.11.31
Commas: 540/539, 4000/3993, 5632/5625


[[POTE tuning|POTE generator]]: 55.304
Comma list: 496/495, 961/960, 4000/3993


Map: [&lt;2 4 4 7 6|, &lt;0 -9 7 -15 10|]
{{Mapping|legend=2| 1 2 2 3 5 | 0 -9 7 10 -1 }}
EDOs: 22, 86, 108, 130, 152, 282


==13-limit==
Optimal tunings:
Commas: 351/350, 364/363, 540/539, 4096/4095
* WE: ~2 = 1199.8050{{c}}, ~32/31 = 55.2669{{c}}
: error map: {{val| -0.195 +0.253 +0.165 +0.766 -1.277 }}
* CWE: ~2 = 1200.0000{{c}}, ~32/31 = 55.2759{{c}}
: error map: {{val| 0.000 +0.562 +0.617 +1.441 -0.311 }}


[[POTE tuning|POTE generator]]: 55.359
{{Optimal ET sequence|legend=0| 21, 22, 43, 65, 87, 152, 369, 521e, 673e }}


Map: [&lt;2 4 4 7 6 5|, &lt;0 -9 7 -15 10 26|]
Badness (Sintel): 0.251
EDOs: 22, 108, 130</pre></div>
 
<h4>Original HTML content:</h4>
= Strong extensions =
<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;Escapade family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:16:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;a href="#Escapade"&gt;Escapade&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#Escaped"&gt;Escaped&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Biscapade"&gt;Biscapade&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;
{| class="wikitable center-all"
&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;br /&gt;
|+ style="font-size: 105%;" | Map to strong full 7- and 11-limit extensions
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Escapade"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Escapade&lt;/h1&gt;
|-
The &lt;strong&gt;escapade family&lt;/strong&gt; tempers out the &lt;a class="wiki_link" href="/escapade%20comma"&gt;escapade comma&lt;/a&gt;, |32 -7 -9&amp;gt;, of size 9.492 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s.&lt;br /&gt;
! rowspan="1" | Extension !! rowspan="1" | Mapping of 7 !! rowspan="1" | Tuning range*
&lt;br /&gt;
|-
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: (~16875/16384) 55.293&lt;br /&gt;
| [[#Escapist|Escapist]] || -4 || ↓ [[65edo|65]]
&lt;br /&gt;
|-
Map: [&amp;lt;1 2 2|, &amp;lt;0 -9 7|]&lt;br /&gt;
| [[#Alphaquarter|Alphaquarter]] || +61 || ↑ 65 <br> ↓ [[87edo|87]]
EDOs: &lt;a class="wiki_link" href="/21edo"&gt;21&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/43edo"&gt;43&lt;/a&gt;, &lt;a class="wiki_link" href="/65edo"&gt;65&lt;/a&gt;, 152, 217, 586, 803&lt;br /&gt;
|-
&lt;br /&gt;
| [[#Escaped|Escaped]] || -26 || ↑ 87
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Escapade-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit&lt;/h2&gt;
|}
Commas: 225/224, 12288/12005&lt;br /&gt;
<nowiki/>* Defined as the range in which the extension specified has a better mapping of 7 compared to its neighboring extensions
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: (~49/48) 55.327&lt;br /&gt;
== Escaped ==
&lt;br /&gt;
This temperament was also known as ''sensa'' in earlier materials because it tempers out 245/243, 352/351, and 385/384 as a sensamagic temperament. ''Not to be confused with the {{nowrap| 19e & 27 }} temperament (sensi extension).''
Map: [&amp;lt;1 2 2 3|, &amp;lt;0 -9 7 -4|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;9 -7 4 -32 -19 29||&lt;br /&gt;
Here, [[245/243]] is tempered out so that [[9/7]] is equated to the square root of 5/3 (at 8 generators) present in the temperament. This works best where 5/3 is slightly flat, therefore on the end of the spectrum approaching [[22edo]].
EDOs: 21, 22, 43, 65&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Escapade-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
 
Commas: 99/98, 176/175, 2560/2541&lt;br /&gt;
[[Comma list]]: 245/243, 65625/65536
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 55.354&lt;br /&gt;
{{Mapping|legend=1| 1 2 2 4 | 0 -9 7 -26 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 2 2 3 3|, &amp;lt;0 -9 7 -4 10|]&lt;br /&gt;
[[Optimal tuning]]s:
EDOs: 21, 22, 43, 65&lt;br /&gt;
* [[WE]]: ~2 = 1199.9190{{c}}, ~28/27 = 55.1186{{c}}
&lt;br /&gt;
: [[error map]]: {{val| -0.081 +1.816 -0.646 -2.232 }}
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Escaped"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Escaped&lt;/h1&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~28/27 = 55.1242{{c}}
Commas: 245/243, 65625/65536&lt;br /&gt;
: error map: {{val| 0.000 +1.927 -0.444 -2.056 }}
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 55.122&lt;br /&gt;
{{Optimal ET sequence|legend=1| 22, 65, 87, 196, 283 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 2 2 4|, &amp;lt;0 -9 7 -26|]&lt;br /&gt;
[[Badness]] (Sintel): 2.25
Wedgie: &amp;lt;&amp;lt;9 -7 26 -32 16 80||&lt;br /&gt;
 
EDOs: 22, 65, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, 196, 283&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Escaped-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;11-limit&lt;/h2&gt;
 
Commas: 245/243, 385/384, 4000/3993&lt;br /&gt;
Comma list: 245/243, 385/384, 4000/3993
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 55.126&lt;br /&gt;
{{Mapping|legend=0| 1 2 2 4 3 | 0 -9 7 -26 10 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 2 2 4 3|, &amp;lt;0 -9 7 -26 10|]&lt;br /&gt;
Optimal tunings:
EDOs: 22, 65, 87, 196, 283&lt;br /&gt;
* WE: ~2 = 1199.9480{{c}}, ~28/27 = 55.1241{{c}}
&lt;br /&gt;
: error map: {{val| -0.052 +1.824 -0.549 -2.261 -0.233 }}
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Biscapade"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Biscapade&lt;/h1&gt;
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 55.1271{{c}}
Commas: 6144/6125, 118098/117649&lt;br /&gt;
: error map: {{val| 0.000 +1.901 -0.424 -2.131 -0.047 }}
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 55.230&lt;br /&gt;
{{Optimal ET sequence|legend=0| 22, 65, 87, 196, 283 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 4 4 7|, &amp;lt;0 -9 7 -15|]&lt;br /&gt;
Badness (Sintel): 1.18
Wedgie: &amp;lt;&amp;lt;18 -14 30 -64 -3 109||&lt;br /&gt;
 
EDOs: 22, &lt;a class="wiki_link" href="/86edo"&gt;86&lt;/a&gt;, 108, 130, 152, 282&lt;br /&gt;
=== 13-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Biscapade-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11-limit&lt;/h2&gt;
 
Commas: 540/539, 4000/3993, 5632/5625&lt;br /&gt;
Comma list: 245/243, 352/351, 385/384, 625/624
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 55.304&lt;br /&gt;
{{Mapping|legend=0| 1 2 2 4 3 2 | 0 -9 7 -26 10 37 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 4 4 7 6|, &amp;lt;0 -9 7 -15 10|]&lt;br /&gt;
Optimal tunings:
EDOs: 22, 86, 108, 130, 152, 282&lt;br /&gt;
* WE: ~2 = 1199.9926{{c}}, ~28/27 = 55.1378{{c}}
&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 55.1382{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Biscapade-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h2&gt;
 
Commas: 351/350, 364/363, 540/539, 4096/4095&lt;br /&gt;
{{Optimal ET sequence|legend=0| 22, 65, 87, 283 }}
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 55.359&lt;br /&gt;
Badness (Sintel): 1.30
&lt;br /&gt;
 
Map: [&amp;lt;2 4 4 7 6 5|, &amp;lt;0 -9 7 -15 10 26|]&lt;br /&gt;
== Alphaquarter ==
EDOs: 22, 108, 130&lt;/body&gt;&lt;/html&gt;</pre></div>
Given the slightly sharp ~[[3/2]] in ideal tunings of escapade (between [[65edo]] and [[87edo]]), it does very little damage to temper out [[5120/5103]] to extend it to prime 7; the cost is that the harmonic 7 is exceedingly complex, located all the way at 61 generators up.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 5120/5103, 29360128/29296875
 
{{Mapping|legend=1| 1 2 2 0 | 0 -9 7 61 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7349{{c}}, ~16128/15625 = 55.2306{{c}}
: [[error map]]: {{val| -0.265 +0.439 -0.230 +0.242 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16128/15625 = 55.2405{{c}}
: error map: {{val| 0.000 +0.880 +0.370 +0.846 }}
 
{{Optimal ET sequence|legend=1| 65d, 87, 152, 239, 391 }}
 
[[Badness]] (Sintel): 2.95
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 4000/3993, 5120/5103
 
{{Mapping|legend=0| 1 2 2 0 3 | 0 -9 7 61 10 }}
 
Optimal tunings:
* WE: ~2 = 1199.7229{{c}}, ~33/32 = 55.2303{{c}}
: error map: {{val| -0.277 +0.418 -0.256 +0.220 +0.153 }}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.2407{{c}}
: error map: {{val| 0.000 +0.879 +0.371 +0.858 +1.089 }}
 
{{Optimal ET sequence|legend=0| 65d, 87, 152, 239, 391 }}
 
Badness (Sintel): 0.980
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 625/624, 847/845, 1575/1573
 
{{Mapping|legend=0| 1 2 2 0 3 2 | 0 -9 7 61 10 37 }}
 
Optimal tunings:
* WE: ~2 = 1199.6491{{c}}, ~33/32 = 55.2200{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.2328{{c}}
 
{{Optimal ET sequence|legend=0| 65d, 87, 152f, 239f }}
 
Badness (Sintel): 1.047
 
== Escapist ==
This temperament makes the identification of the 4-generator interval, representing (16/15)<sup>2</sup>, with [[8/7]] by tempering out [[225/224]] (along with [[12288/12005]]); however, this is somewhat inaccurate as the ~16/15 in escapade is slightly flat, while for a good marvel tuning it needs to be tempered sharpward to equate it with [[15/14]].
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 12288/12005
 
{{Mapping|legend=1| 1 2 2 3 | 0 -9 7 -4 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.9926{{c}}, ~49/48 = 55.2809{{c}}
: [[error map]]: {{val| -1.007 -1.498 -1.363 +7.028 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/48 = 55.3479{{c}}
: error map: {{val| 0.000 -0.086 +1.122 +9.782 }}
 
{{Optimal ET sequence|legend=1| 21, 22, 43, 65d }}
 
[[Badness]] (Sintel): 1.97
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 99/98, 176/175, 2560/2541
 
{{Mapping|legend=0| 1 2 2 3 3 | 0 -9 7 -4 10 }}
 
Optimal tunings:
* WE: ~2 = 1199.0859{{c}}, ~33/32 = 55.3117{{c}}
: error map: {{val| -0.914 -1.588 -0.960 +7.185 -0.944 }}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.3574{{c}}
: error map: {{val| 0.000 -0.172 +1.188 +9.745 +2.256 }}
 
{{Optimal ET sequence|legend=0| 21, 22, 43, 65d }}
 
Badness (Sintel): 1.21
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 78/77, 99/98, 176/175, 507/500
 
{{Mapping|legend=0| 1 2 2 3 3 3 | 0 -9 7 -4 10 15 }}
 
Optimal tunings:
* WE: ~2 = 1199.5949{{c}}, ~33/32 = 55.5317{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.5480{{c}}
 
{{Optimal ET sequence|legend=0| 21, 22, 43 }}
 
Badness (Sintel): 1.457
 
= Weak extensions =
{| class="wikitable center-all"
|+ style="font-size: 105%;" | Map to weak extensions
|-
! rowspan="2" | Extensions !! rowspan="2" | Periods per octave !! colspan="2" | Position of original generator
|-
! Number of generators !! Number of periods
|-
| [[#Septisuperfourth|Septisuperfourth]] || period = 1/2 octave || 1 generator || + 0 periods
|-
| [[#Arch|Arch]] || period = octave || 2 generators || + 0 periods
|}
 
== Septisuperfourth ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 6144/6125, 118098/117649
 
{{Mapping|legend=1| 2 4 4 7 | 0 -9 7 -15 }}
: mapping generators: ~343/243, ~405/392
 
[[Optimal tuning]]s:
* [[WE]]: ~343/243 = 599.8762{{c}}, ~405/392 = 55.3089{{c}}
: [[error map]]: {{val| -0.248 -0.230 +0.353 +0.674 }}
* [[CWE]]: ~343/243 = 600.0000{{c}}, ~405/392 = 55.3273{{c}}
: error map: {{val| 0.000 +0.100 +0.977 +1.265 }}
 
{{Optimal ET sequence|legend=1| 22, 86, 108, 130, 152, 282 }}
 
[[Badness]] (Sintel): 1.50
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 4000/3993, 5632/5625
 
{{Mapping|legend=0| 2 4 4 7 6 | 0 -9 7 -15 10 }}
 
Optimal tunings:
* WE: ~99/70 = 599.8383{{c}}, ~33/32 = 55.2895{{c}}
: error map: {{val| -0.323 -0.207 +0.066 +0.700 +0.606 }}
* CWE: ~99/70 = 600.0000{{c}}, ~33/32 = 55.3081{{c}}
: error map: {{val| 0.000 +0.272 +0.843 +1.553 +1.763 }}
 
{{Optimal ET sequence|legend=0| 22, 86, 108, 130, 152, 282, 434de, 716dee, 1150cdddeee }}
 
Badness (Sintel): 0.814
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 540/539, 729/728, 1575/1573, 3584/3575
 
{{Mapping|legend=0| 2 4 4 7 6 11 | 0 -9 7 -15 10 -39 }}
 
Optimal tunings:
* WE: ~99/70 = 599.8331{{c}}, ~33/32 = 55.3093{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~33/32 = 55.3295{{c}}
 
{{Optimal ET sequence|legend=0| 22f, 108f, 130, 282, 976cddeeeff }}
 
Badness (Sintel): 0.946
 
==== Septisuperquad ====
This temperament is also known as ''biscapade''.
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 364/363, 540/539, 4096/4095
 
{{Mapping|legend=0| 2 4 4 7 6 5 | 0 -9 7 -15 10 26 }}
 
Optimal tunings:
* WE: ~55/39 = 599.9152{{c}}, ~33/32 = 55.3509{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~33/32 = 55.3584{{c}}
 
{{Optimal ET sequence|legend=0| 22, 108, 130 }}
 
Badness (Sintel): 1.37
 
== Arch ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 3136/3125, 5250987/5242880
 
{{Mapping|legend=1| 1 2 2 2 | 0 -18 14 35 }}
: mapping generators: ~2, ~64/63
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9246{{c}}, ~64/63 = 27.6662{{c}}
: [[error map]]: {{val| -0.075 -0.097 +0.862 -0.661 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~64/63 = 27.6676{{c}}
: error map: {{val| 0.000 +0.029 +1.032 -0.461 }}
 
{{Optimal ET sequence|legend=1| 43, 87, 130, 217, 347 }}
 
[[Badness]] (Sintel): 2.39
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 441/440, 3136/3125, 4000/3993
 
{{Mapping|legend=0| 1 2 2 2 3 | 0 -18 14 35 20 }}
 
Optimal tunings:
* WE: ~2 = 1199.8347{{c}}, ~64/63 = 27.6590{{c}}
: error map: {{val| -0.165 -0.147 +0.581 -1.092 +1.366 }}
* CWE: ~2 = 1200.0000{{c}}, ~64/63 = 27.6617{{c}}
: error map: {{val| 0.000 +0.134 +0.950 -0.667 1.916 }}
 
{{Optimal ET sequence|legend=0| 43, 87, 130, 217, 347e }}
 
Badness (Sintel): 1.21
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 364/363, 441/440, 676/675, 3136/3125
 
{{Mapping|legend=0| 1 2 2 2 3 4 | 0 -18 14 35 20 -13 }}
 
Optimal tunings:
* WE: ~2 = 1199.8733{{c}}, ~64/63 = 27.6569{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~64/63 = 27.6594{{c}}
 
{{Optimal ET sequence|legend=0| 43, 87, 130, 217, 347e, 564e }}
 
Badness (Sintel): 0.806
 
[[Category:Escapade family| ]] <!-- main article -->
[[Category:Temperament families]]
[[Category:Catalogs of rank-2 temperaments]]
Retrieved from "https://en.xen.wiki/w/Escapade_family"