Lumatone mapping for 96edo: Difference between revisions

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{{Lumatone mapping intro}} Due to its size, it would not cover the whole gamut even if it was~~. The second best fifth is shared with [[32edo]], so that doesn't work either, making the 55/96 flat fifth the first one that produces a regular, albeit near equalised diatonic scale~~.

{{Lumatone mapping intro}} Due to its size, it would not cover the whole gamut even if it was.

== Diatonic ==

The second best fifth is shared with [[32edo]], so that doesn't work either, making the 55/96 flat fifth the first one that produces a regular, albeit near equalised diatonic scale.

== Würschmidt ==

Instead, the most efficient layout that allows access to all notes is the [[3L 10s]] [[Würschmidt]] mapping, although this does reduce the range to a little under three octaves and many notes are inaccessible at the edges due to the diesis being on the up-right axis.

== Interpental ==

The [[Buzzardsmic_clan#Interpental|Interpental]] mapping is not quite as efficient at accessing the 5-limit, but is easier to navigate overall.

== Compton-related rank 3 temperament ==

[[Bryan Deister]] has demonstrated a mapping for [[96edo]] in which the rightward generator is 8\96 (~[[18/17]]) as in [[12edo]], while the upward generator is 7\96 (~[[20/19]]), in [https://www.youtube.com/shorts/8xqjUkuZFaI ''microtonal improvisation in 96edo''] (2025). The range is just over two octaves, with octaves sloping away and then wrapping around; on the other hand, it is easy to play eight 12edo subsets of 96edo that are displaced slightly from each other, as if one had eight pianos (even if of rather short compass) somehow all in reach at once. (Here, note 0 is in the middle of the left edge instead of Bryan Deister's usual lower left corner, to avoid skipping some of the bottom notes in the lowest note 0 to note 0 octave.) Although not shown in the video, this mapping also enables easy glissandos diagonally up-left or down-right.

~~The [[Interpental]] mapping is not quite as efficient at accessing the 5-limit, but is easier to navigate overall.~~

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-{{Lumatone mapping intro}} Due to its size, it would not cover the whole gamut even if it was. The second best fifth is shared with [[32edo]], so that doesn't work either, making the 55/96 flat fifth the first one that produces a regular, albeit near equalised diatonic scale.
+{{Lumatone mapping intro}} Due to its size, it would not cover the whole gamut even if it was.
+== Diatonic ==
+The second best fifth is shared with [[32edo]], so that doesn't work either, making the 55/96 flat fifth the first one that produces a regular, albeit near equalised diatonic scale.
 {{Lumatone EDO mapping|n=96|start=72|xstep=14|ystep=-1}}
+== Würschmidt ==
 Instead, the most efficient layout that allows access to all notes is the [[3L&nbsp;10s]] [[Würschmidt]] mapping, although this does reduce the range to a little under three octaves and many notes are inaccessible at the edges due to the diesis being on the up-right axis.
 {{Lumatone EDO mapping|n=96|start=14|xstep=3|ystep=19}}
+== Interpental ==
+The [[Buzzardsmic_clan#Interpental|Interpental]] mapping is not quite as efficient at accessing the 5-limit, but is easier to navigate overall.
+{{Lumatone EDO mapping|n=96|start=10|xstep=9|ystep=-7}}
+== Compton-related rank 3 temperament ==
+[[Bryan Deister]] has demonstrated a mapping for [[96edo]] in which the rightward generator is 8\96 (~[[18/17]]) as in [[12edo]], while the upward generator is 7\96 (~[[20/19]]), in [https://www.youtube.com/shorts/8xqjUkuZFaI ''microtonal improvisation in 96edo''] (2025). The range is just over two octaves, with octaves sloping away and then wrapping around; on the other hand, it is easy to play eight 12edo subsets of 96edo that are displaced slightly from each other, as if one had eight pianos (even if of rather short compass) somehow all in reach at once. (Here, note 0 is in the middle of the left edge instead of Bryan Deister's usual lower left corner, to avoid skipping some of the bottom notes in the lowest note 0 to note 0 octave.) Although not shown in the video, this mapping also enables easy glissandos diagonally up-left or down-right.
-The [[Interpental]] mapping is not quite as efficient at accessing the 5-limit, but is easier to navigate overall.
+{{Lumatone EDO mapping|n=96|start=12|xstep=8|ystep=-7}}
-{{Lumatone EDO mapping|n=96|start=10|xstep=9|ystep=-7}}
 {{Navbox Lumatone}}