Lumatone mapping for 54edo: Difference between revisions

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~~[[54edo]] is an interesting case for [[Lumatone]] mappings, since ([[Lumatone mapping for 24edo|like 24edo]]), it is not generated by fifths and octaves, so the [[Standard~~ Lumatone mapping ~~for Pythagorean]] only reaches [[27edo]] intervals.~~ You can use the b val, but it is very flat, to the point where major seconds become 10/9 instead of 9/8.

== Diatonic ==

You can use the b val, but it is very flat, to the point where major seconds become 10/9 instead of 9/8.

== 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.

~~[[Category:~~Lumatone ~~mappings]] [[Category:54edo]]~~

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-[[54edo]] is an interesting case for [[Lumatone]] mappings, since ([[Lumatone mapping for 24edo|like 24edo]]), it is not generated by fifths and octaves, so the [[Standard Lumatone mapping for Pythagorean]] only reaches [[27edo]] intervals. You can use the b val, but it is very flat, to the point where major seconds become 10/9 instead of 9/8.
+{{Lumatone mapping intro}}
+== Diatonic ==
+You can use the b&nbsp;val, but it is very flat, to the point where major seconds become 10/9 instead of 9/8.
 {{Lumatone EDO mapping|n=54|start=42|xstep=8|ystep=-1}}
+== 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}}
-[[Category:Lumatone mappings]] [[Category:54edo]]
+{{Navbox Lumatone}}