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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2012-01-03 23:27:59 UTC</tt>.<br>
: The original revision id was <tt>289422273</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 //137 equal division// divides the octave into 137 equal parts of 8.759 cents each. It is the [[optimal patent val]] for 7-limit [[Semicomma family|orwell temperament]] and for the planar temperament tempering out 2430/2401. It tempers out 2109375/2097152 (the semicomma) in the 5-limit; 225/224 and 1728/1715 in the 7-limit; 243/242 in the 11-limit; 351/350 in the 13-limit; 375/374 and 442/441 in the 17-limit; and 324/323 and 495/494 in the 19-limit. Since it is the 33rd [[prime numbers|prime number]], 137edo has no proper divisors aside from 1.


A diagram of 7-limit Orwell based on the 31\137edo generator:
== Theory ==
[[image:137edo_MOS_031_demo_correction.png]]
137edo is a fairly accurate 5-limit temperament and also a strong no-7 19-limit temperament. The equal temperament [[tempering out|tempers out]] 2109375/2097152 ([[semicomma]]), {{monzo| -13 17 -6 }} ([[graviton]]), {{monzo| 8 14 -13 }} ([[parakleisma]]), and {{monzo| -29 -11 20 }} (gammic comma) in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], [[1728/1715]], 2430/2401 in the 7-limit; [[243/242]] in the 11-limit; [[351/350]] in the 13-limit; [[375/374]] and [[442/441]] in the 17-limit; and [[324/323]] and [[495/494]] in the 19-limit. It provides the [[optimal patent val]] for 7-limit [[orwell]] temperament and for the planar temperament [[tempering out]] [[2430/2401]].
[[file:137edo_MOS_031.svg]]</pre></div>
 
<h4>Original HTML content:</h4>
=== Prime harmonics ===
<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;137edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;137 equal division&lt;/em&gt; divides the octave into 137 equal parts of 8.759 cents each. It is the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 7-limit &lt;a class="wiki_link" href="/Semicomma%20family"&gt;orwell temperament&lt;/a&gt; and for the planar temperament tempering out 2430/2401. It tempers out 2109375/2097152 (the semicomma) in the 5-limit; 225/224 and 1728/1715 in the 7-limit; 243/242 in the 11-limit; 351/350 in the 13-limit; 375/374 and 442/441 in the 17-limit; and 324/323 and 495/494 in the 19-limit. Since it is the 33rd &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime number&lt;/a&gt;, 137edo has no proper divisors aside from 1.&lt;br /&gt;
{{Harmonics in equal|137}}
&lt;br /&gt;
 
A diagram of 7-limit Orwell based on the 31\137edo generator:&lt;br /&gt;
=== Subsets and supersets ===
&lt;!-- ws:start:WikiTextLocalImageRule:0:&amp;lt;img src=&amp;quot;/file/view/137edo_MOS_031_demo_correction.png/285785730/137edo_MOS_031_demo_correction.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/137edo_MOS_031_demo_correction.png/285785730/137edo_MOS_031_demo_correction.png" alt="137edo_MOS_031_demo_correction.png" title="137edo_MOS_031_demo_correction.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:0 --&gt;&lt;br /&gt;
137edo is the 33rd [[prime edo]], following [[131edo]] and before [[139edo]]. [[274edo]], which doubles it, provides a correction for its approximation to harmonic 7.  
&lt;!-- ws:start:WikiTextFileRule:1:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/137edo_MOS_031.svg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@137edo_MOS_031.svg&amp;quot; title=&amp;quot;File: 137edo_MOS_031.svg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/137edo_MOS_031.svg/285785200/137edo_MOS_031.svg" onclick="ws.common.trackFileLink('/file/view/137edo_MOS_031.svg/285785200/137edo_MOS_031.svg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="137edo_MOS_031.svg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/137edo_MOS_031.svg/285785200/137edo_MOS_031.svg" onclick="ws.common.trackFileLink('/file/view/137edo_MOS_031.svg/285785200/137edo_MOS_031.svg');" class="filename" title="137edo_MOS_031.svg"&gt;137edo_MOS_031.svg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/137edo_MOS_031.svg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/137edo_MOS_031.svg/285785200/137edo_MOS_031.svg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;46 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:1 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -217 137 }}
| {{mapping| 137 217 }}
| +0.3865
| 0.3866
| 4.41
|-
| 2.3.5
| {{monzo| -21 3 7 }}, {{monzo| -13 17 -6 }}
| {{mapping| 137 217 318 }}
| +0.3887
| 0.3157
| 3.60
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br />per 8ve
! Generator*
! Cents*
! Associated<br />ratio*
! Temperaments
|-
| 1
| 3\137
| 26.28
| 1594323/1562500
| [[Sfourth]] (5-limit)
|-
| 1
| 4\137
| 35.04
| 1990656/1953125
| [[Gammic]] (137d) / [[gammy]] (137)
|-
| 1
| 31\137
| 271.53
| 75/64
| [[Orwell]] (137e) / [[sabric]] (137d)
|-
| 1
| 36\137
| 315.33
| 6/5
| [[Parakleismic]]
|-
| 1
| 53\137
| 464.23
| 72/55
| [[Borwell]]
|-
| 1
| 59\137
| 516.79
| 27/20
| [[Marvo]] (137)
|-
| 1
| 63\137
| 551.82
| 11/8
| [[Emka]] (137d) / [[emkay]] (137)
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 
== Diagrams ==
A diagram of 7-limit orwell based on the 31\137edo generator:
 
[[File:137edo_MOS_031_demo_correction.png|alt=137edo_MOS_031_demo_correction.png|137edo_MOS_031_demo_correction.png]]
 
[[:File:137edo_MOS_031.svg|137edo_MOS_031.svg]]
 
[[Category:Nuwell]]
[[Category:Orwell]]
[[Category:Orson]]
Retrieved from "https://en.xen.wiki/w/137edo"