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Breedsmic temperaments: Difference between revisions

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Wikispaces>genewardsmith
**Imported revision 516058222 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 537227354 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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>2014-07-11 16:01:54 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-01-13 21:51:57 UTC</tt>.<br>
: The original revision id was <tt>516058222</tt>.<br>
: The original revision id was <tt>537227354</tt>.<br>
: The revision comment was: <tt></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>
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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Map: [&lt;1 19 8 10 8 9|, &lt;0 -46 -15 -19 -12 -14|]
Map: [&lt;1 19 8 10 8 9|, &lt;0 -46 -15 -19 -12 -14|]
EDOs: 37, 103, 140, 243e
EDOs: 37, 103, 140, 243e
Badness: 0.0274</pre></div>
Badness: 0.0274
 
=Mintone=
Commas: 2401/2400, 177147/175000
 
POTE generator: ~10/9 = 186.343
 
Map: [&lt;1 5 9 7|, &lt;0 -22 -43 -27|]
EDOs: 45, 58, 103, 161, 586b, 747bc, 908bc
Badness: 0.12567
 
==11-limit==
Commas: 243/242, 441/440, 43923/43750
 
POTE generator: ~10/9 = 186.345
 
Map: [&lt;1 5 9 7 12|, &lt;0 -22 -43 -27 -55|]
EDOs: 58, 103, 161, 425b, 586b, 747bc
Badness: 0.0400
 
==13-limit==
Commas: 243/242, 351/350, 441/440, 847/845
 
POTE generator: ~10/9 = 186.347
 
Map: [&lt;1 5 9 7 12 11|, &lt;0 -22 -43 -27 -55 -47|]
EDOs: 58, 103, 161
Badness: 0.0218</pre></div>
<h4>Original HTML content:</h4>
<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;Breedsmic temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:86:&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:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;a href="#Hemififths"&gt;Hemififths&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt; | &lt;a href="#Semihemi"&gt;Semihemi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt; | &lt;a href="#Tertiaseptal"&gt;Tertiaseptal&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt;&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&gt; | &lt;a href="#Hemitert"&gt;Hemitert&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt; | &lt;a href="#Harry"&gt;Harry&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt;&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&gt; | &lt;a href="#Quasiorwell"&gt;Quasiorwell&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&gt;&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt;&lt;!-- ws:end:WikiTextTocRule:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&gt; | &lt;a href="#Decoid"&gt;Decoid&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&gt;&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt;&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt; | &lt;a href="#Neominor"&gt;Neominor&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&gt;&lt;!-- ws:end:WikiTextTocRule:109 --&gt;&lt;!-- ws:start:WikiTextTocRule:110: --&gt;&lt;!-- ws:end:WikiTextTocRule:110 --&gt;&lt;!-- ws:start:WikiTextTocRule:111: --&gt; | &lt;a href="#Emmthird"&gt;Emmthird&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:111 --&gt;&lt;!-- ws:start:WikiTextTocRule:112: --&gt; | &lt;a href="#Quinmite"&gt;Quinmite&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:112 --&gt;&lt;!-- ws:start:WikiTextTocRule:113: --&gt; | &lt;a href="#Unthirds"&gt;Unthirds&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:113 --&gt;&lt;!-- ws:start:WikiTextTocRule:114: --&gt;&lt;!-- ws:end:WikiTextTocRule:114 --&gt;&lt;!-- ws:start:WikiTextTocRule:115: --&gt;&lt;!-- ws:end:WikiTextTocRule:115 --&gt;&lt;!-- ws:start:WikiTextTocRule:116: --&gt; | &lt;a href="#Newt"&gt;Newt&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:116 --&gt;&lt;!-- ws:start:WikiTextTocRule:117: --&gt;&lt;!-- ws:end:WikiTextTocRule:117 --&gt;&lt;!-- ws:start:WikiTextTocRule:118: --&gt;&lt;!-- ws:end:WikiTextTocRule:118 --&gt;&lt;!-- ws:start:WikiTextTocRule:119: --&gt; | &lt;a href="#Amicable"&gt;Amicable&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:119 --&gt;&lt;!-- ws:start:WikiTextTocRule:120: --&gt; | &lt;a href="#Septidiasemi"&gt;Septidiasemi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:120 --&gt;&lt;!-- ws:start:WikiTextTocRule:121: --&gt; | &lt;a href="#Maviloid"&gt;Maviloid&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:121 --&gt;&lt;!-- ws:start:WikiTextTocRule:122: --&gt; | &lt;a href="#Subneutral"&gt;Subneutral&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:122 --&gt;&lt;!-- ws:start:WikiTextTocRule:123: --&gt; | &lt;a href="#Osiris"&gt;Osiris&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:123 --&gt;&lt;!-- ws:start:WikiTextTocRule:124: --&gt; | &lt;a href="#Gorgik"&gt;Gorgik&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:124 --&gt;&lt;!-- ws:start:WikiTextTocRule:125: --&gt;&lt;!-- ws:end:WikiTextTocRule:125 --&gt;&lt;!-- ws:start:WikiTextTocRule:126: --&gt;&lt;!-- ws:end:WikiTextTocRule:126 --&gt;&lt;!-- ws:start:WikiTextTocRule:127: --&gt; | &lt;a href="#Fibo"&gt;Fibo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:127 --&gt;&lt;!-- ws:start:WikiTextTocRule:128: --&gt;&lt;!-- ws:end:WikiTextTocRule:128 --&gt;&lt;!-- ws:start:WikiTextTocRule:129: --&gt;&lt;!-- ws:end:WikiTextTocRule:129 --&gt;&lt;!-- ws:start:WikiTextTocRule:130: --&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;Breedsmic temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:92:&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:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;a href="#Hemififths"&gt;Hemififths&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt;&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&gt; | &lt;a href="#Semihemi"&gt;Semihemi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt;&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt; | &lt;a href="#Tertiaseptal"&gt;Tertiaseptal&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&gt;&lt;!-- ws:end:WikiTextTocRule:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&gt;&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt; | &lt;a href="#Hemitert"&gt;Hemitert&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&gt; | &lt;a href="#Harry"&gt;Harry&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&gt;&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt;&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt; | &lt;a href="#Quasiorwell"&gt;Quasiorwell&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&gt;&lt;!-- ws:end:WikiTextTocRule:109 --&gt;&lt;!-- ws:start:WikiTextTocRule:110: --&gt;&lt;!-- ws:end:WikiTextTocRule:110 --&gt;&lt;!-- ws:start:WikiTextTocRule:111: --&gt; | &lt;a href="#Decoid"&gt;Decoid&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:111 --&gt;&lt;!-- ws:start:WikiTextTocRule:112: --&gt;&lt;!-- ws:end:WikiTextTocRule:112 --&gt;&lt;!-- ws:start:WikiTextTocRule:113: --&gt;&lt;!-- ws:end:WikiTextTocRule:113 --&gt;&lt;!-- ws:start:WikiTextTocRule:114: --&gt; | &lt;a href="#Neominor"&gt;Neominor&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:114 --&gt;&lt;!-- ws:start:WikiTextTocRule:115: --&gt;&lt;!-- ws:end:WikiTextTocRule:115 --&gt;&lt;!-- ws:start:WikiTextTocRule:116: --&gt;&lt;!-- ws:end:WikiTextTocRule:116 --&gt;&lt;!-- ws:start:WikiTextTocRule:117: --&gt; | &lt;a href="#Emmthird"&gt;Emmthird&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:117 --&gt;&lt;!-- ws:start:WikiTextTocRule:118: --&gt; | &lt;a href="#Quinmite"&gt;Quinmite&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:118 --&gt;&lt;!-- ws:start:WikiTextTocRule:119: --&gt; | &lt;a href="#Unthirds"&gt;Unthirds&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:119 --&gt;&lt;!-- ws:start:WikiTextTocRule:120: --&gt;&lt;!-- ws:end:WikiTextTocRule:120 --&gt;&lt;!-- ws:start:WikiTextTocRule:121: --&gt;&lt;!-- ws:end:WikiTextTocRule:121 --&gt;&lt;!-- ws:start:WikiTextTocRule:122: --&gt; | &lt;a href="#Newt"&gt;Newt&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:122 --&gt;&lt;!-- ws:start:WikiTextTocRule:123: --&gt;&lt;!-- ws:end:WikiTextTocRule:123 --&gt;&lt;!-- ws:start:WikiTextTocRule:124: --&gt;&lt;!-- ws:end:WikiTextTocRule:124 --&gt;&lt;!-- ws:start:WikiTextTocRule:125: --&gt; | &lt;a href="#Amicable"&gt;Amicable&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:125 --&gt;&lt;!-- ws:start:WikiTextTocRule:126: --&gt; | &lt;a href="#Septidiasemi"&gt;Septidiasemi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:126 --&gt;&lt;!-- ws:start:WikiTextTocRule:127: --&gt; | &lt;a href="#Maviloid"&gt;Maviloid&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:127 --&gt;&lt;!-- ws:start:WikiTextTocRule:128: --&gt; | &lt;a href="#Subneutral"&gt;Subneutral&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:128 --&gt;&lt;!-- ws:start:WikiTextTocRule:129: --&gt; | &lt;a href="#Osiris"&gt;Osiris&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:129 --&gt;&lt;!-- ws:start:WikiTextTocRule:130: --&gt; | &lt;a href="#Gorgik"&gt;Gorgik&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:130 --&gt;&lt;!-- ws:start:WikiTextTocRule:131: --&gt;&lt;!-- ws:end:WikiTextTocRule:131 --&gt;&lt;!-- ws:start:WikiTextTocRule:132: --&gt;&lt;!-- ws:end:WikiTextTocRule:132 --&gt;&lt;!-- ws:start:WikiTextTocRule:133: --&gt; | &lt;a href="#Fibo"&gt;Fibo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:133 --&gt;&lt;!-- ws:start:WikiTextTocRule:134: --&gt;&lt;!-- ws:end:WikiTextTocRule:134 --&gt;&lt;!-- ws:start:WikiTextTocRule:135: --&gt;&lt;!-- ws:end:WikiTextTocRule:135 --&gt;&lt;!-- ws:start:WikiTextTocRule:136: --&gt; | &lt;a href="#Mintone"&gt;Mintone&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:136 --&gt;&lt;!-- ws:start:WikiTextTocRule:137: --&gt;&lt;!-- ws:end:WikiTextTocRule:137 --&gt;&lt;!-- ws:start:WikiTextTocRule:138: --&gt;&lt;!-- ws:end:WikiTextTocRule:138 --&gt;&lt;!-- ws:start:WikiTextTocRule:139: --&gt;
&lt;!-- ws:end:WikiTextTocRule:130 --&gt;&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:139 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Breedsmic temperaments are rank two temperaments tempering out the breedsma, |-5 -1 -2 4&amp;gt; = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.&lt;br /&gt;
Breedsmic temperaments are rank two temperaments tempering out the breedsma, |-5 -1 -2 4&amp;gt; = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.&lt;br /&gt;
Line 848: Line 875:
Map: [&amp;lt;1 19 8 10 8 9|, &amp;lt;0 -46 -15 -19 -12 -14|]&lt;br /&gt;
Map: [&amp;lt;1 19 8 10 8 9|, &amp;lt;0 -46 -15 -19 -12 -14|]&lt;br /&gt;
EDOs: 37, 103, 140, 243e&lt;br /&gt;
EDOs: 37, 103, 140, 243e&lt;br /&gt;
Badness: 0.0274&lt;/body&gt;&lt;/html&gt;</pre></div>
Badness: 0.0274&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:86:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc43"&gt;&lt;a name="Mintone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:86 --&gt;Mintone&lt;/h1&gt;
Commas: 2401/2400, 177147/175000&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 186.343&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 9 7|, &amp;lt;0 -22 -43 -27|]&lt;br /&gt;
EDOs: 45, 58, 103, 161, 586b, 747bc, 908bc&lt;br /&gt;
Badness: 0.12567&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc44"&gt;&lt;a name="Mintone-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;11-limit&lt;/h2&gt;
Commas: 243/242, 441/440, 43923/43750&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 186.345&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 9 7 12|, &amp;lt;0 -22 -43 -27 -55|]&lt;br /&gt;
EDOs: 58, 103, 161, 425b, 586b, 747bc&lt;br /&gt;
Badness: 0.0400&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc45"&gt;&lt;a name="Mintone-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;13-limit&lt;/h2&gt;
Commas: 243/242, 351/350, 441/440, 847/845&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 186.347&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 9 7 12 11|, &amp;lt;0 -22 -43 -27 -55 -47|]&lt;br /&gt;
EDOs: 58, 103, 161&lt;br /&gt;
Badness: 0.0218&lt;/body&gt;&lt;/html&gt;</pre></div>
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