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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | A '''wakalix''' is a scale which is a [[Fokker block]] in multiple ways, so that it belongs to more than one [[Fokker blocks#Arena|Fokker arena]]. In just intonation, a Fokker block is a JI scale in a JI group of rank ''r'', such that there are {{nowrap|''r'' − 1}} rank-two temperaments which temper it to a MOS. If there are more than {{nowrap|''r'' − 1}} such temperaments, we have a wakalix, if there are more than ''r'', it is a '''superwakalix'''; some of both kinds are cataloged below. An ordinary wakalix, which generates a rank-''r'' JI group and has exactly ''r'' different rank two temperaments tempering it to a MOS, is sometimes called an r-wakalix (triple wakalix, quadruple wakalix, etc.) |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-02-27 22:17:52 UTC</tt>.<br>
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| : The original revision id was <tt>492592334</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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| <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]]
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| A //wakalix// is a [[Fokker blocks|Fokker block]] which is a Fokker block in more than one way, so that it belongs in more than one [[Fokker blocks#First definition of a Fokker block|arena]]. A Fokker block is a JI scale in a JI group of rank r, such that there are r-1 rank two temperaments which temper it to a MOS. If there are more than r-1 such temperaments, we have a wakalix, if there are more than r, it is a superwakalix; some of both kinds are cataloged below. An ordinary wakalix, which generates a rank r JI group and has exactly r different rank two temperaments tempering it to a MOS, is sometimes called an r-wakalix (triple wakalix, quadruple wakalix, etc.)
| | == Tritonic == |
| | * [[major and minor triads]] |
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| =Pentatonic= | | == Tetratonic == |
| [[fathbugmean1]] | | * [[addedsixth]] |
| [[fathbugmean2]]
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| =Hexatonic= | | === Super8-wakalixes === |
| [[ternessbabdec]] | | * [[major and minor tetrads]] |
| | * [[supermajor and subminor tetrads]] |
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| =Hepatonic= | | == Pentatonic == |
| [[dimeanmav1]] | | * [[fathbugmean1]] |
| [[dimeanmav2]] | | * [[fathbugmean2]] |
| [[dimeanporc]] | | * [[otonalpentad]] |
| [[dimavenipu]] | | * [[utonalpentad]] |
| [[poole]] | | * [[triensemarch1]] |
| [[waka3-7-17]] | | * [[triensemarch2]] |
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| =Dodecatonic= | | == Hexatonic == |
| [[biggulp]]
| | * [[ternessbabdec]] |
| [[meansruhelm]]
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| [[prism]]
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| [[thirteendene]]
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| [[wilson_class]]
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| [[augdimhextrug]]
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| ==Superwakalix==
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| [[domdimpajinjmean]] | |
| [[domdimpajinjschis]]
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| =15-tone= | | == Heptatonic == |
| [[blackopkeegil1]] | | * [[dimeanmav1]] |
| [[blackopkeegil2]] | | * [[dimeanmav2]] |
| [[primewak15]] | | * [[dimeanporc]] |
| | * [[dimavenipu]] |
| | * [[disixporc1]] |
| | * [[disixporc2]] |
| | * [[poole]] |
| | * [[waka3-7-17]] |
| | * [[jademohaporc]] |
| | * [[ochmohaporc]] |
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| =16-tone= | | === 8-wakalixes === |
| ==Supersuperwakalix== | | * [[dudon mohajira117]] |
| [[supersuper16]] | |
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| =17-tone= | | === 54-wakalixes === |
| [[cartwheel]] | | * [[oheptad]] |
| | * [[uheptad]] |
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| =19-tone= | | == Nonatonic == |
| [[godmeankeeflat1]] | | * [[mavlim scales]] |
| [[godmeankeeflat2]]
| | * [[phorearmlogic1]] |
| [[godmeankeeflat3]] | | * [[phorearmlogic2]] |
| ==Superwakalix==
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| [[superclipgenus19]] | |
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| =22-tone= | | == Decatonic == |
| [[pajhedgepythquas1]] | | * [[line10]] |
| [[pajhedgepythquas2]]
| | * [[cx4]] |
| ==Superwakalix==
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| [[hppshq]] | |
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| =31-tone= | | == Undecatonic == |
| ==Superwakalix==
| | * [[cxi1]] |
| [[meansqunumigpopmo]] | | * [[cxi2]] |
| | * [[cxi3]] |
| | * [[cxi4]] |
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| =Fifth-repeating wakalixes= | | == Dodecatonic == |
| [[superfif7a]] | | * [[biggulp]] |
| [[superfif7b]] | | * [[meansruhelm]]1 |
| | * [[meansruhelm2]] |
| | * [[prism (scale)|prism]] |
| | * [[thirteendene]] |
| | * [[wilson class]] |
| | * [[augdimhextrug]] |
| | * [[parizek-miller hexagon]] |
| | * [[ramis]] |
| | * [[hahnZ]] |
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| =Divisions of the Tetrachord= | | === Superwakalixes === |
| [[dicot-meantone tetrachord arena]] | | * [[domdimpajinjmean]] |
| [[dominant-diminished-pajara tetrachord arena]] | | * [[domdimpajinjschis]] |
| [[august-pajara-augene tetrachord arena]] | | * [[collapsar]] |
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| =Music= | | == 13-tone == |
| [[http://chrisvaisvil.com/?p=2256|Improvisational wakalix survey]] by Chris Vaisvil
| | * [[dwarf13 7d]] |
| [[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/supersuper16.mp3|Supersuperwakalix16]] by Billy Stiltner</pre></div> | | |
| <h4>Original HTML content:</h4>
| | === Superwakalix === |
| <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>Gallery of Wakalixes</title></head><body><!-- ws:start:WikiTextTocRule:36:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><a href="#Pentatonic">Pentatonic</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Hexatonic">Hexatonic</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#Hepatonic">Hepatonic</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Dodecatonic">Dodecatonic</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#x15-tone">15-tone</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | <a href="#x16-tone">16-tone</a><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --> | <a href="#x17-tone">17-tone</a><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#x19-tone">19-tone</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --> | <a href="#x22-tone">22-tone</a><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#x31-tone">31-tone</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Fifth-repeating wakalixes">Fifth-repeating wakalixes</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Divisions of the Tetrachord">Divisions of the Tetrachord</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: -->
| | * [[supertriskaideka]] |
| <!-- ws:end:WikiTextTocRule:55 --><br />
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| A <em>wakalix</em> is a <a class="wiki_link" href="/Fokker%20blocks">Fokker block</a> which is a Fokker block in more than one way, so that it belongs in more than one <a class="wiki_link" href="/Fokker%20blocks#First definition of a Fokker block">arena</a>. A Fokker block is a JI scale in a JI group of rank r, such that there are r-1 rank two temperaments which temper it to a MOS. If there are more than r-1 such temperaments, we have a wakalix, if there are more than r, it is a superwakalix; some of both kinds are cataloged below. An ordinary wakalix, which generates a rank r JI group and has exactly r different rank two temperaments tempering it to a MOS, is sometimes called an r-wakalix (triple wakalix, quadruple wakalix, etc.)<br />
| | == 14-tone == |
| <br />
| | * [[parrot]] |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Pentatonic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Pentatonic</h1>
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| <a class="wiki_link" href="/fathbugmean1">fathbugmean1</a><br />
| | == 15-tone == |
| <a class="wiki_link" href="/fathbugmean2">fathbugmean2</a><br />
| | * [[blackopkeegil1]] |
| <br />
| | * [[blackopkeegil2]] |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Hexatonic"></a><!-- ws:end:WikiTextHeadingRule:2 -->Hexatonic</h1>
| | * [[primewak15]] |
| <a class="wiki_link" href="/ternessbabdec">ternessbabdec</a><br />
| | |
| <br />
| | == 16-tone == |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Hepatonic"></a><!-- ws:end:WikiTextHeadingRule:4 -->Hepatonic</h1>
| | === Supersuperwakalix === |
| <a class="wiki_link" href="/dimeanmav1">dimeanmav1</a><br />
| | * [[supersuper16]] |
| <a class="wiki_link" href="/dimeanmav2">dimeanmav2</a><br />
| | |
| <a class="wiki_link" href="/dimeanporc">dimeanporc</a><br />
| | == 17-tone == |
| <a class="wiki_link" href="/dimavenipu">dimavenipu</a><br />
| | * [[cartwheel]] |
| <a class="wiki_link" href="/poole">poole</a><br />
| | * [[parizekhex]] |
| <a class="wiki_link" href="/waka3-7-17">waka3-7-17</a><br />
| | * [[wilcent17]] |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Dodecatonic"></a><!-- ws:end:WikiTextHeadingRule:6 -->Dodecatonic</h1>
| | == 19-tone == |
| <a class="wiki_link" href="/biggulp">biggulp</a><br />
| | * [[godmeankeeflat1]] |
| <a class="wiki_link" href="/meansruhelm">meansruhelm</a><br />
| | * [[godmeankeeflat2]] |
| <a class="wiki_link" href="/prism">prism</a><br />
| | * [[godmeankeeflat3]] |
| <a class="wiki_link" href="/thirteendene">thirteendene</a><br />
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| <a class="wiki_link" href="/wilson_class">wilson_class</a><br />
| | === Superwakalix === |
| <a class="wiki_link" href="/augdimhextrug">augdimhextrug</a><br />
| | * [[superclipgenus19]] |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Dodecatonic-Superwakalix"></a><!-- ws:end:WikiTextHeadingRule:8 -->Superwakalix</h2>
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| <a class="wiki_link" href="/domdimpajinjmean">domdimpajinjmean</a><br />
| | == 22-tone == |
| <a class="wiki_link" href="/domdimpajinjschis">domdimpajinjschis</a><br />
| | * [[pajhedgepythquas1]] |
| <br />
| | * [[pajhedgepythquas2]] |
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="x15-tone"></a><!-- ws:end:WikiTextHeadingRule:10 -->15-tone</h1>
| | |
| <a class="wiki_link" href="/blackopkeegil1">blackopkeegil1</a><br />
| | === Superwakalix === |
| <a class="wiki_link" href="/blackopkeegil2">blackopkeegil2</a><br />
| | * [[hppshq]] |
| <a class="wiki_link" href="/primewak15">primewak15</a><br />
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| <br />
| | == 31-tone == |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="x16-tone"></a><!-- ws:end:WikiTextHeadingRule:12 -->16-tone</h1>
| | === Superwakalix === |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x16-tone-Supersuperwakalix"></a><!-- ws:end:WikiTextHeadingRule:14 -->Supersuperwakalix</h2>
| | * [[meansqunumigpopmo]] |
| <a class="wiki_link" href="/supersuper16">supersuper16</a><br />
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| <br />
| | == Fifth-repeating wakalixes == |
| <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="x17-tone"></a><!-- ws:end:WikiTextHeadingRule:16 -->17-tone</h1>
| | * [[superfif7a]] |
| <a class="wiki_link" href="/cartwheel">cartwheel</a><br />
| | * [[superfif7b]] |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="x19-tone"></a><!-- ws:end:WikiTextHeadingRule:18 -->19-tone</h1>
| | == Divisions of the Tetrachord == |
| <a class="wiki_link" href="/godmeankeeflat1">godmeankeeflat1</a><br />
| | * [[dicot-meantone tetrachord arena]] |
| <a class="wiki_link" href="/godmeankeeflat2">godmeankeeflat2</a><br />
| | * [[dominant-diminished-pajara tetrachord arena]] |
| <a class="wiki_link" href="/godmeankeeflat3">godmeankeeflat3</a><br />
| | * [[august-pajara-augene tetrachord arena]] |
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="x19-tone-Superwakalix"></a><!-- ws:end:WikiTextHeadingRule:20 -->Superwakalix</h2>
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| <a class="wiki_link" href="/superclipgenus19">superclipgenus19</a><br />
| | == Music == |
| <br />
| | '''[[Billy Stiltner]]''' |
| <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="x22-tone"></a><!-- ws:end:WikiTextHeadingRule:22 -->22-tone</h1>
| | * [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/supersuper16.mp3 Supersuperwakalix16] |
| <a class="wiki_link" href="/pajhedgepythquas1">pajhedgepythquas1</a><br />
| | '''[[Chris Vaisvil]]''' |
| <a class="wiki_link" href="/pajhedgepythquas2">pajhedgepythquas2</a><br />
| | * [http://chrisvaisvil.com/?p=2256 Improvisational wakalix survey] |
| <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="x22-tone-Superwakalix"></a><!-- ws:end:WikiTextHeadingRule:24 -->Superwakalix</h2>
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| <a class="wiki_link" href="/hppshq">hppshq</a><br />
| | {{Navbox scale gallery}} |
| <br />
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| <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="x31-tone"></a><!-- ws:end:WikiTextHeadingRule:26 -->31-tone</h1>
| | [[Category:Wakalixes| ]] <!-- main article --> |
| <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="x31-tone-Superwakalix"></a><!-- ws:end:WikiTextHeadingRule:28 -->Superwakalix</h2>
| | [[Category:Fokker block]] |
| <a class="wiki_link" href="/meansqunumigpopmo">meansqunumigpopmo</a><br />
| | [[Category:Just intonation scales]] |
| <br />
| | [[Category:Pages with mostly numerical content]] |
| <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Fifth-repeating wakalixes"></a><!-- ws:end:WikiTextHeadingRule:30 -->Fifth-repeating wakalixes</h1>
| | [[Category:Lists of scales]] |
| <a class="wiki_link" href="/superfif7a">superfif7a</a><br />
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| <a class="wiki_link" href="/superfif7b">superfif7b</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Divisions of the Tetrachord"></a><!-- ws:end:WikiTextHeadingRule:32 -->Divisions of the Tetrachord</h1>
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| <a class="wiki_link" href="/dicot-meantone%20tetrachord%20arena">dicot-meantone tetrachord arena</a><br />
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| <a class="wiki_link" href="/dominant-diminished-pajara%20tetrachord%20arena">dominant-diminished-pajara tetrachord arena</a><br />
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| <a class="wiki_link" href="/august-pajara-augene%20tetrachord%20arena">august-pajara-augene tetrachord arena</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:34 -->Music</h1>
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| <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=2256" rel="nofollow">Improvisational wakalix survey</a> by Chris Vaisvil<br />
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| <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/supersuper16.mp3" rel="nofollow">Supersuperwakalix16</a> by Billy Stiltner</body></html></pre></div>
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