Gallery of wakalixes: Difference between revisions
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A ''wakalix'' is a [[ | 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= | =Tritonic= | ||
[[ | [[major and minor triads]] | ||
=Tetratonic= | =Tetratonic= | ||
[[ | [[addedsixth]] | ||
==Super8-wakalixes== | ==Super8-wakalixes== | ||
[[ | [[major and minor tetrads]] | ||
[[ | [[supermajor and subminor tetrads]] | ||
=Pentatonic= | =Pentatonic= | ||
[[ | [[fathbugmean1]] | ||
[[ | [[fathbugmean2]] | ||
[[ | [[otonalpentad]] | ||
[[ | [[utonalpentad]] | ||
[[ | [[bluesemarch1]] | ||
[[ | [[bluesemarch2]] | ||
=Hexatonic= | =Hexatonic= | ||
[[ | [[ternessbabdec]] | ||
=Heptatonic= | =Heptatonic= | ||
[[ | [[dimeanmav1]] | ||
[[ | [[dimeanmav2]] | ||
[[ | [[dimeanporc]] | ||
[[ | [[dimavenipu]] | ||
[[ | [[poole]] | ||
[[ | [[waka3-7-17]] | ||
[[ | [[jademohaporc]] | ||
[[ | [[ochmohaporc]] | ||
==8-wakalixes== | ==8-wakalixes== | ||
[[ | [[dudon mohajira117|dudon_mohajira117]] | ||
==54-wakalixes== | ==54-wakalixes== | ||
[[ | [[oheptad]] | ||
[[ | [[uheptad]] | ||
=Nonatonic= | =Nonatonic= | ||
[[ | [[mavlim scales]] | ||
=Decatonic= | =Decatonic= | ||
[[ | [[line10]] | ||
[[ | [[cx4]] | ||
=Undecatonic= | =Undecatonic= | ||
[[ | [[cxi1]] | ||
[[ | [[cxi2]] | ||
[[ | [[cxi3]] | ||
[[ | [[cxi4]] | ||
=Dodecatonic= | =Dodecatonic= | ||
[[ | [[biggulp]] | ||
[[ | [[meansruhelm]]1 | ||
[[meansruhelm2]] | [[meansruhelm2]] | ||
[[ | [[prism]] | ||
[[ | [[thirteendene]] | ||
[[ | [[wilson class|wilson_class]] | ||
[[ | [[augdimhextrug]] | ||
[[ | [[parizek-miller hexagon]] | ||
[[ | [[ramis]] | ||
[[ | [[hahnZ]] | ||
==Superwakalixes== | ==Superwakalixes== | ||
[[ | [[domdimpajinjmean]] | ||
[[ | [[domdimpajinjschis]] | ||
[[ | [[collapsar]] | ||
=13-tone= | =13-tone= | ||
[[ | [[dwarf13 7d|dwarf13_7d]] | ||
==Superwakalix== | ==Superwakalix== | ||
[[ | [[supertriskaideka]] | ||
=14-tone= | =14-tone= | ||
[[ | [[parrot]] | ||
=15-tone= | =15-tone= | ||
[[ | [[blackopkeegil1]] | ||
[[ | [[blackopkeegil2]] | ||
[[ | [[primewak15]] | ||
=16-tone= | =16-tone= | ||
==Supersuperwakalix== | ==Supersuperwakalix== | ||
[[ | [[supersuper16]] | ||
=17-tone= | =17-tone= | ||
[[ | [[cartwheel]] | ||
[[ | [[parizekhex]] | ||
[[ | [[wilcent17]] | ||
=19-tone= | =19-tone= | ||
[[ | [[godmeankeeflat1]] | ||
[[ | [[godmeankeeflat2]] | ||
[[ | [[godmeankeeflat3]] | ||
[[ | [[semmeanflat1]] | ||
[[ | [[semmeanflat2]] | ||
==Superwakalix== | ==Superwakalix== | ||
[[ | [[superclipgenus19]] | ||
=22-tone= | =22-tone= | ||
[[ | [[pajhedgepythquas1]] | ||
[[ | [[pajhedgepythquas2]] | ||
==Superwakalix== | ==Superwakalix== | ||
[[ | [[hppshq]] | ||
=31-tone= | =31-tone= | ||
==Superwakalix== | ==Superwakalix== | ||
[[ | [[meansqunumigpopmo]] | ||
=Fifth-repeating wakalixes= | =Fifth-repeating wakalixes= | ||
[[ | [[superfif7a]] | ||
[[ | [[superfif7b]] | ||
=Divisions of the Tetrachord= | =Divisions of the Tetrachord= | ||
[[ | [[dicot-meantone tetrachord arena]] | ||
[[ | [[dominant-diminished-pajara tetrachord arena]] | ||
[[ | [[august-pajara-augene tetrachord arena]] | ||
=Music= | =Music= | ||
Revision as of 13:51, 5 December 2020
A wakalix is a Fokker block which is a Fokker block in more than one way, so that it belongs in more than one 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
Tetratonic
Super8-wakalixes
supermajor and subminor tetrads
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
dicot-meantone tetrachord arena
dominant-diminished-pajara tetrachord arena
august-pajara-augene tetrachord arena
Music
Improvisational wakalix survey by Chris Vaisvil
Supersuperwakalix16 by Billy Stiltner