Lumatone mapping for 54edo: Difference between revisions
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→Nessafof (Porwell): Insert Bryan Deister's Unidentified rank-3 temperament Lumatone mapping after this |
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== Nessafof (Porwell) == | == 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. | [[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. | ||
{{Lumatone EDO mapping|n=54|start=10|xstep=7|ystep=2}} | |||
{{Lumatone EDO mapping|n=54|start= | == Unidentified 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. | |||
{{Lumatone EDO mapping|n=54|start=2|xstep=7|ystep=3}} | |||
{{Navbox Lumatone}} | {{Navbox Lumatone}} | ||