Lumatone mapping for 49edo: Difference between revisions

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It is possible to get closer to level octaves for [[49edo]] with a slight gain in practical efficiency (having three repeated notes in each octave, but no non-contiguous notes in the lower left and upper right corners compared to the the archipelago + catalan mapping) with a machine scale ([[5L 1s]], with a 9:4 step ratio). [[Bryan Deister]] has demonstrated this in [[Bryan Deister]]'s [https://www.youtube.com/shorts/_yNrDI6nS1I ''49edo riff''] (2026). This mapping has a contiguous range of 5⅓ octaves; and the repeated notes may provide a bit of assistance with mitigation of vertical wraparounds. This mapping uses 9\49 (one key right) as its generator, which functions as a very flat septimal major second ~[[8/7]], a very sharp (and inconsistently-mapped) Pythagorean major second ~[[9/8]], and (much more accurately) a near-just undecimal acute whole tone ~[[25/22]] (both the Archytas comma [[64/63]] and the valinorsma [[176/175]] are tempered out). Two of them make a somewhat sharp septimal major third ~[[9/7]]; four of them make a slightly sharp classic major sixth ~[[5/3]]; seven of them (after octave reduction) make a somewhat flat undecimal neutral third ~[[11/9]]; eight of them make a very sharp undecimal major fourth ~[[11/8]]; and nine of them make a near-just undecimal minor sixth ~[[11/7]]. Thus, this mapping favors mostly xenharmonic intervals.

== Infraorwell ==

The septimal minor third ~[[7/6]] (11\49) of [[49edo]] is only mildly sharp, which suggests its use as a generator, as in [[Orwell]]; however, it is too close to just for actual Orwell eemperament, and so a stack of it manages to miss all of the intervals characteristic of Orwell, other than a fairly flat classic minor sixth ~[[8/5]] — hence [[Orwellismic_temperaments#Infraorwell|infraorwell]]. It is possible to produce a forward chroma [[4L 5s]] (gramitonic, 6:5 step ratio) infraorwell mapping for 49edo, as demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/watch?v=7pK-JcIrd18 Deltarune – ''Man'' (cover)] (2023) and (very differently) in [https://www.youtube.com/shorts/V8t7MyP2Nuo ''microtonal improv in 49edo''] (2024). This mapping gets all notes in each octave and has a range of a bit over 4 octaves with repeated notes to mitigate vertical wraparounds; the octaves alternate between near/far and middle, with double octaves sloping slightly upwards.

== Semisept ==

An alternative to [[infraorwell]] for [[49edo]] (using 11\49 as a mildly sharp ~[[7/6]]) is to take the octave complement (38\49 as a mildly flat septimal major sixth ~[[12/7]]) and split it in half, to get a 19\49 as a near-just undecimal sub-fourth ~[[72/55]] (constituted from a numerator and denominator having huge errors that nearly cancel out), producing a [[5L 3s]] scale with an 8:3 step ratio. This is an oneirotonic scale of which the large steps sound deceptively diatonic (being only moderately flat of a direct-mapped Pythagorean whole tone ~[[9/8]]), as demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/watch?v=aNswQ1-1nlM&list=WL&index=275 ''<nowiki>Prelude in 49edo [short clip]</nowiki>''] (2026). The range is nearly 4⅔ octaves, which slope down mildly, with no missed notes and only a few repeated notes.

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 It is possible to get closer to level octaves for [[49edo]] with a slight gain in practical efficiency (having three repeated notes in each octave, but no non-contiguous notes in the lower left and upper right corners compared to the the archipelago + catalan mapping) with a machine scale ([[5L&nbsp;1s]], with a 9:4 step ratio). [[Bryan Deister]] has demonstrated this in [[Bryan Deister]]'s [https://www.youtube.com/shorts/_yNrDI6nS1I ''49edo riff''] (2026). This mapping has a contiguous range of 5⅓ octaves; and the repeated notes may provide a bit of assistance with mitigation of vertical wraparounds. This mapping uses 9\49 (one key right) as its generator, which functions as a very flat septimal major second ~[[8/7]], a very sharp (and inconsistently-mapped) Pythagorean major second ~[[9/8]], and (much more accurately) a near-just undecimal acute whole tone ~[[25/22]] (both the Archytas comma [[64/63]] and the valinorsma [[176/175]] are tempered out). Two of them make a somewhat sharp septimal major third ~[[9/7]]; four of them make a slightly sharp classic major sixth ~[[5/3]]; seven of them (after octave reduction) make a somewhat flat undecimal neutral third ~[[11/9]]; eight of them make a very sharp undecimal major fourth ~[[11/8]]; and nine of them make a near-just undecimal minor sixth ~[[11/7]]. Thus, this mapping favors mostly xenharmonic intervals.
 {{Lumatone EDO mapping|n=49|start=4|xstep=9|ystep=-5}}
+== Infraorwell ==
+The septimal minor third ~[[7/6]] (11\49) of [[49edo]] is only mildly sharp, which suggests its use as a generator, as in [[Orwell]]; however, it is too close to just for actual Orwell eemperament, and so a stack of it manages to miss all of the intervals characteristic of Orwell, other than a fairly flat classic minor sixth ~[[8/5]] &mdash; hence [[Orwellismic_temperaments#Infraorwell|infraorwell]]. It is possible to produce a forward chroma [[4L&nbsp;5s]] (gramitonic, 6:5 step ratio) infraorwell mapping for 49edo, as demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/watch?v=7pK-JcIrd18 Deltarune – ''Man'' (cover)] (2023) and (very differently) in [https://www.youtube.com/shorts/V8t7MyP2Nuo ''microtonal improv in 49edo''] (2024). This mapping gets all notes in each octave and has a range of a bit over 4 octaves with repeated notes to mitigate vertical wraparounds; the octaves alternate between near/far and middle, with double octaves sloping slightly upwards.
+{{Lumatone EDO mapping|n=49|start=33|xstep=6|ystep=-1}}
+== Semisept ==
+An alternative to [[infraorwell]] for [[49edo]] (using 11\49 as a mildly sharp ~[[7/6]]) is to take the octave complement (38\49 as a mildly flat septimal major sixth ~[[12/7]]) and split it in half, to get a 19\49 as a near-just undecimal sub-fourth ~[[72/55]] (constituted from a numerator and denominator having huge errors that nearly cancel out), producing a [[5L&nbsp;3s]] scale with an 8:3 step ratio. This is an oneirotonic scale of which the large steps sound deceptively diatonic (being only moderately flat of a direct-mapped Pythagorean whole tone ~[[9/8]]), as demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/watch?v=aNswQ1-1nlM&list=WL&index=275 ''<nowiki>Prelude in 49edo [short clip]</nowiki>''] (2026). The range is nearly 4⅔ octaves, which slope down mildly, with no missed notes and only a few repeated notes.
+{{Lumatone EDO mapping|n=49|start=4|xstep=8|ystep=-5}}
 {{Navbox Lumatone}}

Lumatone mapping for 49edo: Difference between revisions

Lucius Chiaraviglio (talk | contribs)