Lumatone mapping for 54edo: Difference between revisions

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{{Lumatone EDO mapping|n=54|start=10|xstep=7|ystep=2}}
{{Lumatone EDO mapping|n=54|start=10|xstep=7|ystep=2}}


== Unidentified rank-3 temperament ==
== 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.
[[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.

Latest revision as of 09:38, 2 September 2026

There are many conceivable ways to map 54edo onto the onto the Lumatone keyboard. However, it has 2 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them.

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.

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Diaschismic

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

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Nessafof (Porwell)

Bryan Deister has used the Nessafof (Porwell) layout for 54edo, as demonstrated in 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 (3♭ × 3♯) / 8. The range is four full octaves.

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Unnamed rank-3 temperament

Bryan Deister's has demonstrated a 2L 4s (10:7 step ratio) mapping of 54edo in 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.

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