Lumatone mapping for 65edo: Difference between revisions

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[[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 7\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.

== Sensipent (1/5-Octave) + Malcolmismic Pseudo-Pinetone (1/5-Octave) ==

[[Bryan Deister]] has demonstrated a rotated [[sensipent]] mapping, in which the [[3L 5s]] (10:7 step ratio) scale proceeds up and somewhat right (usually incurring a vertical wraparound), and a [[5L 5s]] scale (10:3 step ratio) proceeds right and down-right with the 1/5 division of the octave (13\65), in [https://www.youtube.com/shorts/pSIT-4VaGD0 ''65edo improv''] (2026). In accordance with sensipent harmony, the 1/5 division of the octave (13\65, one key right plus one key down-right) functions as both a near-just (only slightly sharp) tricesimoprimal ultramajor second ~[[31/27]], as well as a near-just (only slightly flat) vicesimotertial inframinor third ~[[23/20]]. The normal 31-limit (or even 2.3.5.31 subgroup) sensipent generator 24\65 functions as both a near-just (practically perfect) tricesimoprimal ultramajor third ~[[31/24]] and a near-just (only slightly sharp) tricesimoprimal supermajor third ~[[40/31]]. This is most simply 1/5-octave-reduced to the familiar near-just (only slightly flat) Pythagorean whole tone ~[[9/8]]. Alternatively (and easier to reach), the generator 10\65 (one key right, functioning as a slightly sharp classic whole tone ~[[10/9]]) can be used as a generator; although it is not co-prime with 65edo, it is co-prime with the 1/5-octave; this is like a weak extension of [[pinetone]] (again with the 1/5 division of the octave), but tempering out the malcolmisma [[171/170]] instead of the porcupine comma [[250/243]]. This mapping is maximally efficient, with a range just under 4⅛ octaves with no missed notes and no repeated notes, although the octaves slope down severely and wrap around vertically.

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 [[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 7\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}}
+== Sensipent (<sup>1</sup>/<sub>5</sub>-Octave) + Malcolmismic Pseudo-Pinetone (<sup>1</sup>/<sub>5</sub>-Octave) ==
+[[Bryan Deister]] has demonstrated a rotated [[sensipent]] mapping, in which the [[3L&nbsp;5s]] (10:7 step ratio) scale proceeds up and somewhat right (usually incurring a vertical wraparound), and a [[5L&nbsp;5s]] scale (10:3 step ratio) proceeds right and down-right with the <sup>1</sup>/<sub>5</sub> division of the octave (13\65), in [https://www.youtube.com/shorts/pSIT-4VaGD0 ''65edo improv''] (2026). In accordance with sensipent harmony, the <sup>1</sup>/<sub>5</sub> division of the octave (13\65, one key right plus one key down-right) functions as both a near-just (only slightly sharp) tricesimoprimal ultramajor second ~[[31/27]], as well as a near-just (only slightly flat) vicesimotertial inframinor third ~[[23/20]]. The normal 31-limit (or even 2.3.5.31 subgroup) sensipent generator 24\65 functions as both a near-just (practically perfect) tricesimoprimal ultramajor third ~[[31/24]] and a near-just (only slightly sharp) tricesimoprimal supermajor third ~[[40/31]]. This is most simply <sup>1</sup>/<sub>5</sub>-octave-reduced to the familiar near-just (only slightly flat) Pythagorean whole tone ~[[9/8]]. Alternatively (and easier to reach), the generator 10\65 (one key right, functioning as a slightly sharp classic whole tone ~[[10/9]]) can be used as a generator; although it is not co-prime with 65edo, it is co-prime with the <sup>1</sup>/<sub>5</sub>-octave; this is like a weak extension of [[pinetone]] (again with the <sup>1</sup>/<sub>5</sub> division of the octave), but tempering out the malcolmisma [[171/170]] instead of the porcupine comma [[250/243]]. This mapping is maximally efficient, with a range just under 4⅛ octaves with no missed notes and no repeated notes, although the octaves slope down severely and wrap around vertically.
+{{Lumatone EDO mapping|n=65|start=4|xstep=10|ystep=-7}}
 {{Navbox Lumatone}}