Gallery of wakalixes: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>FREEZE
No edit summary
Squib (talk | contribs)
363 edits
m →Dodecatonic: update link
 
(24 intermediate revisions by 12 users not shown)
Line 1: Line 1:
__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=
== Tritonic ==
[[major_and_minor_triads|major and minor triads]]
* [[major and minor triads]]


=Tetratonic=
== Tetratonic ==
[[addedsixth|addedsixth]]
* [[addedsixth]]


==Super8-wakalixes==
=== Super8-wakalixes ===
[[major_and_minor_tetrads|major and minor tetrads]]
* [[major and minor tetrads]]
* [[supermajor and subminor tetrads]]


[[supermajor_and_subminor_tetrads|supermajor and subminor tetrads]]
== Pentatonic ==
* [[fathbugmean1]]
* [[fathbugmean2]]
* [[otonalpentad]]
* [[utonalpentad]]
* [[triensemarch1]]
* [[triensemarch2]]


=Pentatonic=
== Hexatonic ==
[[fathbugmean1|fathbugmean1]]
* [[ternessbabdec]]


[[fathbugmean2|fathbugmean2]]
== Heptatonic ==
* [[dimeanmav1]]
* [[dimeanmav2]]
* [[dimeanporc]]
* [[dimavenipu]]
* [[disixporc1]]
* [[disixporc2]]
* [[poole]]
* [[waka3-7-17]]
* [[jademohaporc]]
* [[ochmohaporc]]


[[otonalpentad|otonalpentad]]
=== 8-wakalixes ===
* [[dudon mohajira117]]


[[utonalpentad|utonalpentad]]
=== 54-wakalixes ===
* [[oheptad]]
* [[uheptad]]


[[bluesemarch1|bluesemarch1]]
== Nonatonic ==
* [[mavlim scales]]
* [[phorearmlogic1]]
* [[phorearmlogic2]]


[[bluesemarch2|bluesemarch2]]
== Decatonic ==
* [[line10]]
* [[cx4]]


=Hexatonic=
== Undecatonic ==
[[ternessbabdec|ternessbabdec]]
* [[cxi1]]
* [[cxi2]]
* [[cxi3]]
* [[cxi4]]


=Heptatonic=
== Dodecatonic ==
[[dimeanmav1|dimeanmav1]]
* [[biggulp]]
* [[meansruhelm]]1
* [[meansruhelm2]]
* [[prism (scale)|prism]]
* [[thirteendene]]
* [[wilson class]]
* [[augdimhextrug]]
* [[parizek-miller hexagon]]
* [[ramis]]
* [[hahnZ]]


[[dimeanmav2|dimeanmav2]]
=== Superwakalixes ===
* [[domdimpajinjmean]]
* [[domdimpajinjschis]]
* [[collapsar]]


[[dimeanporc|dimeanporc]]
== 13-tone ==
* [[dwarf13 7d]]


[[dimavenipu|dimavenipu]]
=== Superwakalix ===
* [[supertriskaideka]]


[[poole|poole]]
== 14-tone ==
* [[parrot]]


[[waka3-7-17|waka3-7-17]]
== 15-tone ==
* [[blackopkeegil1]]
* [[blackopkeegil2]]
* [[primewak15]]


[[jademohaporc|jademohaporc]]
== 16-tone ==
=== Supersuperwakalix ===
* [[supersuper16]]


[[ochmohaporc|ochmohaporc]]
== 17-tone ==
* [[cartwheel]]
* [[parizekhex]]
* [[wilcent17]]


==8-wakalixes==
== 19-tone ==
[[dudon_mohajira117|dudon_mohajira117]]
* [[godmeankeeflat1]]
* [[godmeankeeflat2]]
* [[godmeankeeflat3]]


==54-wakalixes==
=== Superwakalix ===
[[oheptad|oheptad]]
* [[superclipgenus19]]


[[uheptad|uheptad]]
== 22-tone ==
* [[pajhedgepythquas1]]
* [[pajhedgepythquas2]]


=Nonatonic=
=== Superwakalix ===
[[mavlim_scales|mavlim scales]]
* [[hppshq]]


=Decatonic=
== 31-tone ==
[[line10|line10]]
=== Superwakalix ===
* [[meansqunumigpopmo]]


[[cx4|cx4]]
== Fifth-repeating wakalixes ==
* [[superfif7a]]
* [[superfif7b]]


=Undecatonic=
== Divisions of the Tetrachord ==
[[cxi1|cxi1]]
* [[dicot-meantone tetrachord arena]]
* [[dominant-diminished-pajara tetrachord arena]]
* [[august-pajara-augene tetrachord arena]]


[[cxi2|cxi2]]
== 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]


[[cxi3|cxi3]]
{{Navbox scale gallery}}


[[cxi4|cxi4]]
[[Category:Wakalixes| ]] <!-- main article -->
 
[[Category:Fokker block]]
=Dodecatonic=
[[Category:Just intonation scales]]
[[biggulp|biggulp]]
[[Category:Pages with mostly numerical content]]
 
[[Category:Lists of scales]]
[[meansruhelm|meansruhelm]]
 
[[prism|prism]]
 
[[thirteendene|thirteendene]]
 
[[wilson_class|wilson_class]]
 
[[augdimhextrug|augdimhextrug]]
 
[[parizek-miller_hexagon|parizek-miller hexagon]]
 
[[ramis|ramis]]
 
[[hahnZ|hahnZ]]
 
==Superwakalixes==
[[domdimpajinjmean|domdimpajinjmean]]
 
[[domdimpajinjschis|domdimpajinjschis]]
 
[[collapsar|collapsar]]
 
=13-tone=
[[dwarf13_7d|dwarf13_7d]]
 
==Superwakalix==
[[supertriskaideka|supertriskaideka]]
 
=14-tone=
[[parrot|parrot]]
 
=15-tone=
[[blackopkeegil1|blackopkeegil1]]
 
[[blackopkeegil2|blackopkeegil2]]
 
[[primewak15|primewak15]]
 
=16-tone=
 
==Supersuperwakalix==
[[supersuper16|supersuper16]]
 
=17-tone=
[[cartwheel|cartwheel]]
 
[[parizekhex|parizekhex]]
 
[[wilcent17|wilcent17]]
 
=19-tone=
[[godmeankeeflat1|godmeankeeflat1]]
 
[[godmeankeeflat2|godmeankeeflat2]]
 
[[godmeankeeflat3|godmeankeeflat3]]
 
[[semmeanflat1|semmeanflat1]]
 
[[semmeanflat2|semmeanflat2]]
 
==Superwakalix==
[[superclipgenus19|superclipgenus19]]
 
=22-tone=
[[pajhedgepythquas1|pajhedgepythquas1]]
 
[[pajhedgepythquas2|pajhedgepythquas2]]
 
==Superwakalix==
[[hppshq|hppshq]]
 
=31-tone=
 
==Superwakalix==
[[meansqunumigpopmo|meansqunumigpopmo]]
 
=Fifth-repeating wakalixes=
[[superfif7a|superfif7a]]
 
[[superfif7b|superfif7b]]
 
=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=
[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]]
[[Category:scales]]
[[Category:wakalix]]

Latest revision as of 02:03, 8 March 2026

A wakalix is a scale which is a Fokker block in multiple ways, so that it belongs to more than one Fokker arena. In just intonation, 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

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

Music

Billy Stiltner

Chris Vaisvil


View • Talk • EditScale galleries
JI scales 12-tone JI • Combination product set • Constant structure • Harry Partch-related • Maximal harmony epimorphic • MOS transversal • Non-octave JI • Wakalix • Z-polygon transversal • Other JI
Full list: Category:Just intonation scales
Tempered scales 11-tone MOS • 12-tone tempered • Chromatic pair • Clipper • Double mode • Essentially tempered • Fantasy detemper • Marvel woo • Meantone • Min ambiguity • MOS cradle • Negri-9 • Neutral third • Non-octave tempered • Scalesmith systematic • Ternary • Other tempered
Full list: Category:Tempered scales
Scales in EDOs in 10edo • 11 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 33 • 34 • 35 • 36 • 37 • 38 • 40 • 41 • 42 • 43 • 46 • 49 • 53 • 72 • 80
All other scale gallery pages are included in Category:Lists of scales
Retrieved from "https://en.xen.wiki/index.php?title=Gallery_of_wakalixes&oldid=225405"