Lumatone mapping for 28edo: Difference between revisions

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~~There are many conceivable ways to map [[28edo]] onto the~~ [[~~Lumatone~~]] ~~keyboard. However, as it has multiple small rings of 5ths, the [[Standard Lumatone~~ mapping ~~for Pythagorean]]~~ is ~~not one of them. Instead,~~ the most diatonic-like mapping ~~is the~~ [[~~whitewood~~]] ~~one~~.

== Whitewood ==

The [[Whitewood]] mapping is perhaps the most diatonic-like mapping that covers all notes. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/1nWL2qEcI-Q ''28edo improvisation''] (2022).

Since the 5th harmonic is easily the best tuned interval, the [[~~Wuerschmidt~~]] mapping is a good way to maximise your range and make consonant chords easy to reach.

== Diminished (Demolished) + Würschmidt ==

It is possible to generate [[28edo]] using its near-just classic major third ~[[5/4]] represented by 9\28 (one key right plus one key down-right) as in [[Würschmidt]] temperament, producing a [[3L 1s]] scale with a 9:1 step ratio, or by dividing the octave into four parts and using its quarter-octave-reduced form of the major third as a near-just septimal minor semitone ~[[21/20]] represented by 2\28 as in [[demolished]] temperament (a variety of [[diminished (temperament)|diminished]] temperament), producing a [[4L 4s]] scale with a 5:2 step ratio (in which the 5\28 is a near-just diatismic whole tone ~[[17/15]], and the quarter-octave 7\28 is the flat classic major third ~[[6/5]]). [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/EVZtaYK5mcQ ''28edo groove''] (2026). The octaves slope up with the rows, and the range is seven complete octaves except for a missing note 27 in the highest octave, with a few repeated notes to mitigated vertical wraparounds.

== Würschmidt ==

Since the 5th harmonic is easily the best tuned interval, if you don't need easy access to diminished temperament (as above), the [[Würschmidt]] mapping is a good way to maximise your range (a bit over eight octaves, nearly level, although the bass octave is missing note 4) and make consonant chords easy to reach.

== Machine ==

[[Bryan Deister]] has used a layout for [[28edo]] that was inspired by the layout for [[29edo]] (rather than being made for any specific temperament), as demonstrated in [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025). The right-moving generator is a somewhat sharp Pythagorean whole tone (~[[9/8]], or near-just [[17/15]], 5\28). The up-moving generator is an almost-just tridecimal supraminor second (~[[14/13]], 3\28). The range is a bit over five octaves, with octaves alternating near/far and middle with an overall small upwards slant. Although this layout was not designed for any particular temperament, it so happens that the right-moving generator matches [[Machine]].

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-There are many conceivable ways to map [[28edo]] onto the [[Lumatone]] keyboard. However, as it has multiple small rings of 5ths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. Instead, the most diatonic-like mapping is the [[whitewood]] one.
+{{Lumatone mapping intro}}
+== Whitewood ==
+The [[Whitewood]] mapping is perhaps the most diatonic-like mapping that covers all notes. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/1nWL2qEcI-Q ''28edo improvisation''] (2022).
 {{Lumatone EDO mapping|n=28|start=20|xstep=4|ystep=-1}}
-Since the 5th harmonic is easily the best tuned interval, the [[Wuerschmidt]] mapping is a good way to maximise your range and make consonant chords easy to reach.
+== Diminished (Demolished) + Würschmidt ==
-{{Lumatone EDO mapping|n=28|start=21|xstep=9|ystep=-8}}
+It is possible to generate [[28edo]] using its near-just classic major third ~[[5/4]] represented by 9\28 (one key right plus one key down-right) as in [[Würschmidt]] temperament, producing a [[3L&nbsp;1s]] scale with a 9:1 step ratio, or by dividing the octave into four parts and using its quarter-octave-reduced form of the major third as a near-just septimal minor semitone ~[[21/20]] represented by 2\28 as in [[demolished]] temperament (a variety of [[diminished (temperament)|diminished]] temperament), producing a [[4L&nbsp;4s]] scale with a 5:2 step ratio (in which the 5\28 is a near-just diatismic whole tone ~[[17/15]], and the quarter-octave 7\28 is the flat classic major third ~[[6/5]]). [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/EVZtaYK5mcQ ''28edo groove''] (2026). The octaves slope up with the rows, and the range is seven complete octaves except for a missing note 27 in the highest octave, with a few repeated notes to mitigated vertical wraparounds.
+{{Lumatone EDO mapping|n=28|start=6|xstep=7|ystep=-5}}
+== Würschmidt ==
+Since the 5th harmonic is easily the best tuned interval, if you don't need easy access to diminished temperament (as above), the [[Würschmidt]] mapping is a good way to maximise your range (a bit over eight octaves, nearly level, although the bass octave is missing note 4) and make consonant chords easy to reach.
+{{Lumatone EDO mapping|n=28|start=12|xstep=9|ystep=-8}}
+== Machine ==
+[[Bryan Deister]] has used a layout for [[28edo]] that was inspired by the layout for [[29edo]] (rather than being made for any specific temperament), as demonstrated in [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025). The right-moving generator is a somewhat sharp Pythagorean whole tone (~[[9/8]], or near-just [[17/15]], 5\28). The up-moving generator is an almost-just tridecimal supraminor second (~[[14/13]], 3\28).  The range is a bit over five octaves, with octaves alternating near/far and middle with an overall small upwards slant. Although this layout was not designed for any particular temperament, it so happens that the right-moving generator matches [[Machine]].
+{{Lumatone EDO mapping|n=28|start=4|xstep=5|ystep=-3}}
-{{Lumatone mapping navigation}}
+{{Navbox Lumatone}}