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]] 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.

== Semiquartal (Immunity) ==

The [[Immunity]] mapping gives excellent range, but the resulting [[5L 4s]] scale has a 7:1 step ratio, which makes it very lopsided.

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

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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]].
+{{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]] 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}}
+== Semiquartal (Immunity) ==
+The [[Immunity]] mapping gives excellent range, but the resulting [[5L&nbsp;4s]] scale has a 7:1 step ratio, which makes it very lopsided.
 {{Lumatone EDO mapping|n=39|start=21|xstep=8|ystep=-1}}
-{{Lumatone EDO mapping|n=39|start=0|xstep=6|ystep=-1}}
+{{Navbox Lumatone}}
-[[Category:Lumatone mappings]] [[Category:39edo]]