Lumatone mapping for 39edo: Difference between revisions

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The [[immunity]] mapping gives excellent range (over 6⅓ octaves), but the resulting [[5L 4s]] scale has a 7:1 step ratio, which makes it very lopsided; on the other hand, the octaves slope up in this mapping more gently than they slope down on the previous four mappings.

== Biyatismic ==

[[Bryan Deister]] has used a [[Biyatismic_clan|biyatismic]] layout with a [[7L 1s]] scale (5:4 step ratio) for [[39edo]], as demonstrated in [https://www.youtube.com/shorts/Tf812DJzoEA ''<nowiki>Tilt Your Head Down - 39edo [short]</nowiki>''] (2026). The rightward generator 4\39 is a combination of the Alpharabian tendoneutral second ~[[12/11]] and the undecimal submajor second ~[[11/10]], and two of these make a near-just classic minor third ~[[6/5]], with the biyatisma ([[121/120]]) being tempered out. Although biyatismic is technically rank-3 or rank-4, it functions here as a rank-2 temperament, filling in several useful intervals by rightward progression and octave-reduction: four of these generators make a near-just septimal tritone ~[[10/7]]; five of them make a flat pentacircle minor sixth ~[[11/7]] or a somewhat sharp septimal minor sixth ~[[14/9]]; and six of them make a flat septimal major sixth ~[[12/7]]. After octave-reduction, nine of them make a slightly sharp classic whole tone ~[[10/9]]; ten of them make a flat Alpharabian artoneutral third ~[[11/9]]; eleven of them make a flat fourth ~[[4/3]]; twelve of them make a slightly flat Axirabian paraminor fifth ~[[16/11]]; and thirteen of them make a flat classic minor sixth ~[[8/5]]. The range is just under four octaves, and the octaves slant up.

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 The [[immunity]] mapping gives excellent range (over 6⅓ octaves), but the resulting [[5L&nbsp;4s]] scale has a 7:1 step ratio, which makes it very lopsided; on the other hand, the octaves slope up in this mapping more gently than they slope down on the previous four mappings.
 {{Lumatone EDO mapping|n=39|start=21|xstep=8|ystep=-1}}
+== Biyatismic ==
+[[Bryan Deister]] has used a [[Biyatismic_clan|biyatismic]] layout with a [[7L&nbsp;1s]] scale (5:4 step ratio) for [[39edo]], as demonstrated in [https://www.youtube.com/shorts/Tf812DJzoEA ''<nowiki>Tilt Your Head Down - 39edo [short]</nowiki>''] (2026). The rightward generator 4\39 is a combination of the Alpharabian tendoneutral second ~[[12/11]] and the undecimal submajor second ~[[11/10]], and two of these make a near-just classic minor third ~[[6/5]], with the biyatisma ([[121/120]]) being tempered out. Although biyatismic is technically rank-3 or rank-4, it functions here as a rank-2 temperament, filling in several useful intervals by rightward progression and octave-reduction: four of these generators make a near-just septimal tritone ~[[10/7]]; five of them make a flat pentacircle minor sixth ~[[11/7]] or a somewhat sharp septimal minor sixth ~[[14/9]]; and six of them make a flat septimal major sixth ~[[12/7]]. After octave-reduction, nine of them make a slightly sharp classic whole tone ~[[10/9]]; ten of them make a flat Alpharabian artoneutral third ~[[11/9]]; eleven of them make a flat fourth ~[[4/3]]; twelve of them make a slightly flat Axirabian paraminor fifth ~[[16/11]]; and thirteen of them make a flat classic minor sixth ~[[8/5]]. The range is just under four octaves, and the octaves slant up.
+{{Lumatone EDO mapping|n=39|start=27|xstep=5|ystep=-1}}
 {{Navbox Lumatone}}