Gallery of wakalixes: Difference between revisions
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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 [[ | |||
== Tritonic == | |||
* [[major and minor triads]] | * [[major and minor triads]] | ||
=Tetratonic= | == Tetratonic == | ||
* [[addedsixth]] | * [[addedsixth]] | ||
==Super8-wakalixes== | === Super8-wakalixes === | ||
* [[major and minor tetrads]] | * [[major and minor tetrads]] | ||
* [[supermajor and subminor tetrads]] | * [[supermajor and subminor tetrads]] | ||
=Pentatonic= | == Pentatonic == | ||
* [[fathbugmean1]] | * [[fathbugmean1]] | ||
* [[fathbugmean2]] | * [[fathbugmean2]] | ||
* [[otonalpentad]] | * [[otonalpentad]] | ||
* [[utonalpentad]] | * [[utonalpentad]] | ||
* [[ | * [[triensemarch1]] | ||
* [[ | * [[triensemarch2]] | ||
== Hexatonic == | |||
* [[ternessbabdec]] | * [[ternessbabdec]] | ||
=Heptatonic= | == Heptatonic == | ||
* [[dimeanmav1]] | * [[dimeanmav1]] | ||
* [[dimeanmav2]] | * [[dimeanmav2]] | ||
* [[dimeanporc]] | * [[dimeanporc]] | ||
* [[dimavenipu]] | * [[dimavenipu]] | ||
* [[disixporc1]] | |||
* [[disixporc2]] | |||
* [[poole]] | * [[poole]] | ||
* [[waka3-7-17]] | * [[waka3-7-17]] | ||
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* [[ochmohaporc]] | * [[ochmohaporc]] | ||
==8-wakalixes== | === 8-wakalixes === | ||
* [[dudon mohajira117]] | * [[dudon mohajira117]] | ||
==54-wakalixes== | === 54-wakalixes === | ||
* [[oheptad]] | * [[oheptad]] | ||
* [[uheptad]] | * [[uheptad]] | ||
=Nonatonic= | == Nonatonic == | ||
* [[mavlim scales]] | * [[mavlim scales]] | ||
* [[phorearmlogic1]] | |||
* [[phorearmlogic2]] | |||
=Decatonic= | == Decatonic == | ||
* [[line10]] | * [[line10]] | ||
* [[cx4]] | * [[cx4]] | ||
=Undecatonic= | == Undecatonic == | ||
* [[cxi1]] | * [[cxi1]] | ||
* [[cxi2]] | * [[cxi2]] | ||
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* [[cxi4]] | * [[cxi4]] | ||
=Dodecatonic= | == Dodecatonic == | ||
* [[biggulp]] | * [[biggulp]] | ||
* [[meansruhelm]]1 | * [[meansruhelm]]1 | ||
* [[meansruhelm2]] | * [[meansruhelm2]] | ||
* [[prism]] | * [[prism (scale)|prism]] | ||
* [[thirteendene]] | * [[thirteendene]] | ||
* [[wilson class]] | * [[wilson class]] | ||
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* [[hahnZ]] | * [[hahnZ]] | ||
==Superwakalixes== | === Superwakalixes === | ||
* [[domdimpajinjmean]] | * [[domdimpajinjmean]] | ||
* [[domdimpajinjschis]] | * [[domdimpajinjschis]] | ||
* [[collapsar]] | * [[collapsar]] | ||
=13-tone= | == 13-tone == | ||
* [[dwarf13 7d]] | * [[dwarf13 7d]] | ||
==Superwakalix== | === Superwakalix === | ||
* [[supertriskaideka]] | * [[supertriskaideka]] | ||
=14-tone= | == 14-tone == | ||
* [[parrot]] | * [[parrot]] | ||
=15-tone= | == 15-tone == | ||
* [[blackopkeegil1]] | * [[blackopkeegil1]] | ||
* [[blackopkeegil2]] | * [[blackopkeegil2]] | ||
* [[primewak15]] | * [[primewak15]] | ||
=16-tone= | == 16-tone == | ||
=== Supersuperwakalix === | |||
==Supersuperwakalix== | |||
* [[supersuper16]] | * [[supersuper16]] | ||
=17-tone= | == 17-tone == | ||
* [[cartwheel]] | * [[cartwheel]] | ||
* [[parizekhex]] | * [[parizekhex]] | ||
* [[wilcent17]] | * [[wilcent17]] | ||
=19-tone= | == 19-tone == | ||
* [[godmeankeeflat1]] | * [[godmeankeeflat1]] | ||
* [[godmeankeeflat2]] | * [[godmeankeeflat2]] | ||
* [[godmeankeeflat3]] | * [[godmeankeeflat3]] | ||
=== Superwakalix === | |||
* [[superclipgenus19]] | * [[superclipgenus19]] | ||
=22-tone= | == 22-tone == | ||
* [[pajhedgepythquas1]] | * [[pajhedgepythquas1]] | ||
* [[pajhedgepythquas2]] | * [[pajhedgepythquas2]] | ||
==Superwakalix== | === Superwakalix === | ||
* [[hppshq]] | * [[hppshq]] | ||
=31-tone= | == 31-tone == | ||
=== Superwakalix === | |||
==Superwakalix== | |||
* [[meansqunumigpopmo]] | * [[meansqunumigpopmo]] | ||
=Fifth-repeating wakalixes= | == Fifth-repeating wakalixes == | ||
* [[superfif7a]] | * [[superfif7a]] | ||
* [[superfif7b]] | * [[superfif7b]] | ||
=Divisions of the Tetrachord= | == Divisions of the Tetrachord == | ||
* [[dicot-meantone tetrachord arena]] | * [[dicot-meantone tetrachord arena]] | ||
* [[dominant-diminished-pajara tetrachord arena]] | * [[dominant-diminished-pajara tetrachord arena]] | ||
* [[august-pajara-augene tetrachord arena]] | * [[august-pajara-augene tetrachord arena]] | ||
=Music= | == 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:Fokker block]] | ||
[[Category:Just intonation scales]] | [[Category:Just intonation scales]] | ||
[[Category: | [[Category:Pages with mostly numerical content]] | ||
[[Category:Lists of scales]] | |||