Marveltwin: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>2011-06-21 15:14:24 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-21 16:44:17 UTC</tt>.<br>

: The original revision id was <tt>~~238017831~~</tt>.<br>

: The original revision id was <tt>238036939</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>

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=Marveltwin and Marvel=

The //marveltwin comma//, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the [[11-limit]] version of marvel, which tempers out 225/224 and 385/384, to get [[13-limit]] marvel. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.

The //marveltwin comma//, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the [[11-limit]] version of marvel, which tempers out 225/224 and 385/384, to get [[13-limit]] marvel, aka hecate. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.

=Rank five=

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|| <0 0 1 2 0 -2] ||

|| <0 0 0 0 1 0]] ||

Edos: 12, 19, 41, 53, 72, 166</pre></div>

Edos: 12, 19, 41, 53, 72, 166

==385/384==

==364/363==

==441/440==

==169/168==

==540/539==

==352/351==

==625/624==

=Rank three=

==Portending==

Commas: 325/324, 364/363, 441/440

==Marvel (Hecate)==

Commas: 225/224, 325/324, 385/384

==Sumatra==

Commas: 325/324, 385/384, 625/624

EDOs: 15, 19, 34, 53, 72, 87, 140, 159, 212, 299

Optimal patent val: [[299edo]]

Badness: 0.000680

</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"><html><head><title>Marveltwin</title></head><body><a href="#Marveltwin and Marvel">Marveltwin and Marvel</a> | <a href="#Rank five">Rank five</a> | <a href="#Rank four">Rank four</a>

<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"><html><head><title>Marveltwin</title></head><body><a href="#Marveltwin and Marvel">Marveltwin and Marvel</a> | <a href="#Rank five">Rank five</a> | <a href="#Rank four">Rank four</a> | <a href="#Rank three">Rank three</a>

<br />

<br />

<h1 id="toc0"><a name="Marveltwin and Marvel"></a>Marveltwin and Marvel</h1>

The <em>marveltwin comma</em>, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the <a class="wiki_link" href="/11-limit">11-limit</a> version of marvel, which tempers out 225/224 and 385/384, to get <a class="wiki_link" href="/13-limit">13-limit</a> marvel. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.<br />

The <em>marveltwin comma</em>, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the <a class="wiki_link" href="/11-limit">11-limit</a> version of marvel, which tempers out 225/224 and 385/384, to get <a class="wiki_link" href="/13-limit">13-limit</a> marvel, aka hecate. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.<br />

<br />

<h1 id="toc1"><a name="Rank five"></a>Rank five</h1>

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</table>

Edos: 12, 19, 41, 53, 72, 166</body></html></pre></div>

Edos: 12, 19, 41, 53, 72, 166<br />

<br />

<h2 id="toc4"><a name="Rank four-385/384"></a>385/384</h2>

<br />

<h2 id="toc5"><a name="Rank four-364/363"></a>364/363</h2>

<br />

<h2 id="toc6"><a name="Rank four-441/440"></a>441/440</h2>

<br />

<h2 id="toc7"><a name="Rank four-169/168"></a>169/168</h2>

<br />

<h2 id="toc8"><a name="Rank four-540/539"></a>540/539</h2>

<br />

<h2 id="toc9"><a name="Rank four-352/351"></a>352/351</h2>

<br />

<h2 id="toc10"><a name="Rank four-625/624"></a>625/624</h2>

<br />

<h1 id="toc11"><a name="Rank three"></a>Rank three</h1>

<br />

<h2 id="toc12"><a name="Rank three-Portending"></a>Portending</h2>

Commas: 325/324, 364/363, 441/440<br />

<br />

<h2 id="toc13"><a name="Rank three-Marvel (Hecate)"></a>Marvel (Hecate)</h2>

Commas: 225/224, 325/324, 385/384<br />

<br />

<h2 id="toc14"><a name="Rank three-Sumatra"></a>Sumatra</h2>

Commas: 325/324, 385/384, 625/624<br />

<br />

EDOs: 15, 19, 34, 53, 72, 87, 140, 159, 212, 299<br />

Optimal patent val: <a class="wiki_link" href="/299edo">299edo</a><br />

Badness: 0.000680</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2011-06-21 15:14:24 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-21 16:44:17 UTC</tt>.<br>
-: The original revision id was <tt>238017831</tt>.<br>
+: The original revision id was <tt>238036939</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>
@@ Line 9: / Line 9: @@
 =Marveltwin and Marvel=
-The //marveltwin comma//, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the [[11-limit]] version of marvel, which tempers out 225/224 and 385/384, to get [[13-limit]] marvel. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.
+The //marveltwin comma//, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the [[11-limit]] version of marvel, which tempers out 225/224 and 385/384, to get [[13-limit]] marvel, aka hecate. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.
 =Rank five=
@@ Line 46: / Line 46: @@
 || &lt;0 0 1 2 0 -2] ||
 || &lt;0 0 0 0 1 0]] ||
-Edos: 12, 19, 41, 53, 72, 166</pre></div>
+Edos: 12, 19, 41, 53, 72, 166
+==385/384==
+==364/363==
+==441/440==
+==169/168==
+==540/539==
+==352/351==
+==625/624==
+=Rank three=
+==Portending==
+Commas: 325/324, 364/363, 441/440
+==Marvel (Hecate)==
+Commas: 225/224, 325/324, 385/384
+==Sumatra==
+Commas: 325/324, 385/384, 625/624
+EDOs: 15, 19, 34, 53, 72, 87, 140, 159, 212, 299
+Optimal patent val: [[299edo]]
+Badness: 0.000680
+</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;Marveltwin&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:8:&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:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;a href="#Marveltwin and Marvel"&gt;Marveltwin and Marvel&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt; | &lt;a href="#Rank five"&gt;Rank five&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt; | &lt;a href="#Rank four"&gt;Rank four&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;
+<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;Marveltwin&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:30:&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:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;&lt;a href="#Marveltwin and Marvel"&gt;Marveltwin and Marvel&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#Rank five"&gt;Rank five&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt; | &lt;a href="#Rank four"&gt;Rank four&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt;&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt; | &lt;a href="#Rank three"&gt;Rank three&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt;&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Marveltwin and Marvel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Marveltwin and Marvel&lt;/h1&gt;
-The &lt;em&gt;marveltwin comma&lt;/em&gt;, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; version of marvel, which tempers out 225/224 and 385/384, to get &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; marvel. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.&lt;br /&gt;
+The &lt;em&gt;marveltwin comma&lt;/em&gt;, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; version of marvel, which tempers out 225/224 and 385/384, to get &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; marvel, aka hecate. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Rank five"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Rank five&lt;/h1&gt;
@@ Line 148: / Line 179: @@
 &lt;/table&gt;
-Edos: 12, 19, 41, 53, 72, 166&lt;/body&gt;&lt;/html&gt;</pre></div>
+Edos: 12, 19, 41, 53, 72, 166&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Rank four-385/384"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;385/384&lt;/h2&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Rank four-364/363"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;364/363&lt;/h2&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Rank four-441/440"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;441/440&lt;/h2&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Rank four-169/168"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;169/168&lt;/h2&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Rank four-540/539"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;540/539&lt;/h2&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Rank four-352/351"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;352/351&lt;/h2&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Rank four-625/624"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;625/624&lt;/h2&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Rank three"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Rank three&lt;/h1&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Rank three-Portending"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Portending&lt;/h2&gt;
+Commas: 325/324, 364/363, 441/440&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Rank three-Marvel (Hecate)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Marvel (Hecate)&lt;/h2&gt;
+Commas: 225/224, 325/324, 385/384&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Rank three-Sumatra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Sumatra&lt;/h2&gt;
+Commas: 325/324, 385/384, 625/624&lt;br /&gt;
+&lt;br /&gt;
+EDOs: 15, 19, 34, 53, 72, 87, 140, 159, 212, 299&lt;br /&gt;
+Optimal patent val: &lt;a class="wiki_link" href="/299edo"&gt;299edo&lt;/a&gt;&lt;br /&gt;
+Badness: 0.000680&lt;/body&gt;&lt;/html&gt;</pre></div>