Gallery of wakalixes: Difference between revisions
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A '''wakalix''' is a [[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 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]] | ||
* [[fathbugmean2]] | * [[fathbugmean2]] | ||
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* [[triensemarch2]] | * [[triensemarch2]] | ||
==Hexatonic== | == Hexatonic == | ||
* [[ternessbabdec]] | * [[ternessbabdec]] | ||
==Heptatonic== | == Heptatonic == | ||
* [[dimeanmav1]] | * [[dimeanmav1]] | ||
* [[dimeanmav2]] | * [[dimeanmav2]] | ||
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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]] | * [[phorearmlogic1]] | ||
* [[phorearmlogic2]] | * [[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 | ||
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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=== | === 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]]''' | '''[[Billy Stiltner]]''' | ||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/supersuper16.mp3 Supersuperwakalix16] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/supersuper16.mp3 Supersuperwakalix16] | ||
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* [http://chrisvaisvil.com/?p=2256 Improvisational wakalix survey] | * [http://chrisvaisvil.com/?p=2256 Improvisational wakalix survey] | ||
{{ | {{Navbox scale gallery}} | ||
[[Category:Wakalixes| ]] | [[Category:Wakalixes| ]] <!-- main article --> | ||
<!-- main article --> | |||
[[Category:Fokker block]] | [[Category:Fokker block]] | ||
[[Category:Just intonation scales]] | [[Category:Just intonation scales]] | ||
[[Category:Lists of scales]] | [[Category:Lists of scales]] | ||
Revision as of 20:08, 11 February 2025
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
Pentatonic
Hexatonic
Heptatonic
- dimeanmav1
- dimeanmav2
- dimeanporc
- dimavenipu
- disixporc1
- disixporc2
- poole
- waka3-7-17
- jademohaporc
- ochmohaporc
8-wakalixes
54-wakalixes
Nonatonic
Decatonic
Undecatonic
Dodecatonic
- biggulp
- meansruhelm1
- meansruhelm2
- prism
- thirteendene
- wilson class
- augdimhextrug
- parizek-miller hexagon
- ramis
- hahnZ
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
| View • Talk • EditScale galleries | |
|---|---|
| JI scales | 12-tone JI scales • Combination product sets • CS scales • Maximal harmony epimorphic scales • MOS transversals • Non-octave JI scales • Wakalixes • Z-polygon transversals • Other JI scales Full list: Category:Just intonation scales |
| Tempered scales | 12-tone tempered scales • Clippers • Essentially tempered scales • Marvel woo scales • MOS cradle scales • Non-octave tempered scales • Scalesmith systematic scales • Other tempered scales Full list: Category:Tempered scales |
| ET subsets | 11edo modes, 19edo modes, 22edo modes, 24edo scales, 31edo modes |
All other scale gallery pages are included in Category:Lists of scales | |