Gallery of wakalixes: Difference between revisions

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Fokker blocks exist in tempered scales
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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]]. 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.)
A '''wakalix''' is a scale which is a [[Fokker block]] in multiple ways, so that it belongs to the 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 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 ==

Revision as of 12:00, 25 March 2025

A wakalix is a scale which is a Fokker block in multiple ways, so that it belongs to the 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


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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
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