Lumatone mapping for 78edo: Difference between revisions

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There are many conceivable ways to map [[78edo]] onto the onto the Lumatone keyboard. However, since it has 2 mutually-exclusive rings of [[39edo]] fifths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. The second best 5th produces three mutually-exclusive rings of [[26edo]] 5ths, so that doesn't work either, and the third ~~& 4th~~ best are out of the diatonic tuning range. On the other hand, the [[keen]] mapping can cover the whole gamut and make harmonics easy to play together, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to hit every ~~single~~ note.

There are many conceivable ways to map [[78edo]] onto the onto the Lumatone keyboard. However, since it has 2 mutually-exclusive rings of [[39edo]] fifths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. The second best 5th produces three mutually-exclusive rings of [[26edo]] 5ths, so that doesn't work either, and the third and fourth best are out of the diatonic tuning range.

== Keen ==

On the other hand, the [[keen]] mapping can cover the whole gamut and make harmonics easy to play together, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to hit every note.

The [[7L 3s]] neutral thirds mapping also covers the whole gamut about as efficiently as possible and keeps octaves closer to horizontal.

== Neutral thirds ==

The [[7L 3s]] neutral thirds mapping also covers the whole gamut about as efficiently as possible and keeps octaves closer to horizontal.

== Unnamed rank-3 temperament mapping ==

[[Bryan Deister]] has demonsrated a Lumatone mapping for [[78edo]] that lays out scales [[11L 1s]] (7:1 step ratio) and [[6L 6s]] (7:6 step ratio), in [https://www.youtube.com/shorts/jxYRAo6jHaE ''microtonal improvisation in 78edo''] (2025). The rightward generator 7\78 is slightly sharp large septendecimal semitone ~[[17/16]]; two of them make a slightly flat biyatismic whole tone ~[[17/15]]; and six of them readh a slightly flat undecimal minor fifth ~[[16/11]]. The down-right generator 6\78 is a somewhat sharp small undevicesimal semitone ~[[20/19]]; stacking these can yield both a slightly sharp undecimal major fourth ~[[11/8]] (as 36\78, six generators) and slightly flat undecimal minor fifth ~16/11 (as 42\78, seven down-right generators, same as six rightward generators). The range is somewhat under three octaves, with all notes represented; octaves alternate between far and near, with an overall upwards slant.

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-There are many conceivable ways to map [[78edo]] onto the onto the Lumatone keyboard. However, since it has 2 mutually-exclusive rings of [[39edo]] fifths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. The second best 5th produces three mutually-exclusive rings of [[26edo]] 5ths, so that doesn't work either, and the third & 4th best are out of the diatonic tuning range. On the other hand, the [[keen]] mapping can cover the whole gamut and make harmonics easy to play together, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to hit every single note.
+There are many conceivable ways to map [[78edo]] onto the onto the Lumatone keyboard. However, since it has 2 mutually-exclusive rings of [[39edo]] fifths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. The second best 5th produces three mutually-exclusive rings of [[26edo]] 5ths, so that doesn't work either, and the third and fourth best are out of the diatonic tuning range.
+== Keen ==
+On the other hand, the [[keen]] mapping can cover the whole gamut and make harmonics easy to play together, although it needs to be expanded from [[2L&nbsp;8s]] to [[10L&nbsp;2s]] to hit every note.
 {{Lumatone EDO mapping|n=78|start=33|xstep=7|ystep=4}}
 {{Lumatone EDO mapping|n=78|start=71|xstep=7|ystep=-3}}
-The [[7L 3s]] neutral thirds mapping also covers the whole gamut about as efficiently as possible and keeps octaves closer to horizontal.
+== Neutral thirds ==
+The [[7L&nbsp;3s]] neutral thirds mapping also covers the whole gamut about as efficiently as possible and keeps octaves closer to horizontal.
 {{Lumatone EDO mapping|n=78|start=76|xstep=9|ystep=-4}}
+== Unnamed rank-3 temperament mapping ==
+[[Bryan Deister]] has demonsrated a Lumatone mapping for [[78edo]] that lays out scales [[11L&nbsp;1s]] (7:1 step ratio) and [[6L&nbsp;6s]] (7:6 step ratio), in [https://www.youtube.com/shorts/jxYRAo6jHaE ''microtonal improvisation in 78edo''] (2025). The rightward generator 7\78 is slightly sharp large septendecimal semitone ~[[17/16]]; two of them make a slightly flat biyatismic whole tone ~[[17/15]]; and six of them readh a slightly flat undecimal minor fifth ~[[16/11]]. The down-right generator 6\78 is a somewhat sharp small undevicesimal semitone ~[[20/19]]; stacking these can yield both a slightly sharp undecimal major fourth ~[[11/8]] (as 36\78, six generators) and slightly flat undecimal minor fifth ~16/11 (as 42\78, seven down-right generators, same as six rightward generators). The range is somewhat under three octaves, with all notes represented; octaves alternate between far and near, with an overall upwards slant.
+{{Lumatone EDO mapping|n=78|start=61|xstep=7|ystep=-1}}
 {{Navbox Lumatone}}