Lumatone mapping for 68edo: Difference between revisions

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To give you a little more range while keeping octaves fairly near horizontal, the [[2L 7s]] mapping generated by 31/68 works decently, especially if you favor using the 11th harmonic in compositions.

== Biyatismic (Zeus) ==

[[Bryan Deister]] has used a [[Biyatismic clan#Zeus|Biyatismic (Zeus)]] layout with a [[7L 1s]] scale (9:5 step ratio) for [[68edo]], as demonstrated in [https://www.youtube.com/shorts/CO1AslAu9E0 ''microtonal improvisation in 68edo''] (2025). The rightward generator 9\68 is a combination of the Alpharabian tendoneutral second ~[[12/11]] and the undecimal submajor second ~[[11/10]], and two of these make a near-just classic minor third ~[[6/5]], with the biyatisma ([[121/120]]) being tempered out. The chroma of the scale (4\68, upwards on this layout) is the near-just diptolemaic chromatic semitone ~[[25/24]], and is convenient to use as a second generator (even though such is not required to avoid [[contorsion]]) to access other consonant intervals quickly, although sometimes with strange preferences built in — for instance, the septimal whole tone ~[[8/7]] is much easier to reach (at 13\68) than the Pythagorean whole tone ~[[9/8]] (which requires a substantial vertical reach at 12\68), while the septimal minor third ~[[7/6]] (at 15\18) is a much longer vertical reach than the classic minor third ~6/5 (at 18\68), and the septimal major third ~[[9/7]] is a much longer vertical reach (at 25\68) than the classic major third ~[[5/4]] (at 22\68). Fortunately the fourth (~[[4/3]], at 28\68), the Axirabian paramajor fourth (~[[11/8]], at 31\68), the Axirabian paraminor fifth (~[[16/11]], at 37\68) and fifth (~[[3/2]], at 40\68) are all easy to reach as long as they do not go through a vertical wraparound (as happens to the fourth in the bass octave). The range is four octaves plus two notes, and octaves slope upwards — not severely, but a vertical wraparound is unavoidable if note 0 is placed to get complete octaves as defined to reach from note 0 to note 0.

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 To give you a little more range while keeping octaves fairly near horizontal, the [[2L 7s]] mapping generated by 31/68 works decently, especially if you favor using the 11th harmonic in compositions.
 {{Lumatone EDO mapping|n=68|start=57|xstep=6|ystep=7}}
+== Biyatismic (Zeus) ==
+[[Bryan Deister]] has used a [[Biyatismic clan#Zeus|Biyatismic (Zeus)]] layout with a [[7L&nbsp;1s]] scale (9:5 step ratio) for [[68edo]], as demonstrated in [https://www.youtube.com/shorts/CO1AslAu9E0 ''microtonal improvisation in 68edo''] (2025). The rightward generator 9\68 is a combination of the Alpharabian tendoneutral second ~[[12/11]] and the undecimal submajor second ~[[11/10]], and two of these make a near-just classic minor third ~[[6/5]], with the biyatisma ([[121/120]]) being tempered out. The chroma of the scale (4\68, upwards on this layout) is the near-just diptolemaic chromatic semitone ~[[25/24]], and is convenient to use as a second generator (even though such is not required to avoid [[contorsion]]) to access other consonant intervals quickly, although sometimes with strange preferences built in &mdash; for instance, the septimal whole tone ~[[8/7]] is much easier to reach (at 13\68) than the Pythagorean whole tone ~[[9/8]] (which requires a substantial vertical reach at 12\68), while the septimal minor third ~[[7/6]] (at 15\18) is a much longer vertical reach than the classic minor third ~6/5 (at 18\68), and the septimal major third ~[[9/7]] is a much longer vertical reach (at 25\68) than the classic major third ~[[5/4]] (at 22\68). Fortunately the fourth (~[[4/3]], at 28\68), the Axirabian paramajor fourth (~[[11/8]], at 31\68), the Axirabian paraminor fifth (~[[16/11]], at 37\68) and fifth (~[[3/2]], at 40\68) are all easy to reach as long as they do not go through a vertical wraparound (as happens to the fourth in the bass octave). The range is four octaves plus two notes, and octaves slope upwards &mdash; not severely, but a vertical wraparound is unavoidable if note 0 is placed to get complete octaves as defined to reach from note 0 to note 0.
+{{Lumatone EDO mapping|n=68|start=0|xstep=9|ystep=-4}}
 {{Navbox Lumatone}}