Lumatone mapping for 28edo: Difference between revisions

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== Whitewood ==

The [[Whitewood]] mapping is perhaps the most diatonic-like mapping that covers all notes.

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).

== 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, the [[Würschmidt]] mapping is a good way to maximise your range and make consonant chords easy to reach.

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]].

@@ Line 2: / Line 2: @@
 == Whitewood ==
-The [[Whitewood]] mapping is perhaps the most diatonic-like mapping that covers all notes.
+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}}
+== 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&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, the [[Würschmidt]] mapping is a good way to maximise your range and make consonant chords easy to reach.
+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=21|xstep=9|ystep=-8}}
+{{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}}
 {{Navbox Lumatone}}