Gallery of wakalixes
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[[toc|flat]] 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%20definition%20of%20a%20Fokker%20block|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]] =Tetratonic= [[addedsixth]] ==Super8-wakalixes== [[major and minor tetrads]] [[supermajor and subminor tetrads]] =Pentatonic= [[fathbugmean1]] [[fathbugmean2]] [[otonalpentad]] [[utonalpentad]] =Hexatonic= [[ternessbabdec]] =Heptatonic= [[dimeanmav1]] [[dimeanmav2]] [[dimeanporc]] [[dimavenipu]] [[poole]] [[waka3-7-17]] ==54-wakalixes== [[oheptad]] [[uheptad]] =Nonatonic= [[mavlim scales]] =Decatonic= [[line10]] [[cx4]] =Undecatonic= [[cxi1]] [[cxi2]] [[cxi3]] [[cxi4]] =Dodecatonic= [[biggulp]] [[meansruhelm]] [[prism]] [[thirteendene]] [[wilson_class]] [[augdimhextrug]] [[parizek-miller hexagon]] ==Superwakalixes== [[domdimpajinjmean]] [[domdimpajinjschis]] [[collapsar]] =13-tone= [[dwarf13_7d]] ==Superwakalix== [[supertriskaideka]] =14-tone= [[parrot]] =15-tone= [[blackopkeegil1]] [[blackopkeegil2]] [[primewak15]] =16-tone= ==Supersuperwakalix== [[supersuper16]] =17-tone= [[cartwheel]] [[parizekhex]] =19-tone= [[godmeankeeflat1]] [[godmeankeeflat2]] [[godmeankeeflat3]] ==Superwakalix== [[superclipgenus19]] =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= [[http://chrisvaisvil.com/?p=2256|Improvisational wakalix survey]] by Chris Vaisvil [[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/supersuper16.mp3|Supersuperwakalix16]] by Billy Stiltner
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<html><head><title>Gallery of Wakalixes</title></head><body><!-- ws:start:WikiTextTocRule:56:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><a href="#Tritonic">Tritonic</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Tetratonic">Tetratonic</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Pentatonic">Pentatonic</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | <a href="#Hexatonic">Hexatonic</a><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Heptatonic">Heptatonic</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --> | <a href="#Nonatonic">Nonatonic</a><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --> | <a href="#Decatonic">Decatonic</a><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --> | <a href="#Undecatonic">Undecatonic</a><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --> | <a href="#Dodecatonic">Dodecatonic</a><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --> | <a href="#x13-tone">13-tone</a><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --> | <a href="#x14-tone">14-tone</a><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#x15-tone">15-tone</a><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --> | <a href="#x16-tone">16-tone</a><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --> | <a href="#x17-tone">17-tone</a><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --> | <a href="#x19-tone">19-tone</a><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --> | <a href="#x22-tone">22-tone</a><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --> | <a href="#x31-tone">31-tone</a><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> | <a href="#Fifth-repeating wakalixes">Fifth-repeating wakalixes</a><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --> | <a href="#Divisions of the Tetrachord">Divisions of the Tetrachord</a><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --> <!-- ws:end:WikiTextTocRule:85 --><br /> 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%20definition%20of%20a%20Fokker%20block">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 /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Tritonic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Tritonic</h1> <a class="wiki_link" href="/major%20and%20minor%20triads">major and minor triads</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Tetratonic"></a><!-- ws:end:WikiTextHeadingRule:2 -->Tetratonic</h1> <a class="wiki_link" href="/addedsixth">addedsixth</a><br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Tetratonic-Super8-wakalixes"></a><!-- ws:end:WikiTextHeadingRule:4 -->Super8-wakalixes</h2> <a class="wiki_link" href="/major%20and%20minor%20tetrads">major and minor tetrads</a><br /> <a class="wiki_link" href="/supermajor%20and%20subminor%20tetrads">supermajor and subminor tetrads</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Pentatonic"></a><!-- ws:end:WikiTextHeadingRule:6 -->Pentatonic</h1> <a class="wiki_link" href="/fathbugmean1">fathbugmean1</a><br /> <a class="wiki_link" href="/fathbugmean2">fathbugmean2</a><br /> <a class="wiki_link" href="/otonalpentad">otonalpentad</a><br /> <a class="wiki_link" href="/utonalpentad">utonalpentad</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Hexatonic"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hexatonic</h1> <a class="wiki_link" href="/ternessbabdec">ternessbabdec</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="Heptatonic"></a><!-- ws:end:WikiTextHeadingRule:10 -->Heptatonic</h1> <a class="wiki_link" href="/dimeanmav1">dimeanmav1</a><br /> <a class="wiki_link" href="/dimeanmav2">dimeanmav2</a><br /> <a class="wiki_link" href="/dimeanporc">dimeanporc</a><br /> <a class="wiki_link" href="/dimavenipu">dimavenipu</a><br /> <a class="wiki_link" href="/poole">poole</a><br /> <a class="wiki_link" href="/waka3-7-17">waka3-7-17</a><br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Heptatonic-54-wakalixes"></a><!-- ws:end:WikiTextHeadingRule:12 -->54-wakalixes</h2> <a class="wiki_link" href="/oheptad">oheptad</a><br /> <a class="wiki_link" href="/uheptad">uheptad</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Nonatonic"></a><!-- ws:end:WikiTextHeadingRule:14 -->Nonatonic</h1> <a class="wiki_link" href="/mavlim%20scales">mavlim scales</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="Decatonic"></a><!-- ws:end:WikiTextHeadingRule:16 -->Decatonic</h1> <a class="wiki_link" href="/line10">line10</a><br /> <a class="wiki_link" href="/cx4">cx4</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="Undecatonic"></a><!-- ws:end:WikiTextHeadingRule:18 -->Undecatonic</h1> <a class="wiki_link" href="/cxi1">cxi1</a><br /> <a class="wiki_link" href="/cxi2">cxi2</a><br /> <a class="wiki_link" href="/cxi3">cxi3</a><br /> <a class="wiki_link" href="/cxi4">cxi4</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h1> --><h1 id="toc10"><a name="Dodecatonic"></a><!-- ws:end:WikiTextHeadingRule:20 -->Dodecatonic</h1> <a class="wiki_link" href="/biggulp">biggulp</a><br /> <a class="wiki_link" href="/meansruhelm">meansruhelm</a><br /> <a class="wiki_link" href="/prism">prism</a><br /> <a class="wiki_link" href="/thirteendene">thirteendene</a><br /> <a class="wiki_link" href="/wilson_class">wilson_class</a><br /> <a class="wiki_link" href="/augdimhextrug">augdimhextrug</a><br /> <a class="wiki_link" href="/parizek-miller%20hexagon">parizek-miller hexagon</a><br /> <!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="Dodecatonic-Superwakalixes"></a><!-- ws:end:WikiTextHeadingRule:22 -->Superwakalixes</h2> <a class="wiki_link" href="/domdimpajinjmean">domdimpajinjmean</a><br /> <a class="wiki_link" href="/domdimpajinjschis">domdimpajinjschis</a><br /> <a class="wiki_link" href="/collapsar">collapsar</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h1> --><h1 id="toc12"><a name="x13-tone"></a><!-- ws:end:WikiTextHeadingRule:24 -->13-tone</h1> <a class="wiki_link" href="/dwarf13_7d">dwarf13_7d</a><br /> <!-- ws:start:WikiTextHeadingRule:26:<h2> --><h2 id="toc13"><a name="x13-tone-Superwakalix"></a><!-- ws:end:WikiTextHeadingRule:26 -->Superwakalix</h2> <a class="wiki_link" href="/supertriskaideka">supertriskaideka</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:28:<h1> --><h1 id="toc14"><a name="x14-tone"></a><!-- ws:end:WikiTextHeadingRule:28 -->14-tone</h1> <a class="wiki_link" href="/parrot">parrot</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:30:<h1> --><h1 id="toc15"><a name="x15-tone"></a><!-- ws:end:WikiTextHeadingRule:30 -->15-tone</h1> <a class="wiki_link" href="/blackopkeegil1">blackopkeegil1</a><br /> <a class="wiki_link" href="/blackopkeegil2">blackopkeegil2</a><br /> <a class="wiki_link" href="/primewak15">primewak15</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h1> --><h1 id="toc16"><a name="x16-tone"></a><!-- ws:end:WikiTextHeadingRule:32 -->16-tone</h1> <!-- ws:start:WikiTextHeadingRule:34:<h2> --><h2 id="toc17"><a name="x16-tone-Supersuperwakalix"></a><!-- ws:end:WikiTextHeadingRule:34 -->Supersuperwakalix</h2> <a class="wiki_link" href="/supersuper16">supersuper16</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:36:<h1> --><h1 id="toc18"><a name="x17-tone"></a><!-- ws:end:WikiTextHeadingRule:36 -->17-tone</h1> <a class="wiki_link" href="/cartwheel">cartwheel</a><br /> <a class="wiki_link" href="/parizekhex">parizekhex</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:38:<h1> --><h1 id="toc19"><a name="x19-tone"></a><!-- ws:end:WikiTextHeadingRule:38 -->19-tone</h1> <a class="wiki_link" href="/godmeankeeflat1">godmeankeeflat1</a><br /> <a class="wiki_link" href="/godmeankeeflat2">godmeankeeflat2</a><br /> <a class="wiki_link" href="/godmeankeeflat3">godmeankeeflat3</a><br /> <!-- ws:start:WikiTextHeadingRule:40:<h2> --><h2 id="toc20"><a name="x19-tone-Superwakalix"></a><!-- ws:end:WikiTextHeadingRule:40 -->Superwakalix</h2> <a class="wiki_link" href="/superclipgenus19">superclipgenus19</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:42:<h1> --><h1 id="toc21"><a name="x22-tone"></a><!-- ws:end:WikiTextHeadingRule:42 -->22-tone</h1> <a class="wiki_link" href="/pajhedgepythquas1">pajhedgepythquas1</a><br /> <a class="wiki_link" href="/pajhedgepythquas2">pajhedgepythquas2</a><br /> <!-- ws:start:WikiTextHeadingRule:44:<h2> --><h2 id="toc22"><a name="x22-tone-Superwakalix"></a><!-- ws:end:WikiTextHeadingRule:44 -->Superwakalix</h2> <a class="wiki_link" href="/hppshq">hppshq</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:46:<h1> --><h1 id="toc23"><a name="x31-tone"></a><!-- ws:end:WikiTextHeadingRule:46 -->31-tone</h1> <!-- ws:start:WikiTextHeadingRule:48:<h2> --><h2 id="toc24"><a name="x31-tone-Superwakalix"></a><!-- ws:end:WikiTextHeadingRule:48 -->Superwakalix</h2> <a class="wiki_link" href="/meansqunumigpopmo">meansqunumigpopmo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:50:<h1> --><h1 id="toc25"><a name="Fifth-repeating wakalixes"></a><!-- ws:end:WikiTextHeadingRule:50 -->Fifth-repeating wakalixes</h1> <a class="wiki_link" href="/superfif7a">superfif7a</a><br /> <a class="wiki_link" href="/superfif7b">superfif7b</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:52:<h1> --><h1 id="toc26"><a name="Divisions of the Tetrachord"></a><!-- ws:end:WikiTextHeadingRule:52 -->Divisions of the Tetrachord</h1> <a class="wiki_link" href="/dicot-meantone%20tetrachord%20arena">dicot-meantone tetrachord arena</a><br /> <a class="wiki_link" href="/dominant-diminished-pajara%20tetrachord%20arena">dominant-diminished-pajara tetrachord arena</a><br /> <a class="wiki_link" href="/august-pajara-augene%20tetrachord%20arena">august-pajara-augene tetrachord arena</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:54:<h1> --><h1 id="toc27"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:54 -->Music</h1> <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=2256" rel="nofollow">Improvisational wakalix survey</a> by Chris Vaisvil<br /> <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>