Lumatone mapping for 65edo - Revision history

Lucius Chiaraviglio: /* Squirrel */ Fix typo, and add 7L 1s scale step ratio

2026-03-22T05:06:54Z

Squirrel: Fix typo, and add 7L 1s scale step ratio

← Older revision		Revision as of 05:06, 22 March 2026
Line 6:		Line 6:

	== Squirrel ==		== Squirrel ==
	It is possible to map [[65edo]] with [[squirrel]] temperament, using as a generator the near-just undecimal submajor second ~[[11/10]], reminiscent of [[tetracot]] but producing a a [[1L 6s]] scale (11:9 step ratio) instead of [[6L 1s]]. Three of these generators make the near-just perfect fourth ~[[4/3]]; six of them make the near-just Pythagorean.minor seventh ~[[16/9]]; nine of them (with octave reduction) make the slightly flat otonal (undevesimal) minor third ~[[19/16]]; and twenty-one of them (with more octave reduction) make the near-just classic major seventh ~[[15/8]]. Unfortunately, this mapping does not cover all of the notes in the range of over 4½ octaves; even so, [[Bryan Deister]] has used this mapping in [[https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026).		It is possible to map [[65edo]] with [[squirrel]] temperament, using as a generator the near-just undecimal submajor second ~[[11/10]], reminiscent of [[tetracot]] but producing a a [[1L 6s]] scale (11:9 step ratio) instead of [[6L 1s]]. Three of these generators make the near-just perfect fourth ~[[4/3]]; six of them make the near-just Pythagorean.minor seventh ~[[16/9]]; nine of them (with octave reduction) make the slightly flat otonal (undevesimal) minor third ~[[19/16]]; and twenty-one of them (with more octave reduction) make the near-just classic major seventh ~[[15/8]]. Unfortunately, this mapping does not cover all of the notes in the range of over 4½ octaves; even so, [Bryan Deister]] has used this mapping in [[https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026).
	{{Lumatone EDO mapping\|n=65\|start=26\|xstep=9\|ystep=2}}		{{Lumatone EDO mapping\|n=65\|start=26\|xstep=9\|ystep=2}}

	This can be expanded to a [[7L 1s]] scale that does cover the full gamut in the middle octaves, but has a range of slightly less than 4 octaves and a stronger upward slant.		This can be expanded to a [[7L 1s]] scale (9:2 step ratio) that does cover the full gamut in the middle octaves, but has a range of slightly less than 4 octaves and a stronger upward slant.

	{{Lumatone EDO mapping\|n=65\|start=13\|xstep=9\|ystep=-7}}		{{Lumatone EDO mapping\|n=65\|start=13\|xstep=9\|ystep=-7}}

Yourmusic Productions: Add expanded squirrel mapping, since that's also pretty efficient in this edo.

2026-03-21T22:11:37Z

Add expanded squirrel mapping, since that's also pretty efficient in this edo.

← Older revision		Revision as of 22:11, 21 March 2026
Line 8:		Line 8:
	It is possible to map [[65edo]] with [[squirrel]] temperament, using as a generator the near-just undecimal submajor second ~[[11/10]], reminiscent of [[tetracot]] but producing a a [[1L 6s]] scale (11:9 step ratio) instead of [[6L 1s]]. Three of these generators make the near-just perfect fourth ~[[4/3]]; six of them make the near-just Pythagorean.minor seventh ~[[16/9]]; nine of them (with octave reduction) make the slightly flat otonal (undevesimal) minor third ~[[19/16]]; and twenty-one of them (with more octave reduction) make the near-just classic major seventh ~[[15/8]]. Unfortunately, this mapping does not cover all of the notes in the range of over 4½ octaves; even so, [[Bryan Deister]] has used this mapping in [[https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026).		It is possible to map [[65edo]] with [[squirrel]] temperament, using as a generator the near-just undecimal submajor second ~[[11/10]], reminiscent of [[tetracot]] but producing a a [[1L 6s]] scale (11:9 step ratio) instead of [[6L 1s]]. Three of these generators make the near-just perfect fourth ~[[4/3]]; six of them make the near-just Pythagorean.minor seventh ~[[16/9]]; nine of them (with octave reduction) make the slightly flat otonal (undevesimal) minor third ~[[19/16]]; and twenty-one of them (with more octave reduction) make the near-just classic major seventh ~[[15/8]]. Unfortunately, this mapping does not cover all of the notes in the range of over 4½ octaves; even so, [[Bryan Deister]] has used this mapping in [[https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026).
	{{Lumatone EDO mapping\|n=65\|start=26\|xstep=9\|ystep=2}}		{{Lumatone EDO mapping\|n=65\|start=26\|xstep=9\|ystep=2}}

			This can be expanded to a [[7L 1s]] scale that does cover the full gamut in the middle octaves, but has a range of slightly less than 4 octaves and a stronger upward slant.

			{{Lumatone EDO mapping\|n=65\|start=13\|xstep=9\|ystep=-7}}

	== Sensipent ==		== Sensipent ==
	The [[Sensipent]] mapping ~~does cover~~ the whole gamut, keeps 5-limit chords fairly easy to play, and has a range ~~of four close to complete octaves~~ (due to being chopped by the left and right edges, the first note 0 to note 0 octave is missing notes 5 and 8, while the last is missing notes 43, 53, 56, 60, and 63; apart from this, each octave has one repeated note). [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/zxgVvwXnIGQ ''Waltz in 65edo''] (2026).		The [[5L 3s]] [[Sensipent]] mapping also covers the whole gamut, keeps 5-limit chords fairly easy to play, and has a slightly wider range where it covers all the notes (due to being chopped by the left and right edges, the first note 0 to note 0 octave is missing notes 5 and 8, while the last is missing notes 43, 53, 56, 60, and 63; apart from this, each octave has one repeated note). [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/zxgVvwXnIGQ ''Waltz in 65edo''] (2026).
	{{Lumatone EDO mapping\|n=65\|start=28\|xstep=7\|ystep=3}}		{{Lumatone EDO mapping\|n=65\|start=28\|xstep=7\|ystep=3}}

Lucius Chiaraviglio: Add Bryan Deister's Squirrel mapping

2026-03-21T05:41:05Z

Add Bryan Deister's Squirrel mapping

← Older revision		Revision as of 05:41, 21 March 2026
Line 4:		Line 4:
	Note that since 65edo is a [[schismatic]] tuning, the best approximation to [[5/4]] is the diminished fourth. Due to the size of the edo, this mapping does not cover all the notes. Despite the missing notes, [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/UJZw9NQuGnY ''Zanarkand - Nobuo Uematsu (microtonal cover in 65edo)''] (2026).		Note that since 65edo is a [[schismatic]] tuning, the best approximation to [[5/4]] is the diminished fourth. Due to the size of the edo, this mapping does not cover all the notes. Despite the missing notes, [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/UJZw9NQuGnY ''Zanarkand - Nobuo Uematsu (microtonal cover in 65edo)''] (2026).
	{{Lumatone EDO mapping\|n=65\|start=2\|xstep=11\|ystep=-6}}		{{Lumatone EDO mapping\|n=65\|start=2\|xstep=11\|ystep=-6}}

			== Squirrel ==
			It is possible to map [[65edo]] with [[squirrel]] temperament, using as a generator the near-just undecimal submajor second ~[[11/10]], reminiscent of [[tetracot]] but producing a a [[1L 6s]] scale (11:9 step ratio) instead of [[6L 1s]]. Three of these generators make the near-just perfect fourth ~[[4/3]]; six of them make the near-just Pythagorean.minor seventh ~[[16/9]]; nine of them (with octave reduction) make the slightly flat otonal (undevesimal) minor third ~[[19/16]]; and twenty-one of them (with more octave reduction) make the near-just classic major seventh ~[[15/8]]. Unfortunately, this mapping does not cover all of the notes in the range of over 4½ octaves; even so, [[Bryan Deister]] has used this mapping in [[https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026).
			{{Lumatone EDO mapping\|n=65\|start=26\|xstep=9\|ystep=2}}

	== Sensipent ==		== Sensipent ==

Lucius Chiaraviglio: /* Sensipent */ Add demo video, and move note 0 to match

2026-03-17T09:28:46Z

Sensipent: Add demo video, and move note 0 to match

← Older revision		Revision as of 09:28, 17 March 2026
Line 6:		Line 6:

	== Sensipent ==		== Sensipent ==
	The [[Sensipent]] mapping does cover the whole gamut, keeps 5-limit chords fairly easy to play, and has ~~only~~ a ~~slightly smaller~~ range.		The [[Sensipent]] mapping does cover the whole gamut, keeps 5-limit chords fairly easy to play, and has a range of four close to complete octaves (due to being chopped by the left and right edges, the first note 0 to note 0 octave is missing notes 5 and 8, while the last is missing notes 43, 53, 56, 60, and 63; apart from this, each octave has one repeated note). [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/zxgVvwXnIGQ ''Waltz in 65edo''] (2026).
	{{Lumatone EDO mapping\|n=65\|start=52\|xstep=7\|ystep=3}}		{{Lumatone EDO mapping\|n=65\|start=28\|xstep=7\|ystep=3}}

	== Würschmidt (divided generator) ==		== Würschmidt (divided generator) ==

Lucius Chiaraviglio: /* Diatonic / / Sensipent */ Move misplaced description of Diatonic into Diatonic; add demo video

2026-02-06T07:03:52Z

Diatonic: Sensipent: Move misplaced description of Diatonic into Diatonic; add demo video

← Older revision		Revision as of 07:03, 6 February 2026
Line 2:		Line 2:

	== Diatonic ==		== Diatonic ==
	Note that since 65edo is a [[schismatic]] tuning, the best approximation to [[5/4]] is the diminished fourth.		Note that since 65edo is a [[schismatic]] tuning, the best approximation to [[5/4]] is the diminished fourth. Due to the size of the edo, this mapping does not cover all the notes. Despite the missing notes, [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/UJZw9NQuGnY ''Zanarkand - Nobuo Uematsu (microtonal cover in 65edo)''] (2026).
	{{Lumatone EDO mapping\|n=65\|start=2\|xstep=11\|ystep=-6}}		{{Lumatone EDO mapping\|n=65\|start=2\|xstep=11\|ystep=-6}}

	== Sensipent ==		== Sensipent ==
	~~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.		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}}		{{Lumatone EDO mapping\|n=65\|start=52\|xstep=7\|ystep=3}}

Yourmusic Productions: Fix math error.

2025-07-26T06:16:58Z

Fix math error.

← Older revision		Revision as of 06:16, 26 July 2025
Line 10:		Line 10:

	== Würschmidt (divided generator) ==		== 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.		[[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.
	{{Lumatone EDO mapping\|n=65\|start=10\|xstep=7\|ystep=-6}}		{{Lumatone EDO mapping\|n=65\|start=10\|xstep=7\|ystep=-6}}

	{{Navbox Lumatone}}		{{Navbox Lumatone}}

Lucius Chiaraviglio: Add Bryan Deister's Würschmidt (divided generator) Lumatone mapping for 65edo

2025-07-24T08:43:09Z

Add Bryan Deister's Würschmidt (divided generator) Lumatone mapping for 65edo

← Older revision		Revision as of 08:43, 24 July 2025
Line 8:		Line 8:
	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.		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}}		{{Lumatone EDO mapping\|n=65\|start=52\|xstep=7\|ystep=3}}

			== 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.
			{{Lumatone EDO mapping\|n=65\|start=10\|xstep=7\|ystep=-6}}

	{{Navbox Lumatone}}		{{Navbox Lumatone}}

ArrowHead294 at 15:29, 23 March 2025

2025-03-23T15:29:02Z

← Older revision		Revision as of 15:29, 23 March 2025
Line 1:		Line 1:
	{{Lumatone mapping intro}} Note that since 65edo is a [[schismatic]] tuning, the best approximation to [[5/4]] is the diminished fourth.		{{Lumatone mapping intro}}

			== Diatonic ==
			Note that since 65edo is a [[schismatic]] tuning, the best approximation to [[5/4]] is the diminished fourth.
	{{Lumatone EDO mapping\|n=65\|start=2\|xstep=11\|ystep=-6}}		{{Lumatone EDO mapping\|n=65\|start=2\|xstep=11\|ystep=-6}}

			== Sensipent ==
	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.		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}}		{{Lumatone EDO mapping\|n=65\|start=52\|xstep=7\|ystep=3}}

	{{Navbox Lumatone}}		{{Navbox Lumatone}}

ArrowHead294 at 18:38, 14 March 2025

2025-03-14T18:38:07Z

← Older revision		Revision as of 18:38, 14 March 2025
Line 1:		Line 1:
	~~There are many conceivable ways to map [[65edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard~~ Lumatone mapping ~~for Pythagorean]].~~ Note that since 65edo is a [[schismatic]] tuning, the best approximation to ~~the 5th harmonic~~ is the diminished ~~4th~~.		{{Lumatone mapping intro}} Note that since 65edo is a [[schismatic]] tuning, the best approximation to [[5/4]] is the diminished fourth.
	{{Lumatone EDO mapping\|n=65\|start=2\|xstep=11\|ystep=-6}}		{{Lumatone EDO mapping\|n=65\|start=2\|xstep=11\|ystep=-6}}


	~~However, 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.		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}}		{{Lumatone EDO mapping\|n=65\|start=52\|xstep=7\|ystep=3}}

	{{Navbox Lumatone}}		{{Navbox Lumatone}}

ArrowHead294 at 16:58, 11 February 2025

2025-02-11T16:58:31Z

← Older revision		Revision as of 16:58, 11 February 2025
Line 1:		Line 1:
	There are many conceivable ways to map [[65edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]]. Note that since 65edo is a [[schismatic]] tuning, the best approximation to the 5th harmonic is the diminished 4th.		There are many conceivable ways to map [[65edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]]. Note that since 65edo is a [[schismatic]] tuning, the best approximation to the 5th harmonic is the diminished 4th.
	{{Lumatone EDO mapping\|n=65\|start=2\|xstep=11\|ystep=-6}}		{{Lumatone EDO mapping\|n=65\|start=2\|xstep=11\|ystep=-6}}


	However, 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.		However, 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}}		{{Lumatone EDO mapping\|n=65\|start=52\|xstep=7\|ystep=3}}

			{{Navbox Lumatone}}
	{{Lumatone ~~mapping navigation~~}}