Lumatone mapping for 54edo: Difference between revisions

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== Diaschismic ==

Despite having a smaller range, the [[diaschismic]] mapping makes it much easier to play harmonics together.

== Nessafof (Porwell) ==

[[Bryan Deister]] has used the [[Porwell temperaments#Nessafof|Nessafof (Porwell)]] layout for [[54edo]], as demonstrated in [https://www.youtube.com/shorts/Bi5-YQUQHek ''microtonal improvisation in 54edo''] (2025). At 7\54, the generator is a near-just septimal neutral second (~[[35/32]]), of which 2 make a slightly flat minor third ~[[6/5]] (constituted in 54b), and 11 make a sharp ~[[8/3]] (which corresponds to the 54b flat fifth). The [[7L 1s]] scale (with a step ratio of 7:5) is expanded similar to the expanded [[Lumatone mapping for porcupine]] if represented as 7L 1s, but even more expanded. On the one hand, this makes octaves recede rapidly; but on the other hand, this also means that down and right gives a convenient ascending whole tone scale shared with [[12edo]], although this requires constituting the ~[[9/8]] whole steps as {{nowrap|(3♭ × 3♯) / 8}}. The range is four full octaves.

== Unnamed rank-3 temperament ==

[[Bryan Deister]]'s has demonstrated a [[2L 4s]] (10:7 step ratio) mapping of [[54edo]] in [https://www.youtube.com/watch?v=t6ryT0cPTr0&list=WL&index=270 ''54edo groove''] (2026). The rightward generator 7\54 is a sharp undecimal neutral second ~[[12/11]] (also a flat large undecimal neutral second ~[[11/10]] if the 54c val is used); two of them make a mildly flat classic minor third ~[[6/5]] (again assuming the use of the 54c val) The down-right generator 10\54 is a flat septimal whole tone ~[[8/7]]; stacking four rightward generators minus one down-right generator makes the same sharp classic major third ~[[5/4]] as in [[12edo]] (although again a wart is required for 54edo). The range is slightly over 4¼ octaves (with one repeated note in each octave), but the octaves slope down severely, enough to incur two vertical wraparounds, but not enough to make a simple near-far alternating pattern.

== 54edo as 108ed4 ==

One of the odder ways to map [[54edo]] is to treat it as 108ed4 with a [[2L 8s (4/1-equivalent)]] scale (11:10 step ratio), as demonstrated in [[Bryan Deister's]] [https://www.youtube.com/watch?v=OsfvW25R0Cw ''54edo improv''] (2026). With this mapping, many notes are missing from each octave, but every note is available in some octave. In the linked video, Bryan Deister set all MIDI channels to map to the same octave, so all notes are available within that octave.

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 04:58, 17 September 2026 (UTC)

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 == Diaschismic ==
 Despite having a smaller range, the [[diaschismic]] mapping makes it much easier to play harmonics together.
 {{Lumatone EDO mapping|n=54|start=27|xstep=5|ystep=2}}
+== Nessafof (Porwell) ==
+[[Bryan Deister]] has used the [[Porwell temperaments#Nessafof|Nessafof (Porwell)]] layout for [[54edo]], as demonstrated in [https://www.youtube.com/shorts/Bi5-YQUQHek ''microtonal improvisation in 54edo''] (2025). At 7\54, the generator is a near-just septimal neutral second (~[[35/32]]), of which 2 make a slightly flat minor third ~[[6/5]] (constituted in 54b), and 11 make a sharp ~[[8/3]] (which corresponds to the 54b flat fifth). The [[7L&nbsp;1s]] scale (with a step ratio of 7:5) is expanded similar to the expanded [[Lumatone mapping for porcupine]] if represented as 7L&nbsp;1s, but even more expanded. On the one hand, this makes octaves recede rapidly; but on the other hand, this also means that down and right gives a convenient ascending whole tone scale shared with [[12edo]], although this requires constituting the ~[[9/8]] whole steps as {{nowrap|(3♭ × 3♯) / 8}}. The range is four full octaves.
+{{Lumatone EDO mapping|n=54|start=10|xstep=7|ystep=2}}
+== Unnamed rank-3 temperament ==
+[[Bryan Deister]]'s has demonstrated a [[2L&nbsp;4s]] (10:7 step ratio) mapping of [[54edo]] in [https://www.youtube.com/watch?v=t6ryT0cPTr0&list=WL&index=270 ''54edo groove''] (2026). The rightward generator 7\54 is a sharp undecimal neutral second ~[[12/11]] (also a flat large undecimal neutral second ~[[11/10]] if the 54c val is used); two of them make a mildly flat classic minor third ~[[6/5]] (again assuming the use of the 54c val) The down-right generator 10\54 is a flat septimal whole tone ~[[8/7]]; stacking four rightward generators minus one down-right generator makes the same sharp classic major third ~[[5/4]] as in [[12edo]] (although again a wart is required for 54edo). The range is slightly over 4¼ octaves (with one repeated note in each octave), but the octaves slope down severely, enough to incur two vertical wraparounds, but not enough to make a simple near-far alternating pattern.
+{{Lumatone EDO mapping|n=54|start=2|xstep=7|ystep=3}}
+== 54edo as 108ed4 ==
+One of the odder ways to map [[54edo]] is to treat it as 108ed4 with a [[2L&nbsp;8s (4/1-equivalent)]] scale (11:10 step ratio), as demonstrated in [[Bryan Deister's]] [https://www.youtube.com/watch?v=OsfvW25R0Cw ''54edo improv''] (2026). With this mapping, many notes are missing from each octave, but every note is available in some octave. In the linked video, Bryan Deister set all MIDI channels to map to the same octave, so all notes are available within that octave.
+{{Lumatone EDO mapping|n=54|start=0|xstep=16|ystep=1}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 04:58, 17 September 2026 (UTC)
 {{Navbox Lumatone}}