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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 '''sensamagic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] the sensamagic comma, [[245/243]].
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-20 07:07:56 UTC</tt>.<br>
: The original revision id was <tt>277343772</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]]


=Sensamagic=
For a list of rank-2 temperaments, see [[Sensamagic clan]].
[[Comma]]: 245/243


[[7-limit]] [[minimax]]
== Sensamagic ==
[|1 0 0 0&gt;, |0 0 1/5 2/5&gt;, |0 0 1 0&gt;, |0 0 0 1&gt;]
{{Main| Sensamagic }}
[[Eigenmonzo]]s: 2, 8/7, 5/4


[[9-limit]] minimax
Sensamagic is generated by a perfect fifth and a wide supermajor third of ~[[9/7]], two of which make ~[[5/3]]. Among the good edo tunings are [[87edo]] and [[128edo]], as well as the [[optimal patent val]] [[283edo]].
[|1 0 0 0&gt;, |0 1 0 0&gt;, |0 5/3 2/3 -2/3&gt;, |0 5/3 -1/3 1/3&gt;]
Eigenmonzos: 2, 4/3, 7/5


Lattice basis: 3/2 0.9644 9/7 1.0807
Another notable tuning is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 703.7424{{c}}, 440.9020{{c}} with pure octaves since prime 2 is not involved in the comma to begin with, though its difference from [[CWE]] is practically unnoticeable.
Angle(3/2, 9/7) = 86.5288
Map to lattice: [&lt;0 1 1 2|, &lt;0 0 2 -1|]


Map: [&lt;1 0 0 0|, &lt;0 1 1 2|, &lt;0 0 2 -1|]
[[Subgroup]]: 2.3.5.7
Generators: 2, 3, 9/7
 
Edos: [[17edo|,17]] [[19edo|19]], [[22edo|22]], [[24edo|24]], [[27edo|27]], [[41edo|41]], [[46edo|46]], [[60edo|60]], [[68edo|68]], [[87edo|87]], [[109edo|109]], [[128edo|128]], [[169edo|169]], [[177edo|177]], [[237edo|237]]
[[Comma list]]: 245/243
[[Badness]]: 0.000129
 
{{Mapping|legend=1| 1 0 0 0 | 0 1 1 2 | 0 0 2 -1 }}
: mapping generators: ~2, ~3, ~9/7
 
[[Mapping to lattice]]: [{{val| 0 1 1 2 }}, {{val| 0 0 2 -1 }}]
 
Lattice basis:
: 3/2 length = 0.9644, 9/7 length = 1.0807
: Angle (3/2, 9/7) = 86.5288°
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9983{{c}}, ~3/2 = 703.7414{{c}}, ~9/7 = 440.9014{{c}}
: [[error map]]: {{val| -0.002 +1.785 -0.771 -2.248 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7411{{c}}, ~9/7 = 440.9017{{c}}
: error map: {{val| 0.000 +1.786 -0.769 -2.245 }}
 
[[Minimax tuning]]:
* [[7-odd-limit]]
: {{monzo list| 1 0 0 0 | 0 0 1/5 2/5 | 0 0 1 0 | 0 0 0 1 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7
* [[9-odd-limit]]
: {{monzo list| 1 0 0 0 | 0 1 0 0 | 0 5/3 2/3 -2/3 | 0 5/3 -1/3 1/3 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5
 
{{Optimal ET sequence|legend=1| 5, 8d, 14c, 17, 19, 27, 41, 68, 87, 128, 196, 283 }}
 
[[Badness]] (Sintel): 0.570


[[Projection pair]]: 5 243/49 to 2.3.7
[[Projection pair]]: 5 243/49 to 2.3.7


===[[Minkowski blocks]]===
{{Databox|[[Minkowski block]]s|
{2, 3, 7} subgroup
2.3.7 subgroup
* 12: 729/686, 64/63
* 17: 64/63, 19683/19208
* 19: 49/48, 177147/175616
* 22: 64/63, 537824/531441
* 24: 64/63, 15059072/14348907
}}
 
=== Overview to extensions ===
The second comma in the comma list defines which [[11-limit]] family member we are looking at. Undecimal sensamagic adds [[385/384]], sensawer adds [[441/440]], octarod adds [[100/99]], shrusus adds [[176/175]]. These temperaments use the same generators as sensamagic. Bisector adds [[121/120]] with a half-octave period.
 
Temperaments discussed elsewhere include [[supernatural]] (→ [[Keemic family #Supernatural|Keemic family]]) and [[sensigh]] (→ [[Sengic family #Sensigh|Sengic family]]). The rest are considered below.
 
== Undecimal sensamagic ==
{{Main| Sensamagic }}
 
Undecimal sensamagic tempers out not only [[385/384]], but [[896/891]], making itself a [[strong extension]] of [[parapyth]].
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 245/243, 385/384
 
{{Mapping|legend=1| 1 0 0 0 7 | 0 1 1 2 -2 | 0 0 2 -1 -1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9667{{c}}, ~3/2 = 703.7809{{c}}, ~9/7 = 440.9056{{c}}
: [[error map]]: {{val| -0.033 +1.793 -0.755 -2.236 +0.048 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7948{{c}}, ~9/7 = 440.9180{{c}}
: error map: {{val| 0.000 +1.840 -0.683 -2.154 +0.175 }}
 
[[Minimax tuning]]:
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 21/13 6/13 -1/13 1/13 -3/13 }}, {{monzo| 35/13 10/13 7/13 -7/13 -5/13 }}, {{monzo| 35/13 10/13 -6/13 6/13 -5/13 }}, {{monzo| 42/13 -14/13 -2/13 2/13 7/13 }}]
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/9
 
{{Optimal ET sequence|legend=1| 17, 19, 22, 41, 68, 87, 196, 283 }}
 
[[Badness]] (Sintel): 0.868
 
[[Projection pair]]s: 5 243/49 11 896/81 to 2.3.7
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 245/243, 352/351, 364/363
 
Mapping: {{mapping| 1 0 0 0 7 12 | 0 1 1 2 -2 -5 | 0 0 2 -1 -1 -1 }}
 
Optimal tunings:
* WE: ~2 = 1199.9905{{c}}, ~3/2 = 703.7325{{c}}, ~9/7 = 440.9149{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.7381{{c}}, ~9/7 = 440.9184{{c}}
 
{{Optimal ET sequence|legend=0| 17, 19f, 22, 41, 46, 63, 87, 237, 283 }}
 
Badness (Sintel): 1.12
 
== Sensawer ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 245/243, 441/440
 
{{Mapping|legend=1| 1 0 0 0 -3 | 0 1 1 2 5 | 0 0 2 -1 -4 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1654{{c}}, ~3/2 = 703.2870{{c}}, ~9/7 = 441.1967{{c}}
: [[error map]]: {{val| -0.033 +1.793 -0.755 -2.236 +0.048 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.2917{{c}}, ~9/7 = 441.1849{{c}}
: error map: {{val| 0.000 +1.840 -0.683 -2.1554 +0.175 }}
 
{{Optimal ET sequence|legend=1| 14c, 19e, 27e, 41, 60e, 87 }}
 
[[Badness]] (Sintel): 0.957
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 245/243, 352/351
 
Mapping: {{mapping| 1 0 0 0 -3 2 | 0 1 1 2 5 2 | 0 0 2 -1 -4 -4 }}
 
Optimal tunings:
* WE: ~2 = 1199.9800{{c}}, ~3/2 = 703.4468{{c}}, ~9/7 = 441.3705{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.4494{{c}}, ~9/7 = 441.3758{{c}}
 
{{Optimal ET sequence|legend=0| 14c, 19e, 27e, 41, 46, 60e, 68e, 87, 522bd }}
 
Badness (Sintel): 0.868
 
== Octarod ==
Octarod tempers out [[100/99]] and the interval class of [[11/1|11]] is found as a stack of four ~9/7's. The name ''octarod'' was the former name of the sensamagic comma before being reused for this 11-limit extension, and comes from [[octacot]] and [[rodan]]; it should be noted however that rodan does not temper out 100/99 and therefore does not support this temperament.
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 100/99, 245/243
 
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 2 0 | 0 0 2 -1 4 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.2854{{c}}, ~3/2 = 704.6266{{c}}, ~9/7 = 439.2433{{c}}
: [[error map]]: {{val| -0.715 +1.957 -3.915 -0.245 +4.226 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.5246{{c}}, ~9/7 = 439.2798{{c}}
: error map: {{val| 0.000 +2.570 -3.230 +0.944 +5.801 }}
 
{{Optimal ET sequence|legend=1| 14c, 19, 22, 27e, 41, 90e, 131e}}*
 
<nowiki/>*[[Optimal patent val]]: [[104edo|104]]
 
[[Badness]] (Sintel): 0.698
 
Scales: [[octarod1]], [[octarod2]], [[octarod3]], [[octarod4]], [[octarod5]]
 
== Shrusus ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 176/175, 245/243
 
{{Mapping|legend=1| 1 0 0 0 -4 | 0 1 1 2 4 | 0 0 2 -1 3 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.9114{{c}}, ~3/2 = 705.7294{{c}}, ~9/7 = 441.7137{{c}}
: [[error map]]: {{val| -1.089 +2.686 +1.754 -1.258 -3.259 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 705.8402{{c}}, ~9/7 = 442.1064{{c}}
: error map: {{val| 0.000 +3.885 +3.739 +0.748 -1.638 }}
 
{{Optimal ET sequence|legend=1| 19e, 22, 27e, 46, 68, 95, 141bc, 163bc }}
 
[[Badness]] (Sintel): 1.05
 
=== Shrusic ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 91/90, 176/175, 245/243


12: 729/686, 64/63
Mapping: {{mapping| 1 0 0 0 -4 1 | 0 1 1 2 4 1 | 0 0 2 -1 3 3 }}
17: 64/63, 19683/19208
19: 49/48, 177147/175616
22: 64/63, 537824/531441
24: 64/63, 15059072/14348907


==Unidecimal sensamagic==
Optimal tunings:
Commas: 245/243, 385/384
* WE: ~2 = 1199.7256{{c}}, ~3/2 = 704.9071{{c}}, ~9/7 = 443.1303{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.9572{{c}}, ~9/7 = 443.2018{{c}}


[[11-limit]] minimax
{{Optimal ET sequence|legend=0| 19e, 22, 27e, 46 }}
[|1 0 0 0 0&gt;, |21/13 6/13 -1/13 1/13 -3/13&gt;,  
|35/13 10/13 7/13 -7/13 -5/13&gt;,
|35/13 10/13 -6/13 6/13 -5/13&gt;,
|42/13 -14/13 -2/13 2/13 7/13&gt;]
Eigenmonzos: 2, 11/9, 7/5


Map: [&lt;1 0 0 0 7|, &lt;0 1 1 2 -2|, &lt;0 0 2 -1 -1|]
Badness (Sintel): 1.05
Generators: 2, 3, 9/7
EDOs: [[5edo|5]], 17, 19, 22, 41, 68, 87, [[196edo|196]], [[283edo|283]], 607bd, 694bd
Badness: 0.000722


Projection pairs: 5 243/49 11 896/81 to 2.3.7
== Bisector ==
[[Subgroup]]: 2.3.5.7.11


==13-limit==
[[Comma list]]: 121/120, 245/243
Commas: 245/243, 352/351, 385/384


Map: [&lt;1 0 0 0 7 12|, &lt;0 1 1 2 -2 -5|, &lt;0 0 2 -1 -1 -1|]
{{Mapping|legend=1| 2 0 0 0 3 | 0 1 1 2 1 | 0 0 2 -1 1 }}
Generators: 2, 3, 9/7
: mapping generators: ~77/54, ~3, ~9/7
EDOs: 17, 22, 41, 46, 63, 87, 237, 283, 324d, 370bd, 411bd, 607bd, 694bd
Badness: 0.00120


=Sensawer=
[[Optimal tuning]]s:
Commas: 245/243, 441/440
* [[WE]]: ~2 = 600.3096{{c}}, ~3/2 = 703.4512{{c}}, ~9/7 = 441.3336{{c}}
: [[error map]]: {{val| +0.619 +2.115 +0.424 -2.019 -4.985 }}
* [[CWE]]: ~2 = 600.0000{{c}}, ~3/2 = 703.5671{{c}}, ~9/7 = 441.2436{{c}}
: error map: {{val| 0.000 +1.612 -0.259 -2.935 -6.507 }}


Map: [&lt;1 0 0 0 -3|, &lt;0 1 1 2 5|, &lt;0 0 2 -1 -4|]
{{Optimal ET sequence|legend=1| 8d, 14c, 22, 38d, 46, 60e, 68, 106de, 128e, 174e }}
EDOs: 41, 87, 302d, 389d, 476bd
Badness: 0.000796


==13-limit==
[[Badness]] (Sintel): 1.31
Commas: 196/195, 245/243, 352/351


Map: [&lt;1 0 0 0 -3 2|, &lt;0 1 1 2 5 2|, &lt;0 0 2 -1 -4 -4|]
[[Category:Temperament families]]
EDOs: 41, 46, 87, 522bd
[[Category:Sensamagic family| ]] <!-- main article -->
Badness: 0.000928
[[Category:Rank 3]]
</pre></div>
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Sensamagic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Sensamagic"&gt;Sensamagic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Sensamagic--Minkowski blocks"&gt;Minkowski blocks&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Sensamagic-Unidecimal sensamagic"&gt;Unidecimal sensamagic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Sensamagic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Sensawer"&gt;Sensawer&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Sensawer-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Sensamagic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Sensamagic&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;: 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; &lt;a class="wiki_link" href="/minimax"&gt;minimax&lt;/a&gt;&lt;br /&gt;
[|1 0 0 0&amp;gt;, |0 0 1/5 2/5&amp;gt;, |0 0 1 0&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzo&lt;/a&gt;s: 2, 8/7, 5/4&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/9-limit"&gt;9-limit&lt;/a&gt; minimax&lt;br /&gt;
[|1 0 0 0&amp;gt;, |0 1 0 0&amp;gt;, |0 5/3 2/3 -2/3&amp;gt;, |0 5/3 -1/3 1/3&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 4/3, 7/5 &lt;br /&gt;
&lt;br /&gt;
Lattice basis: 3/2 0.9644 9/7 1.0807&lt;br /&gt;
Angle(3/2, 9/7) = 86.5288&lt;br /&gt;
Map to lattice: [&amp;lt;0 1 1 2|, &amp;lt;0 0 2 -1|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0|, &amp;lt;0 1 1 2|, &amp;lt;0 0 2 -1|]&lt;br /&gt;
Generators: 2, 3, 9/7&lt;br /&gt;
Edos: &lt;a class="wiki_link" href="/17edo"&gt;,17&lt;/a&gt; &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo"&gt;46&lt;/a&gt;, &lt;a class="wiki_link" href="/60edo"&gt;60&lt;/a&gt;, &lt;a class="wiki_link" href="/68edo"&gt;68&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/109edo"&gt;109&lt;/a&gt;, &lt;a class="wiki_link" href="/128edo"&gt;128&lt;/a&gt;, &lt;a class="wiki_link" href="/169edo"&gt;169&lt;/a&gt;, &lt;a class="wiki_link" href="/177edo"&gt;177&lt;/a&gt;, &lt;a class="wiki_link" href="/237edo"&gt;237&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.000129&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;: 5 243/49 to 2.3.7&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="Sensamagic--Minkowski blocks"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;a class="wiki_link" href="/Minkowski%20blocks"&gt;Minkowski blocks&lt;/a&gt;&lt;/h3&gt;
{2, 3, 7} subgroup&lt;br /&gt;
&lt;br /&gt;
12: 729/686, 64/63&lt;br /&gt;
17: 64/63, 19683/19208&lt;br /&gt;
19: 49/48, 177147/175616&lt;br /&gt;
22: 64/63, 537824/531441&lt;br /&gt;
24: 64/63, 15059072/14348907&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Sensamagic-Unidecimal sensamagic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Unidecimal sensamagic&lt;/h2&gt;
Commas: 245/243, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; minimax&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |21/13 6/13 -1/13 1/13 -3/13&amp;gt;, &lt;br /&gt;
|35/13 10/13 7/13 -7/13 -5/13&amp;gt;, &lt;br /&gt;
|35/13 10/13 -6/13 6/13 -5/13&amp;gt;, &lt;br /&gt;
|42/13 -14/13 -2/13 2/13 7/13&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 11/9, 7/5&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0 7|, &amp;lt;0 1 1 2 -2|, &amp;lt;0 0 2 -1 -1|]&lt;br /&gt;
Generators: 2, 3, 9/7&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, 17, 19, 22, 41, 68, 87, &lt;a class="wiki_link" href="/196edo"&gt;196&lt;/a&gt;, &lt;a class="wiki_link" href="/283edo"&gt;283&lt;/a&gt;, 607bd, 694bd&lt;br /&gt;
Badness: 0.000722&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 5 243/49 11 896/81 to 2.3.7&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Sensamagic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
Commas: 245/243, 352/351, 385/384&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0 7 12|, &amp;lt;0 1 1 2 -2 -5|, &amp;lt;0 0 2 -1 -1 -1|]&lt;br /&gt;
Generators: 2, 3, 9/7&lt;br /&gt;
EDOs: 17, 22, 41, 46, 63, 87, 237, 283, 324d, 370bd, 411bd, 607bd, 694bd&lt;br /&gt;
Badness: 0.00120&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Sensawer"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Sensawer&lt;/h1&gt;
Commas: 245/243, 441/440&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0 -3|, &amp;lt;0 1 1 2 5|, &amp;lt;0 0 2 -1 -4|]&lt;br /&gt;
EDOs: 41, 87, 302d, 389d, 476bd&lt;br /&gt;
Badness: 0.000796&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Sensawer-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit&lt;/h2&gt;
Commas: 196/195, 245/243, 352/351&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0 -3 2|, &amp;lt;0 1 1 2 5 2|, &amp;lt;0 0 2 -1 -4 -4|]&lt;br /&gt;
EDOs: 41, 46, 87, 522bd&lt;br /&gt;
Badness: 0.000928&lt;/body&gt;&lt;/html&gt;</pre></div>
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