Lumatone mapping for 39edo: Difference between revisions

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== Augmented + ~~immunity~~ ==

== Augmented + Immunity ==

[[Bryan Deister]] has used a [[porcupine]]-inspired layout for [[39edo]], as demonstrated in [https://www.youtube.com/watch?v=XLRaG_pBN7k&lc=UgwfjZwncsryQjeNUg14AaABAg.AHVkw8aNSEGAHZU_J2qOPM ''39edo jam''] (2025). To take advantage of the fact that 39edo is at the intersection of [[augmented (temperament)|augmented]] and [[immunity]], the rightward generator is 5\39, half of a [[6/5]] minor third as [[12/11]]~[[11/10]] (but much closer to 12/11). This enables a modmos derived from [[1L 6s]] by shrinking the large step from 9\39 to 8\39 and expanding one of the small steps from 5\39 to 6\39, to enable chords such as 12/11 (somewhat sharp, at 5\39) – 6/5 (slightly flat, at 10\39) – [[11/8]] (near-just, at 18\39) – [[3/2]] (mildly sharp, 23\39) – [[18/11]] (moderately sharp, at 28\39) – [[9/5]] (near-just, at 33\39). Playing this chord uses almost the same geometry of depressed keys as that for playing a diatonic scale in a diatonic mapping (but has a very different sound effect), save when proceeding to the next octave. The range is slightly over 6 octaves overall (which slant moderately downwards), but with the first and last octaves missing some notes due to clipping in the upper left and lower right corners of the layout.

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== Semiquartal (~~immunity~~) ==

== Semiquartal (Immunity) ==

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.

The [[immunity]] mapping gives excellent range (over 6⅓ octaves), but the resulting mapping ([[4L 1s]] scale with an 8:7 step ratio and rotated [[5L 4s]] scale with a 7:1 step ratio) is very lopsided; on the other hand, the octaves slope up in this mapping more gently than they slope down on the previous four mappings. [[Bryan Deister]] has used this mapping for [https://www.youtube.com/shorts/oeFI957W-xg ''39edo''] (2023), although not using all of the range due to mapping to a single MIDI channel (and the note 0 position is different).

== 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.

@@ Line 6: / Line 6: @@
 {{Lumatone EDO mapping|n=39|start=6|xstep=7|ystep=-5}}
-== Augmented + immunity ==
+== Augmented + Immunity ==
 [[Bryan Deister]] has used a [[porcupine]]-inspired layout for [[39edo]], as demonstrated in [https://www.youtube.com/watch?v=XLRaG_pBN7k&lc=UgwfjZwncsryQjeNUg14AaABAg.AHVkw8aNSEGAHZU_J2qOPM ''39edo jam''] (2025). To take advantage of the fact that 39edo is at the intersection of [[augmented (temperament)|augmented]] and [[immunity]], the rightward generator is 5\39, half of a [[6/5]] minor third as [[12/11]]~[[11/10]] (but much closer to 12/11). This enables a modmos derived from [[1L&nbsp;6s]] by shrinking the large step from 9\39 to 8\39 and expanding one of the small steps from 5\39 to 6\39, to enable chords such as 12/11 (somewhat sharp, at 5\39) – 6/5 (slightly flat, at 10\39) – [[11/8]] (near-just, at 18\39) – [[3/2]] (mildly sharp, 23\39) – [[18/11]] (moderately sharp, at 28\39) – [[9/5]] (near-just, at 33\39). Playing this chord uses almost the same geometry of depressed keys as that for playing a diatonic scale in a diatonic mapping (but has a very different sound effect), save when proceeding to the next octave. The range is slightly over 6 octaves overall (which slant moderately downwards), but with the first and last octaves missing some notes due to clipping in the upper left and lower right corners of the layout.
@@ Line 23: / Line 23: @@
 {{Lumatone EDO mapping|n=39|start=0|xstep=10|ystep=-7}}
-== Semiquartal (immunity) ==
+== Semiquartal (Immunity) ==
-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.
+The [[immunity]] mapping gives excellent range (over 6⅓ octaves), but the resulting mapping ([[4L&nbsp;1s]] scale with an 8:7 step ratio and rotated [[5L&nbsp;4s]] scale with a 7:1 step ratio) is very lopsided; on the other hand, the octaves slope up in this mapping more gently than they slope down on the previous four mappings. [[Bryan Deister]] has used this mapping for [https://www.youtube.com/shorts/oeFI957W-xg ''39edo''] (2023), although not using all of the range due to mapping to a single MIDI channel (and the note 0 position is different).
 {{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}}