Lumatone mapping for 84edo: Difference between revisions

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{{Lumatone mapping intro}} Due to the edos size, it would not cover the whole gamut even if it was. Neither the second, third, nor fourth-best fifths work either, and the maviloid scale generated by 47/84 is even flatter than [[25edo]].

== Antidiatonic ==

== Sensei ==

Instead, the most efficient layout that allows access to all notes is the [[Sensei]] mapping, although this does reduce the range to a little over three octaves.

== Orwell ==

The [[Orwell]] mapping has a smaller range, but is closer to the optimal tuning for the temperament and makes it easier to play harmonics together.

== Diploid Marvel extension ==

[[Bryan Deister]] has demonstrated a [[10L 4s]] (8:1 step ratio) mapping for [[84edo]] in [https://www.youtube.com/shorts/Sqkxrmwggr0 ''microtonal improvisation in 84edo''] (2025). The rightward generator 8\84 (shared with the [[Orwell]] mapping) functions as both ~[[15/14]] and ~[[16/15]], making this a [[Marvel]] temperament; two of these make a slightly flat septimal supermajor second (~[[8/7]]); four of these make a slightly flat Barbados third (~[[13/10]]). However, by itself this generator would produce a [[contorted]] mapping even with the [[semioctave]] [[period]] implied by 10L 4s, so a second generator is required. The chroma of the scale (7\84, the upwards generator) is not very convenient as a secondary generator, and also produces a contorted mapping if used alone, so it makes sense to use the down-right generator 1\84 (the small step of the scale) as the secondary generator. This functions as a near-just version of the starling chroma (~[[126/125]]), but also functions as a narrow version of the syntonic chroma (~[[81/80]]), a slightly narrow version of the animist chroma (~[[105/104]]), and as a wide version of the buzurgismic/dhanvantarismic chroma (~[[169/168]]) or the mycunumic chroma (~[[196/195]]); two of these make a near-just septimal chroma (~[[64/63]]); and adding three of these to the aforementioned Barbados third (reached with the rightward generator) yields the very accurate fourth (~[[4/3]]) at 35\84 (shared with [[12edo]] as 5\12). (Nevertheless, sheer distance may be a problem for people who do not have long fingers — a problem hard to avoid with large EDO sizes, that force octaves to be long to avoid missing notes.) Near-just versions of common intervals are reachable using both generators in combination: three rightward generators minus two down-right generators to get the classic major third ~[[6/5]] at 22\84, and three of each generator to get the classic major third ~[[5/4]] at 27\84. The range would be 2½ octaves with no missed notes if note for a missed note 36 in the highest semioctave; some notes are repeated for ease in vertical transitions; and the octaves are perfectly level.

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 {{Lumatone mapping intro}} Due to the edos size, it would not cover the whole gamut even if it was. Neither the second, third, nor fourth-best fifths work either, and the maviloid scale generated by 47/84 is even flatter than [[25edo]].
+== Antidiatonic ==
 {{Lumatone EDO mapping|n=84|start=36|xstep=10|ystep=7}}
+== Sensei ==
 Instead, the most efficient layout that allows access to all notes is the [[Sensei]] mapping, although this does reduce the range to a little over three octaves.
 {{Lumatone EDO mapping|n=84|start=2|xstep=9|ystep=-5}}
+== Orwell ==
 The [[Orwell]] mapping has a smaller range, but is closer to the optimal tuning for the temperament and makes it easier to play harmonics together.
 {{Lumatone EDO mapping|n=84|start=4|xstep=8|ystep=-5}}
+== Diploid Marvel extension ==
+[[Bryan Deister]] has demonstrated a [[10L&nbsp;4s]] (8:1 step ratio) mapping for [[84edo]] in [https://www.youtube.com/shorts/Sqkxrmwggr0 ''microtonal improvisation in 84edo''] (2025). The rightward generator 8\84 (shared with the [[Orwell]] mapping) functions as both ~[[15/14]] and ~[[16/15]], making this a [[Marvel]] temperament; two of these make a slightly flat septimal supermajor second (~[[8/7]]); four of these make a slightly flat Barbados third (~[[13/10]]). However, by itself this generator would produce a [[contorted]] mapping even with the [[semioctave]] [[period]] implied by 10L&nbsp;4s, so a second generator is required. The chroma of the scale (7\84, the upwards generator) is not very convenient as a secondary generator, and also produces a contorted mapping if used alone, so it makes sense to use the down-right generator 1\84 (the small step of the scale) as the secondary generator.  This functions as a near-just version of the starling chroma (~[[126/125]]), but also functions as a narrow version of the syntonic chroma (~[[81/80]]), a slightly narrow version of the animist chroma (~[[105/104]]), and as a wide version of the buzurgismic/dhanvantarismic chroma (~[[169/168]]) or the mycunumic chroma (~[[196/195]]); two of these make a near-just septimal chroma (~[[64/63]]); and adding three of these to the aforementioned Barbados third (reached with the rightward generator) yields the very accurate fourth (~[[4/3]]) at 35\84 (shared with [[12edo]] as 5\12). (Nevertheless, sheer distance may be a problem for people who do not have long fingers &mdash; a problem hard to avoid with large EDO sizes, that force octaves to be long to avoid missing notes.) Near-just versions of common intervals are reachable using both generators in combination: three rightward generators minus two down-right generators to get the classic major third ~[[6/5]] at 22\84, and three of each generator to get the classic major third ~[[5/4]] at 27\84. The range would be 2½ octaves with no missed notes if note for a missed note 36 in the highest semioctave; some notes are repeated for ease in vertical transitions; and the octaves are perfectly level.
+{{Lumatone EDO mapping|n=84|start=12|xstep=8|ystep=-7}}
 {{Navbox Lumatone}}