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-__FORCETOC__
+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.)
-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]]
-=Tritonic=
+== Tetratonic ==
-[[major and minor triads]]
+* [[addedsixth]]
-=Tetratonic=
+=== Super8-wakalixes ===
-[[addedsixth]]
+* [[major and minor tetrads]]
+* [[supermajor and subminor tetrads]]
-==Super8-wakalixes==
+== Pentatonic ==
-[[major and minor tetrads]]
+* [[fathbugmean1]]
+* [[fathbugmean2]]
+* [[otonalpentad]]
+* [[utonalpentad]]
+* [[triensemarch1]]
+* [[triensemarch2]]
-[[supermajor and subminor tetrads]]
+== Hexatonic ==
+* [[ternessbabdec]]
-=Pentatonic=
+== Heptatonic ==
-[[fathbugmean1]]
+* [[dimeanmav1]]
+* [[dimeanmav2]]
+* [[dimeanporc]]
+* [[dimavenipu]]
+* [[disixporc1]]
+* [[disixporc2]]
+* [[poole]]
+* [[waka3-7-17]]
+* [[jademohaporc]]
+* [[ochmohaporc]]
-[[fathbugmean2]]
+=== 8-wakalixes ===
+* [[dudon mohajira117]]
-[[otonalpentad]]
+=== 54-wakalixes ===
+* [[oheptad]]
+* [[uheptad]]
-[[utonalpentad]]
+== Nonatonic ==
+* [[mavlim scales]]
+* [[phorearmlogic1]]
+* [[phorearmlogic2]]
-[[bluesemarch1]]
+== Decatonic ==
+* [[line10]]
+* [[cx4]]
-[[bluesemarch2]]
+== Undecatonic ==
+* [[cxi1]]
+* [[cxi2]]
+* [[cxi3]]
+* [[cxi4]]
-=Hexatonic=
+== Dodecatonic ==
-[[ternessbabdec]]
+* [[biggulp]]
+* [[meansruhelm]]1
+* [[meansruhelm2]]
+* [[prism (scale)|prism]]
+* [[thirteendene]]
+* [[wilson class]]
+* [[augdimhextrug]]
+* [[parizek-miller hexagon]]
+* [[ramis]]
+* [[hahnZ]]
-=Heptatonic=
+=== Superwakalixes ===
-[[dimeanmav1]]
+* [[domdimpajinjmean]]
+* [[domdimpajinjschis]]
+* [[collapsar]]
-[[dimeanmav2]]
+== 13-tone ==
+* [[dwarf13 7d]]
-[[dimeanporc]]
+=== Superwakalix ===
+* [[supertriskaideka]]
-[[dimavenipu]]
+== 14-tone ==
+* [[parrot]]
-[[poole]]
+== 15-tone ==
+* [[blackopkeegil1]]
+* [[blackopkeegil2]]
+* [[primewak15]]
-[[waka3-7-17]]
+== 16-tone ==
+=== Supersuperwakalix ===
+* [[supersuper16]]
-[[jademohaporc]]
+== 17-tone ==
+* [[cartwheel]]
+* [[parizekhex]]
+* [[wilcent17]]
-[[ochmohaporc]]
+== 19-tone ==
+* [[godmeankeeflat1]]
+* [[godmeankeeflat2]]
+* [[godmeankeeflat3]]
-==8-wakalixes==
+=== Superwakalix ===
-[[dudon mohajira117|dudon_mohajira117]]
+* [[superclipgenus19]]
-==54-wakalixes==
+== 22-tone ==
-[[oheptad]]
+* [[pajhedgepythquas1]]
+* [[pajhedgepythquas2]]
-[[uheptad]]
+=== Superwakalix ===
+* [[hppshq]]
-=Nonatonic=
+== 31-tone ==
-[[mavlim scales]]
+=== Superwakalix ===
+* [[meansqunumigpopmo]]
-=Decatonic=
+== Fifth-repeating wakalixes ==
-[[line10]]
+* [[superfif7a]]
+* [[superfif7b]]
-[[cx4]]
+== Divisions of the Tetrachord ==
+* [[dicot-meantone tetrachord arena]]
+* [[dominant-diminished-pajara tetrachord arena]]
+* [[august-pajara-augene tetrachord arena]]
-=Undecatonic=
+== Music ==
-[[cxi1]]
+'''[[Billy Stiltner]]'''
+* [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/supersuper16.mp3 Supersuperwakalix16]
+'''[[Chris Vaisvil]]'''
+* [http://chrisvaisvil.com/?p=2256 Improvisational wakalix survey]
-[[cxi2]]
+{{Navbox scale gallery}}
-[[cxi3]]
+[[Category:Wakalixes| ]] <!-- main article -->
+[[Category:Fokker block]]
-[[cxi4]]
-=Dodecatonic=
-[[biggulp]]
-[[meansruhelm]]1
-[[meansruhelm2]]
-[[prism]]
-[[thirteendene]]
-[[wilson class|wilson_class]]
-[[augdimhextrug]]
-[[parizek-miller hexagon]]
-[[ramis]]
-[[hahnZ]]
-==Superwakalixes==
-[[domdimpajinjmean]]
-[[domdimpajinjschis]]
-[[collapsar]]
-=13-tone=
-[[dwarf13 7d|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]]
-[[semmeanflat1]]
-[[semmeanflat2]]
-==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
-[[Category:fokker block]]
-[[Category:gallery]]
 [[Category:Just intonation scales]]
-[[Category:wakalix]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Lists of scales]]

Gallery of wakalixes: Difference between revisions