Gallery of wakalixes: Difference between revisions

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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>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-03-12 14:59:33 UTC</tt>.<br>
: The original revision id was <tt>310248066</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>
<h4>Original Wikitext 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;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.


=Pentatonic=
== Tritonic ==
[[fathbugmean1]]
* [[major and minor triads]]
[[fathbugmean2]]


=Hexatonic=
== Tetratonic ==
[[ternessbabdec]]
* [[addedsixth]]


=Hepatonic=
=== Super8-wakalixes ===
[[dimeanmav1]]
* [[major and minor tetrads]]
[[dimeanmav2]]
* [[supermajor and subminor tetrads]]
[[dimeanporc]]


=Dodecatonic=
== Pentatonic ==
[[meansruhelm]]
* [[fathbugmean1]]
==Superwakalix==
* [[fathbugmean2]]
[[domdimpajinjmean]]
* [[otonalpentad]]
[[domdimpajinjschis]]
* [[utonalpentad]]
* [[triensemarch1]]
* [[triensemarch2]]


=19-tone=
== Hexatonic ==
[[godmeankeeflat1]]
* [[ternessbabdec]]
[[godmeankeeflat2]]
 
[[godmeankeeflat3]]
== Heptatonic ==
</pre></div>
* [[dimeanmav1]]
<h4>Original HTML content:</h4>
* [[dimeanmav2]]
<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;Gallery of Wakalixes&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;em&gt;wakalix&lt;/em&gt; is a &lt;a class="wiki_link" href="/Fokker%20blocks"&gt;Fokker block&lt;/a&gt; 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.&lt;br /&gt;
* [[dimeanporc]]
&lt;br /&gt;
* [[dimavenipu]]
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Pentatonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Pentatonic&lt;/h1&gt;
* [[disixporc1]]
&lt;a class="wiki_link" href="/fathbugmean1"&gt;fathbugmean1&lt;/a&gt;&lt;br /&gt;
* [[disixporc2]]
&lt;a class="wiki_link" href="/fathbugmean2"&gt;fathbugmean2&lt;/a&gt;&lt;br /&gt;
* [[poole]]
&lt;br /&gt;
* [[waka3-7-17]]
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Hexatonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Hexatonic&lt;/h1&gt;
* [[jademohaporc]]
&lt;a class="wiki_link" href="/ternessbabdec"&gt;ternessbabdec&lt;/a&gt;&lt;br /&gt;
* [[ochmohaporc]]
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Hepatonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Hepatonic&lt;/h1&gt;
=== 8-wakalixes ===
&lt;a class="wiki_link" href="/dimeanmav1"&gt;dimeanmav1&lt;/a&gt;&lt;br /&gt;
* [[dudon mohajira117]]
&lt;a class="wiki_link" href="/dimeanmav2"&gt;dimeanmav2&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/dimeanporc"&gt;dimeanporc&lt;/a&gt;&lt;br /&gt;
=== 54-wakalixes ===
&lt;br /&gt;
* [[oheptad]]
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Dodecatonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Dodecatonic&lt;/h1&gt;
* [[uheptad]]
&lt;a class="wiki_link" href="/meansruhelm"&gt;meansruhelm&lt;/a&gt;&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Dodecatonic-Superwakalix"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Superwakalix&lt;/h2&gt;
== Nonatonic ==
&lt;a class="wiki_link" href="/domdimpajinjmean"&gt;domdimpajinjmean&lt;/a&gt;&lt;br /&gt;
* [[mavlim scales]]
&lt;a class="wiki_link" href="/domdimpajinjschis"&gt;domdimpajinjschis&lt;/a&gt;&lt;br /&gt;
* [[phorearmlogic1]]
&lt;br /&gt;
* [[phorearmlogic2]]
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="x19-tone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;19-tone&lt;/h1&gt;
 
&lt;a class="wiki_link" href="/godmeankeeflat1"&gt;godmeankeeflat1&lt;/a&gt;&lt;br /&gt;
== Decatonic ==
&lt;a class="wiki_link" href="/godmeankeeflat2"&gt;godmeankeeflat2&lt;/a&gt;&lt;br /&gt;
* [[line10]]
&lt;a class="wiki_link" href="/godmeankeeflat3"&gt;godmeankeeflat3&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
* [[cx4]]
 
== Undecatonic ==
* [[cxi1]]
* [[cxi2]]
* [[cxi3]]
* [[cxi4]]
 
== Dodecatonic ==
* [[biggulp]]
* [[meansruhelm]]1
* [[meansruhelm2]]
* [[prism (scale)|prism]]
* [[thirteendene]]
* [[wilson class]]
* [[augdimhextrug]]
* [[parizek-miller hexagon]]
* [[ramis]]
* [[hahnZ]]
 
=== 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]]
* [[wilcent17]]
 
== 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 ==
'''[[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]]

Latest revision as of 02:03, 8 March 2026

A wakalix is a scale which is a Fokker block in multiple ways, so that it belongs to more than one Fokker arena. In just intonation, 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

Tetratonic

Super8-wakalixes

Pentatonic

Hexatonic

Heptatonic

8-wakalixes

54-wakalixes

Nonatonic

Decatonic

Undecatonic

Dodecatonic

Superwakalixes

13-tone

Superwakalix

14-tone

15-tone

16-tone

Supersuperwakalix

17-tone

19-tone

Superwakalix

22-tone

Superwakalix

31-tone

Superwakalix

Fifth-repeating wakalixes

Divisions of the Tetrachord

Music

Billy Stiltner

Chris Vaisvil


ViewTalkEditScale galleries
JI scales 12-tone JICombination product setConstant structureHarry Partch-relatedMaximal harmony epimorphicMOS transversalNon-octave JIWakalixZ-polygon transversalOther JI
Full list: Category:Just intonation scales
Tempered scales 11-tone MOS12-tone temperedChromatic pairClipperDouble modeEssentially temperedFantasy detemperMarvel wooMeantoneMin ambiguityMOS cradleNegri-9Neutral thirdNon-octave temperedScalesmith systematicTernaryOther tempered
Full list: Category:Tempered scales
Scales in EDOs in 10edo1113141516171819202122232425262728293031333435363738404142434649537280
All other scale gallery pages are included in Category:Lists of scales