User:Lucius Chiaraviglio/Keyboard Layout Lab/Various other Lumatone mappings: Difference between revisions

== Sevond Lumatone mappings ==

=== 56edo (demonstrated to work) ===

Since [[56edo]] is a multiple of [[7edo]], it can be used with a mapping that divides the octave into seven parts in the manner of [[whitewood]], but with more accuracy due to having a much better fifth; in this case, the actual temperament is [[sevond]], which if restricted to the [[5-limit]] uses a generator of a mildly sharp fifth ~[[3/2]] and a period mapped inconsistently as a very flat classic whole tone ~[[10/9]] to 8\56, which 1/7-octave-reduces the generator to 1\56 (proceeding down), which functions as a very flat (and inconsistently mapped) chromium quartertone ~[[250/243]]. With higher prime limits, more accurate mappings are available — for instance, in the [[13-limit]], remapping the 1/7-octave period as a moderately sharp but consistently mapped large undecimal neutral second ~[[11/10]], and likewise remapping the 1/7-octave-reduced ~3/2 generator: technically as a very flat and inconsistently-mapped ~[[15000/14641]], but more practically as a slightly flat and consistently-mapped negustma ~[[78/77]]. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/5j-TAkmdWqc ''56edo groove''] (2026). The range is a bit over four octaves, which slope upwards with the rows.

{{Lumatone EDO mapping|n=56|start=16|xstep=8|ystep=1}}

Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 02:34, 1 July 2026 (UTC)<br>

Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 03:21, 2 July 2026 (UTC)

=== 87edo (demonstrated to work) ===

[[Bryan Deister]] has demonstrated a [[11L&nbsp;5s]] (7:2 step ratio) mapping for [[87edo]] in [https://www.youtube.com/shorts/rINJKiMQE78 ''Circuit Bent - Stomach Book (microtonal cover in 87edo)''] (2025). The generator 14\87, which is two keys right from the root note, is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it near-just; two of them make an essentially just classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 87edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals &mdash; the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) Since this interval is two keys right instead of just one (as needed to avoid missing notes), this version of the temperament can be viewed as a split generator version, in which each ~19/17 is split into two equal intervals that function as both a small septendecimal semitone ~[[18/17]] and a large undevicesimal semitone ~[[19/18]], both being close to just (and the photisma [[324/323]] is tempered out). Although no second generator is needed to reach all of the notes, for convenience, down-right by one key (2\87) can be used for convenience as a second generator that functions as ~[[49/48]] (inconsistently mapped), ~[[55/54]], ~[[64/63]], ~[[65/64]], and ~[[81/80]], of which the septimal chroma ~64/63 is near-just, and four of these make a near-just classic diatonic semitone ~[[16/15]] (the currently unnamed unnoticeable comma [[5250987/5242880]] is tempered out). The range is somewhat over two octaves (which slant very slightly downwards) with no missed notes and some repeated notes to mitigate vertical wraparounds.

Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:39, 15 November 2025 (UTC)<br>

Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 00:07, 4 May 2026 (UTC)

The septimal minor third ~[[7/6]] (11\49) of [[49edo]] is near-just, 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.

Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 03:40, 21 April 2026 (UTC)