Lumatone mapping for 89edo: Difference between revisions

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== ~~Other Mappings~~ ==

== Orgone ==

~~The smallest mapping that covers~~ the whole gamut is ~~the~~ [[4L 7s]] ~~one~~. ~~Interestingly~~, ~~there are two different mappings~~ that ~~fit that criteria~~, ~~both good~~.

One way to cover the whole gamut (in at least the middle of the range) covers is with an [[orgone]] [[4L 7s]] scale (10:7 step ratio). This mapping focuses on making the 2.7.11 subgroup easy to play, but is extremely efficient at covering that and only a tenth of a cent off the minimax tuning, plus it skips or repeats fewer notes at the edges. The overall range is a bit over three octaves, with a gentle downwards slope, but the bass and treble octaves lose some notes at the left and right edges.

=== Myna ===

~~The~~ [[myna]] ~~mapping is quite lopsided~~, ~~but~~ is the optimal patent val ~~for the temperament and~~ efficiently gives access to the full 11-limit.

== Myna ==

It is possible to map [[89edo]] by stacking mildly flat classic minor thirds ~[[6/5]] (23\89), as in [[myna]] temperament, for which [[89edo]] is the optimal patent val. Two generators make a slightly sharp greater septimal tritone ~[[10/7]]; three of them make a slightly flat septimal major sixth ~[[12/7]]; after octave-reduction, five of them make a mildly sharp undecimal neutral third ~[[11/9]]; seven of them make a slightly sharp septimal minor seventh ~[[7/4]]; nine of them make a mildly sharp classic major third ~[[5/4]]; ten of them make a near-just fifth ~[[3/2]].

=== 4L 7s ===

A [[4L 7s]] scale (17:3 step ratio) efficiently gives access to the full 11-limit, although it is very lopsided. The overall range is a bit over three octaves, with a gentle downwards slope, but the bass and treble octaves lose many notes at the left and right edges (although the middle of the range does cover the whole gamut, even having a few repeated notes).

=== ~~Orgone~~ ===

=== 8L 3s ===

~~The~~ [[~~Orgone~~]] mapping ~~focusses on making the 2~~.7.~~11 subgroup easy to play, but~~ is ~~extremely~~ efficient ~~at covering that and only~~ a ~~tenth~~ of ~~a cent off the minimax tuning~~, ~~plus it skips or repeats fewer~~ notes at the ~~edges~~.

A much less lopsided [[8L 3s]] (10:3 step ratio) scale minimizes note loss at the left and right edges. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/watch?v=Rjx1zr3HIE0 ''89edo improv''] (2026-10-28). This mapping is maximally efficient, with a range of just over three octaves (which slope upwards very gently), with no missed notes (even in the bass and treble note 0 to note 0 octaves) and no repeated notes.

== Char-based + Sesquart rank-3 temperament ==

@@ Line 5: / Line 5: @@
 {{Lumatone EDO mapping|n=89|start=2|xstep=15|ystep=-8}}
-== Other Mappings ==
+== Orgone ==
-The smallest mapping that covers the whole gamut is the [[4L 7s]] one. Interestingly, there are two different mappings that fit that criteria, both good.
+One way to cover the whole gamut (in at least the middle of the range) covers is with an [[orgone]] [[4L&nbsp;7s]] scale (10:7 step ratio). This mapping focuses on making the 2.7.11 subgroup easy to play, but is extremely efficient at covering that and only a tenth of a cent off the minimax tuning, plus it skips or repeats fewer notes at the edges. The overall range is a bit over three octaves, with a gentle downwards slope, but the bass and treble octaves lose some notes at the left and right edges.
-=== Myna ===
+{{Lumatone EDO mapping|n=89|start=76|xstep=7|ystep=3}}
-The [[myna]] mapping is quite lopsided, but is the optimal patent val for the temperament and efficiently gives access to the full 11-limit.
+== Myna ==
+It is possible to map [[89edo]] by stacking mildly flat classic minor thirds ~[[6/5]] (23\89), as in [[myna]] temperament, for which [[89edo]] is the optimal patent val. Two generators make a slightly sharp greater septimal tritone ~[[10/7]]; three of them make a slightly flat septimal major sixth ~[[12/7]]; after octave-reduction, five of them make a mildly sharp undecimal neutral third ~[[11/9]]; seven of them make a slightly sharp septimal minor seventh ~[[7/4]]; nine of them make a mildly sharp classic major third ~[[5/4]]; ten of them make a near-just fifth ~[[3/2]].
+=== 4L&nbsp;7s ===
+A [[4L&nbsp;7s]] scale (17:3 step ratio) efficiently gives access to the full 11-limit, although it is very lopsided. The overall range is a bit over three octaves, with a gentle downwards slope, but the bass and treble octaves lose many notes at the left and right edges (although the middle of the range does cover the whole gamut, even having a few repeated notes).
 {{Lumatone EDO mapping|n=89|start=58|xstep=3|ystep=14}}
-=== Orgone ===
+=== 8L&nbsp;3s ===
-The [[Orgone]] mapping focusses on making the 2.7.11 subgroup easy to play, but is extremely efficient at covering that and only a tenth of a cent off the minimax tuning, plus it skips or repeats fewer notes at the edges.
+A much less lopsided [[8L&nbsp;3s]] (10:3 step ratio) scale minimizes note loss at the left and right edges. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/watch?v=Rjx1zr3HIE0 ''89edo improv''] (2026-10-28). This mapping is maximally efficient, with a range of just over three octaves (which slope upwards very gently), with no missed notes (even in the bass and treble note 0 to note 0 octaves) and no repeated notes.
-{{Lumatone EDO mapping|n=89|start=76|xstep=7|ystep=3}}
+{{Lumatone EDO mapping|n=89|start=5|xstep=10|ystep=-7}}
 == Char-based + Sesquart rank-3 temperament ==

Lumatone mapping for 89edo: Difference between revisions

Lucius Chiaraviglio (talk | contribs)