Lumatone mapping for 39edo: Difference between revisions

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~~There are many conceivable ways to map [[39edo]] onto~~ the [[~~Lumatone~~]] ~~keyboard. Only one~~, ~~however, agrees with~~ the ~~[[Standard Lumatone mapping~~ for ~~Pythagorean]]~~.

== Diatonic ==

Although not as imbalanced as the diatonic scale for [[37edo]] (step ratio 7:1), the diatonic scale for 39edo is still fairly imbalanced (step ratio 7:2).

Since it is ~~it's~~ optimal patent val, the [[triforce]] mapping is also a particularly good way to organise the intervals of 39edo.

== 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.

== Triforce ==

Since it is its optimal patent val, the [[triforce]] mapping is also a particularly good way to organise the intervals of 39edo.

The [[~~immunity]] and [[~~amity]] ~~mappings are~~ also above average at putting good intervals close together, and ~~make~~ chromatic runs much easier than the previous two layouts.

== Amity ==

The [[Lumatone mapping for amity]] is also above average at putting good intervals close together, and makes chromatic runs much easier than the previous two layouts.

== Familia ==

Related to amity is [[Amity_family#Familia|familia]]. [[Bryan Deister]] has demonstrated a [[3L 4s]] (10:3 step ratio) layout for this, in [https://www.youtube.com/shorts/1T_xrZpUslQ ''39edo improv''] (2025). Right by 1 key (10\39) is a somewhat flat classic minor third ~[[6/5]], while down-right by 1 key (3\39) functions both as an inconsistently mapped sharp diptolmeic chromatic semitone (~[[25/24]]) and an inconsistently mapped flat ptolemaic diatonic semitone (~[[16/15]]), which means that right 1 key + down-right 1 key (total 13\39) yields a sharp (400{{c}}) classic major third ~[[5/4]]). The range is six octaves, although the octaves slope down enough to cause a vertical wraparound.

== 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.

== 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.

~~{{Lumatone mapping navigation~~}}

~~[[Category:~~Lumatone ~~mappings]] [[Category:39edo]]~~

@@ Line 1: / Line 1: @@
-There are many conceivable ways to map [[39edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]].
+{{Lumatone mapping intro}}
+== Diatonic ==
+Although not as imbalanced as the diatonic scale for [[37edo]] (step ratio 7:1), the diatonic scale for 39edo is still fairly imbalanced (step ratio 7:2).
 {{Lumatone EDO mapping|n=39|start=6|xstep=7|ystep=-5}}
-Since it is it's optimal patent val, the [[triforce]] mapping is also a particularly good way to organise the intervals of 39edo.
+== 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.
+{{Lumatone EDO mapping|n=39|start=34|xstep=5|ystep=3}}
+== Triforce ==
+Since it is its optimal patent val, the [[triforce]] mapping is also a particularly good way to organise the intervals of 39edo.
 {{Lumatone EDO mapping|n=39|start=0|xstep=8|ystep=-3}}
-The [[immunity]] and [[amity]] mappings are also above average at putting good intervals close together, and make chromatic runs much easier than the previous two layouts.
+== Amity ==
+The [[Lumatone mapping for amity]] is also above average at putting good intervals close together, and makes chromatic runs much easier than the previous two layouts.
+{{Lumatone EDO mapping|n=39|start=0|xstep=6|ystep=-1}}
+== Familia ==
+Related to amity is [[Amity_family#Familia|familia]]. [[Bryan Deister]] has demonstrated a [[3L&nbsp;4s]] (10:3 step ratio) layout for this, in [https://www.youtube.com/shorts/1T_xrZpUslQ ''39edo improv''] (2025). Right by 1 key (10\39) is a somewhat flat classic minor third ~[[6/5]], while down-right by 1 key (3\39) functions both as an inconsistently mapped sharp diptolmeic chromatic semitone (~[[25/24]]) and an inconsistently mapped flat ptolemaic diatonic semitone (~[[16/15]]), which means that right 1 key + down-right 1 key (total 13\39) yields a sharp (400{{c}}) classic major third ~[[5/4]]). The range is six octaves, although the octaves slope down enough to cause a vertical wraparound.
+{{Lumatone EDO mapping|n=39|start=0|xstep=10|ystep=-7}}
+== 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.
 {{Lumatone EDO mapping|n=39|start=21|xstep=8|ystep=-1}}
-{{Lumatone EDO mapping|n=39|start=0|xstep=6|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 mapping navigation}}
+{{Lumatone EDO mapping|n=39|start=27|xstep=5|ystep=-1}}
-[[Category:Lumatone mappings]] [[Category:39edo]]
+{{Navbox Lumatone}}