Lumatone mapping for 57edo: Difference between revisions

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There are many conceivable ways to map [[57edo]] onto the onto the Lumatone keyboard. However, it has 3 mutually-exclusive rings of fifths, so the [[Standard Lumatone mapping for Pythagorean]] is not one of them, unless the very sharp b val is used. Due to the large number of notes, even those that do will have limited range.

== Diatonic (sharp fifth ~~only~~) ==

== Diatonic (sharp fifth) ==

The 57b val has a fifth so sharp that it would sound more like a circulating temperament of [[5edo]]. The sharp fifth does have the feature that six of them add up to 12/1, which octave-reduces to the [[Patent val|patent]] fifth, and the diatonic mapping does provide easy access to the patent fifth (just up and left of the sharp fifth), so on a hypothetical XL-sized Lumatone having enough keys to avoid skipping notes, it would be a reasonable mapping despite giving an extremely hard [[5L 2s]] scale.

== Unnamed temperament ==

[[Bryan Deister]] has used a layout for [[57edo]] in which the right generator is 9\57 ({{nowrap|[[10/9]] ~ [[9/8]]}}, as in [[meantone]], but this would be [[Saturation, torsion, and contorsion|contorted]] without an additional generator); and the upward generator is 8\57, which maps to a just slightly flat ~[[11/10]] (and not to ~[[12/11]] or ~[[10/9]] in the patent val, thus differing from [[Porcupine]] despite producing a rotated but otherwise similar [[1L 6s]] scale). Octaves are nearly level, just barely sloping downwards; the compass is somewhat under 4 octaves. This layout is demonstrated in [https://www.youtube.com/watch?v=4NZvSgS3ryY ''57edo improv''] (2025); in the video, some notes are cut off in the lower and middle left edge and the upper right corner due to the use of only 2 MIDI channels; on the plus side, this shows where to put note 0 on the left side to avoid losing notes in the bottom octave due to running off the edge of the keyboard. Note that down and right proceeds by 1\57, thus making for an easy glissando (also demonstrated in the video).

[[Bryan Deister]] has used a layout for [[57edo]] in which the right generator is 9\57 ([[10/9]] ~ [[9/8]], as in [[~~Meantone~~]], but this would be [[Saturation, torsion, and contorsion|contorted]] without an additional generator); and the upward generator is 8\57, which maps to a just slightly flat ~[[11/10]] (and not to ~[[12/11]] or ~[[10/9]] in the patent val, thus differing from [[Porcupine]] despite producing a rotated but otherwise similar [[1L 6s]] scale). Octaves are nearly level, just barely sloping downwards; the compass is somewhat under 4 octaves. This layout is demonstrated in [https://www.youtube.com/watch?v=4NZvSgS3ryY ''57edo improv''] (2025); in the video, some notes are cut off in the lower and middle left edge and the upper right corner due to the use of only 2 MIDI channels; on the plus side, this shows where to put note 0 on the left side to avoid losing notes in the bottom octave due to running off the edge of the keyboard. Note that down and right proceeds by 1\57, thus making for an easy glissando (also demonstrated in the video).

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 There are many conceivable ways to map [[57edo]] onto the onto the Lumatone keyboard. However, it has 3 mutually-exclusive rings of fifths, so the [[Standard Lumatone mapping for Pythagorean]] is not one of them, unless the very sharp b val is used. Due to the large number of notes, even those that do will have limited range.
-== Diatonic (sharp fifth only) ==
+== Diatonic (sharp fifth) ==
 The 57b val has a fifth so sharp that it would sound more like a circulating temperament of [[5edo]]. The sharp fifth does have the feature that six of them add up to 12/1, which octave-reduces to the [[Patent val|patent]] fifth, and the diatonic mapping does provide easy access to the patent fifth (just up and left of the sharp fifth), so on a hypothetical XL-sized Lumatone having enough keys to avoid skipping notes, it would be a reasonable mapping despite giving an extremely hard [[5L&nbsp;2s]] scale.
 {{Lumatone EDO mapping|n=57|start=18|xstep=11|ystep=-10}}
 == Unnamed temperament ==
+[[Bryan Deister]] has used a layout for [[57edo]] in which the right generator is 9\57 ({{nowrap|[[10/9]] ~ [[9/8]]}}, as in [[meantone]], but this would be [[Saturation, torsion, and contorsion|contorted]] without an additional generator); and the upward generator is 8\57, which maps to a just slightly flat ~[[11/10]] (and not to ~[[12/11]] or ~[[10/9]] in the patent val, thus differing from [[Porcupine]] despite producing a rotated but otherwise similar [[1L&nbsp;6s]] scale).  Octaves are nearly level, just barely sloping downwards; the compass is somewhat under 4 octaves. This layout is demonstrated in [https://www.youtube.com/watch?v=4NZvSgS3ryY ''57edo improv''] (2025); in the video, some notes are cut off in the lower and middle left edge and the upper right corner due to the use of only 2 MIDI channels; on the plus side, this shows where to put note 0 on the left side to avoid losing notes in the bottom octave due to running off the edge of the keyboard. Note that down and right proceeds by 1\57, thus making for an easy glissando (also demonstrated in the video).
-[[Bryan Deister]] has used a layout for [[57edo]] in which the right generator is 9\57 ([[10/9]] ~ [[9/8]], as in [[Meantone]], but this would be [[Saturation, torsion, and contorsion|contorted]] without an additional generator); and the upward generator is 8\57, which maps to a just slightly flat ~[[11/10]] (and not to ~[[12/11]] or ~[[10/9]] in the patent val, thus differing from [[Porcupine]] despite producing a rotated but otherwise similar [[1L&nbsp;6s]] scale).  Octaves are nearly level, just barely sloping downwards; the compass is somewhat under 4 octaves. This layout is demonstrated in [https://www.youtube.com/watch?v=4NZvSgS3ryY ''57edo improv''] (2025); in the video, some notes are cut off in the lower and middle left edge and the upper right corner due to the use of only 2 MIDI channels; on the plus side, this shows where to put note 0 on the left side to avoid losing notes in the bottom octave due to running off the edge of the keyboard. Note that down and right proceeds by 1\57, thus making for an easy glissando (also demonstrated in the video).
 {{Lumatone EDO mapping|n=57|start=5|xstep=9|ystep=-8}}
 {{Navbox Lumatone}}