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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>2012-03-31 22:30:50 UTC</tt>.<br>
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| : The original revision id was <tt>316534932</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">A //wakalix// is a [[Fokker blocks|Fokker block]] which is a Fokker block in more than one way. 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.)
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| =Pentatonic= | | == Tritonic == |
| [[fathbugmean1]] | | * [[major and minor triads]] |
| [[fathbugmean2]]
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| =Hexatonic= | | == Tetratonic == |
| [[ternessbabdec]] | | * [[addedsixth]] |
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| =Hepatonic= | | === Super8-wakalixes === |
| [[dimeanmav1]] | | * [[major and minor tetrads]] |
| [[dimeanmav2]]
| | * [[supermajor and subminor tetrads]] |
| [[dimeanporc]]
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| [[dimavenipu]] | |
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| =Dodecatonic= | | == Pentatonic == |
| [[meansruhelm]] | | * [[fathbugmean1]] |
| [[prism]] | | * [[fathbugmean2]] |
| [[wilson_class]] | | * [[otonalpentad]] |
| ==Superwakalix==
| | * [[utonalpentad]] |
| [[domdimpajinjmean]] | | * [[triensemarch1]] |
| [[domdimpajinjschis]] | | * [[triensemarch2]] |
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| =15-tone= | | == Hexatonic == |
| [[blackopkeegil1]] | | * [[ternessbabdec]] |
| [[blackopkeegil2]]
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| =19-tone= | | == Heptatonic == |
| [[godmeankeeflat1]] | | * [[dimeanmav1]] |
| [[godmeankeeflat2]] | | * [[dimeanmav2]] |
| [[godmeankeeflat3]] | | * [[dimeanporc]] |
| ==Superwakalix==
| | * [[dimavenipu]] |
| [[superclipgenus19]] | | * [[disixporc1]] |
| | * [[disixporc2]] |
| | * [[poole]] |
| | * [[waka3-7-17]] |
| | * [[jademohaporc]] |
| | * [[ochmohaporc]] |
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| =22-tone= | | === 8-wakalixes === |
| [[pajhedgepythquas1]]
| | * [[dudon mohajira117]] |
| [[pajhedgepythquas2]]
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| ==Superwakalix== | |
| [[hppshq]] | |
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| =31-tone= | | === 54-wakalixes === |
| ==Superwakalix== | | * [[oheptad]] |
| [[meansqunumigpopmo]]</pre></div> | | * [[uheptad]] |
| <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gallery of Wakalixes</title></head><body>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. 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 />
| | == Nonatonic == |
| <br />
| | * [[mavlim scales]] |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Pentatonic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Pentatonic</h1>
| | * [[phorearmlogic1]] |
| <a class="wiki_link" href="/fathbugmean1">fathbugmean1</a><br />
| | * [[phorearmlogic2]] |
| <a class="wiki_link" href="/fathbugmean2">fathbugmean2</a><br />
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| <br />
| | == Decatonic == |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Hexatonic"></a><!-- ws:end:WikiTextHeadingRule:2 -->Hexatonic</h1>
| | * [[line10]] |
| <a class="wiki_link" href="/ternessbabdec">ternessbabdec</a><br />
| | * [[cx4]] |
| <br />
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| <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Hepatonic"></a><!-- ws:end:WikiTextHeadingRule:4 -->Hepatonic</h1>
| | == Undecatonic == |
| <a class="wiki_link" href="/dimeanmav1">dimeanmav1</a><br />
| | * [[cxi1]] |
| <a class="wiki_link" href="/dimeanmav2">dimeanmav2</a><br />
| | * [[cxi2]] |
| <a class="wiki_link" href="/dimeanporc">dimeanporc</a><br />
| | * [[cxi3]] |
| <a class="wiki_link" href="/dimavenipu">dimavenipu</a><br />
| | * [[cxi4]] |
| <br />
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| <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Dodecatonic"></a><!-- ws:end:WikiTextHeadingRule:6 -->Dodecatonic</h1>
| | == Dodecatonic == |
| <a class="wiki_link" href="/meansruhelm">meansruhelm</a><br />
| | * [[biggulp]] |
| <a class="wiki_link" href="/prism">prism</a><br />
| | * [[meansruhelm]]1 |
| <a class="wiki_link" href="/wilson_class">wilson_class</a><br />
| | * [[meansruhelm2]] |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Dodecatonic-Superwakalix"></a><!-- ws:end:WikiTextHeadingRule:8 -->Superwakalix</h2>
| | * [[prism (scale)|prism]] |
| <a class="wiki_link" href="/domdimpajinjmean">domdimpajinjmean</a><br />
| | * [[thirteendene]] |
| <a class="wiki_link" href="/domdimpajinjschis">domdimpajinjschis</a><br />
| | * [[wilson class]] |
| <br />
| | * [[augdimhextrug]] |
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="x15-tone"></a><!-- ws:end:WikiTextHeadingRule:10 -->15-tone</h1>
| | * [[parizek-miller hexagon]] |
| <a class="wiki_link" href="/blackopkeegil1">blackopkeegil1</a><br />
| | * [[ramis]] |
| <a class="wiki_link" href="/blackopkeegil2">blackopkeegil2</a><br />
| | * [[hahnZ]] |
| <br />
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| <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="x19-tone"></a><!-- ws:end:WikiTextHeadingRule:12 -->19-tone</h1>
| | === Superwakalixes === |
| <a class="wiki_link" href="/godmeankeeflat1">godmeankeeflat1</a><br />
| | * [[domdimpajinjmean]] |
| <a class="wiki_link" href="/godmeankeeflat2">godmeankeeflat2</a><br />
| | * [[domdimpajinjschis]] |
| <a class="wiki_link" href="/godmeankeeflat3">godmeankeeflat3</a><br />
| | * [[collapsar]] |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x19-tone-Superwakalix"></a><!-- ws:end:WikiTextHeadingRule:14 -->Superwakalix</h2>
| | |
| <a class="wiki_link" href="/superclipgenus19">superclipgenus19</a><br />
| | == 13-tone == |
| <br />
| | * [[dwarf13 7d]] |
| <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="x22-tone"></a><!-- ws:end:WikiTextHeadingRule:16 -->22-tone</h1>
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| <a class="wiki_link" href="/pajhedgepythquas1">pajhedgepythquas1</a><br />
| | === Superwakalix === |
| <a class="wiki_link" href="/pajhedgepythquas2">pajhedgepythquas2</a><br />
| | * [[supertriskaideka]] |
| <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x22-tone-Superwakalix"></a><!-- ws:end:WikiTextHeadingRule:18 -->Superwakalix</h2>
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| <a class="wiki_link" href="/hppshq">hppshq</a><br />
| | == 14-tone == |
| <br />
| | * [[parrot]] |
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="x31-tone"></a><!-- ws:end:WikiTextHeadingRule:20 -->31-tone</h1>
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| <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="x31-tone-Superwakalix"></a><!-- ws:end:WikiTextHeadingRule:22 -->Superwakalix</h2>
| | == 15-tone == |
| <a class="wiki_link" href="/meansqunumigpopmo">meansqunumigpopmo</a></body></html></pre></div>
| | * [[blackopkeegil1]] |
| | * [[blackopkeegil2]] |
| | * [[primewak15]] |
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| | == 16-tone == |
| | === Supersuperwakalix === |
| | * [[supersuper16]] |
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| | == 17-tone == |
| | * [[cartwheel]] |
| | * [[parizekhex]] |
| | * [[wilcent17]] |
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| | == 19-tone == |
| | * [[godmeankeeflat1]] |
| | * [[godmeankeeflat2]] |
| | * [[godmeankeeflat3]] |
| | |
| | === Superwakalix === |
| | * [[superclipgenus19]] |
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| | == 22-tone == |
| | * [[pajhedgepythquas1]] |
| | * [[pajhedgepythquas2]] |
| | |
| | === Superwakalix === |
| | * [[hppshq]] |
| | |
| | == 31-tone == |
| | === Superwakalix === |
| | * [[meansqunumigpopmo]] |
| | |
| | == Fifth-repeating wakalixes == |
| | * [[superfif7a]] |
| | * [[superfif7b]] |
| | |
| | == Divisions of the Tetrachord == |
| | * [[dicot-meantone tetrachord arena]] |
| | * [[dominant-diminished-pajara tetrachord arena]] |
| | * [[august-pajara-augene tetrachord arena]] |
| | |
| | == Music == |
| | '''[[Billy Stiltner]]''' |
| | * [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/supersuper16.mp3 Supersuperwakalix16] |
| | '''[[Chris Vaisvil]]''' |
| | * [http://chrisvaisvil.com/?p=2256 Improvisational wakalix survey] |
| | |
| | {{Navbox scale gallery}} |
| | |
| | [[Category:Wakalixes| ]] <!-- main article --> |
| | [[Category:Fokker block]] |
| | [[Category:Just intonation scales]] |
| | [[Category:Pages with mostly numerical content]] |
| | [[Category:Lists of scales]] |