Gallery of wakalixes: Difference between revisions
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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.) | 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]] | * [[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]] | ||
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* [[bluesemarch2]] | * [[bluesemarch2]] | ||
=Hexatonic= | ==Hexatonic== | ||
* [[ternessbabdec]] | * [[ternessbabdec]] | ||
=Heptatonic= | ==Heptatonic== | ||
* [[dimeanmav1]] | * [[dimeanmav1]] | ||
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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]] | ||
=Decatonic= | ==Decatonic== | ||
* [[line10]] | * [[line10]] | ||
* [[cx4]] | * [[cx4]] | ||
=Undecatonic= | ==Undecatonic== | ||
* [[cxi1]] | * [[cxi1]] | ||
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* [[cxi4]] | * [[cxi4]] | ||
=Dodecatonic= | ==Dodecatonic== | ||
* [[biggulp]] | * [[biggulp]] | ||
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* [[hahnZ]] | * [[hahnZ]] | ||
==Superwakalixes== | ===Superwakalixes=== | ||
* [[domdimpajinjmean]] | * [[domdimpajinjmean]] | ||
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* [[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]] | ||
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* [[primewak15]] | * [[primewak15]] | ||
=16-tone= | ==16-tone== | ||
==Supersuperwakalix== | ===Supersuperwakalix=== | ||
* [[supersuper16]] | * [[supersuper16]] | ||
=17-tone= | ==17-tone== | ||
* [[cartwheel]] | * [[cartwheel]] | ||
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* [[wilcent17]] | * [[wilcent17]] | ||
=19-tone= | ==19-tone== | ||
* [[godmeankeeflat1]] | * [[godmeankeeflat1]] | ||
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* [[semmeanflat2]] | * [[semmeanflat2]] | ||
==Superwakalix== | ===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]] | ||
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* [[august-pajara-augene tetrachord arena]] | * [[august-pajara-augene tetrachord arena]] | ||
=Music= | ==Music== | ||
* [http://chrisvaisvil.com/?p=2256 Improvisational wakalix survey] by [[Chris Vaisvil]] | * [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]] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/supersuper16.mp3 Supersuperwakalix16] by [[Billy Stiltner]] | ||
[[Category:Wakalixes| ]] <!-- main article --> | |||
[[Category:Fokker block]] | [[Category:Fokker block]] | ||
[[Category:Just intonation scales]] | [[Category:Just intonation scales]] | ||
[[Category: | [[Category:Lists of scales]] | ||