Lumatone mapping for 65edo: Difference between revisions

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Due to the size of the edo, this mapping does not quite cover all the notes. The [[Sensipent]] mapping does cover the whole gamut, keeps 5-limit chords fairly easy to play, and has only a slightly smaller range.

== Würschmidt (divided generator) ==

[[Bryan Deister]] has used the [[9L 2s]] (7:1 step ratio) mapping for [[65edo]] in [https://www.youtube.com/shorts/W5PXWFduPco ''microtonal improvisation in 65edo''] (2025). The rightward generator 9\65 is a slightly flat acute minor second ~[[27/25]], and three of these make a near-just classic major third ~[[5/4]]; in turn eight classic major thirds (21\65) make a near-just 6th harmonic ~[[6/1]], qualifying this for [[Würschmidt]] temperament, or an extension thereof that divides the Würschmidt generator into three equal parts, but using ~27/25 instead of the tridecimal supraminor second ~[[14/13]], which technically maps to the same interval in 65edo, but is composed of a very flat 7th harmonic and a very sharp 13th harmonic and is thus subject to wart adjustment to another interval for consistency improvement. The range is somewhat under three octaves, and the octaves slant up mildly, with some repeated notes to ease vertical wraparounds.

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 Due to the size of the edo, this mapping does not quite cover all the notes. The [[Sensipent]] mapping does cover the whole gamut, keeps 5-limit chords fairly easy to play, and has only a slightly smaller range.
 {{Lumatone EDO mapping|n=65|start=52|xstep=7|ystep=3}}
+== Würschmidt (divided generator) ==
+[[Bryan Deister]] has used the [[9L&nbsp;2s]] (7:1 step ratio) mapping for [[65edo]] in [https://www.youtube.com/shorts/W5PXWFduPco ''microtonal improvisation in 65edo''] (2025). The rightward generator 9\65 is a slightly flat acute minor second ~[[27/25]], and three of these make a near-just classic major third ~[[5/4]]; in turn eight classic major thirds (21\65) make a near-just 6th harmonic ~[[6/1]], qualifying this for [[Würschmidt]] temperament, or an extension thereof that divides the Würschmidt generator into three equal parts, but using ~27/25 instead of the tridecimal supraminor second ~[[14/13]], which technically maps to the same interval in 65edo, but is composed of a very flat 7th harmonic and a very sharp 13th harmonic and is thus subject to wart adjustment to another interval for consistency improvement. The range is somewhat under three octaves, and the octaves slant up mildly, with some repeated notes to ease vertical wraparounds.
+{{Lumatone EDO mapping|n=65|start=10|xstep=7|ystep=-6}}
 {{Navbox Lumatone}}