Lumatone mapping for 34edo - Revision history

Lucius Chiaraviglio: /* Hanson */ --> Kleismic (Hanson); add headings for the 2 existing mappings; insert Bryan Deister's Kleismic + Würschmidt mapping between these

2026-08-05T20:02:49Z

Hanson: --> Kleismic (Hanson); add headings for the 2 existing mappings; insert Bryan Deister's Kleismic + Würschmidt mapping between these

← Older revision		Revision as of 20:02, 5 August 2026
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	{{Lumatone EDO mapping\|n=34\|start=19\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=34\|start=19\|xstep=7\|ystep=-1}}

	== Hanson ==		== Kleismic (Hanson) ==
	The [[Hanson]] mapping also puts 5-limit consonances within easy reach of each other, but does not cover the full gamut ~~unless expanded from the [[3L 1s]] mapping to [[4L 3s]]~~.		=== Compressed (3L 1s) ===
			The kleismic [[Hanson]] mapping also puts 5-limit consonances within easy reach of each other, but does not cover the full gamut.
	{{Lumatone EDO mapping\|n=34\|start=19\|xstep=9\|ystep=-2}}		{{Lumatone EDO mapping\|n=34\|start=19\|xstep=9\|ystep=-2}}

			=== Compressed and rotated (3L 1s, adding Würschmidt) ===
			It is possible to accommodate both [[kleismic]] (stacking classic minor thirds) and [[würschmidt]] (stacking classic major thirds) temperaments in a [[34edo]] mapping by using a rotated [[3L 1s]] scale (9:7 step ratio), as demonstrated in [https://www.youtube.com/watch?v=JKblQe375pw ''34edo bossa''] (2026). This mapping puts both the classic minor third ~[[6/5]] and the classic major third ~[[5/4]] (both just slightly sharp) right next to both the root note and to the fifth ~[[3/2]], as 9\34 (one key down-right) and 11\34 (one key right), respectively. This comes at the cost of missing some notes (including some instances of note 0) due to trying to get too much range (close to ten octaves) to fit them all on a standard-sized Lumatone, as well as causing the octaves to alternate between near and far. (Note that in the demo video, the range appears far less due to mapping of only a single MIDI channel.)
			{{Lumatone EDO mapping\|n=34\|start=21\|xstep=11\|ystep=-2}}

			=== Expanded (4L 3s) ===
			To achieve the full gamut, it is necessary to expand the mapping to [[4L 3s]], which adds space between the root note, the major and minor thirds, and the fifth.
	{{Lumatone EDO mapping\|n=34\|start=3\|xstep=7\|ystep=-5}}		{{Lumatone EDO mapping\|n=34\|start=3\|xstep=7\|ystep=-5}}

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

Lucius Chiaraviglio: /* Tetracot */ Moved note 0 to match Bryan Deister's layout, to maximize range of complete octaves.

2025-09-24T21:18:18Z

Tetracot: Moved note 0 to match Bryan Deister's layout, to maximize range of complete octaves.

← Older revision		Revision as of 21:18, 24 September 2025
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	== Tetracot ==		== Tetracot ==
	The [[6L 1s]] [[Tetracot]] mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect fifth is in a straight line from the root, the [[7L 6s]] MOS makes 5-limit major and minor chords very easily accessible, and single steps are neatly mapped to the vertical axis. ~~However, the~~ range is ~~reduced to slightly over four~~ octaves. [[Bryan Deister]] has demonstrated this layout in [https://www.youtube.com/shorts/uVZ6tJ1y6ak ''34edo improv''] (2025).		The [[6L 1s]] [[Tetracot]] mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect fifth is in a straight line from the root, the [[7L 6s]] MOS makes 5-limit major and minor chords very easily accessible, and single steps are neatly mapped to the vertical axis. The range is still nearly five octaves, although instead of missing the last note of the highest octave, this layout misses the note two before that. [[Bryan Deister]] has demonstrated this layout in [https://www.youtube.com/shorts/uVZ6tJ1y6ak ''34edo improv''] (2025).
	{{Lumatone EDO mapping\|n=34\|start=25\|xstep=5\|ystep=-1}}		{{Lumatone EDO mapping\|n=34\|start=31\|xstep=5\|ystep=-1}}

	== Semiquartal (Immunity) ==		== Semiquartal (Immunity) ==

Lucius Chiaraviglio: /* Tetracot */ Add demo video

2025-09-22T19:41:57Z

Tetracot: Add demo video

← Older revision		Revision as of 19:41, 22 September 2025
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	== Tetracot ==		== Tetracot ==
	The [[6L 1s]] [[Tetracot]] mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect fifth is in a straight line from the root, the [[7L 6s]] MOS makes 5-limit major and minor chords very easily accessible, and single steps are neatly mapped to the vertical axis. However, the range is reduced to slightly over four octaves.		The [[6L 1s]] [[Tetracot]] mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect fifth is in a straight line from the root, the [[7L 6s]] MOS makes 5-limit major and minor chords very easily accessible, and single steps are neatly mapped to the vertical axis. However, the range is reduced to slightly over four octaves. [[Bryan Deister]] has demonstrated this layout in [https://www.youtube.com/shorts/uVZ6tJ1y6ak ''34edo improv''] (2025).
	{{Lumatone EDO mapping\|n=34\|start=25\|xstep=5\|ystep=-1}}		{{Lumatone EDO mapping\|n=34\|start=25\|xstep=5\|ystep=-1}}

ArrowHead294 at 22:07, 17 May 2025

2025-05-17T22:07:18Z

← Older revision		Revision as of 22:07, 17 May 2025
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	== Mabila ==		== Mabila ==
	You can use the b val instead, which generates [[Mabila]], but this puts the perfect ~~fith~~ in awkward places.		You can use the b val instead, which generates [[Mabila]], but this puts the perfect fifth in awkward places.
	{{Lumatone EDO mapping\|n=34\|start=14\|xstep=4\|ystep=3}}		{{Lumatone EDO mapping\|n=34\|start=14\|xstep=4\|ystep=3}}

ArrowHead294: /* Tetracot */

2025-05-17T14:52:06Z

Tetracot

← Older revision		Revision as of 14:52, 17 May 2025
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	== Tetracot ==		== Tetracot ==
	The [[6L 1s]] [[Tetracot]] mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect ~~5th~~ is in a straight line from the root, 5-limit major and minor chords ~~are~~ very easily accessible, and single steps are neatly mapped to the vertical axis. However, the range is reduced to slightly over four octaves.		The [[6L 1s]] [[Tetracot]] mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect fifth is in a straight line from the root, the [[7L 6s]] MOS makes 5-limit major and minor chords very easily accessible, and single steps are neatly mapped to the vertical axis. However, the range is reduced to slightly over four octaves.
	{{Lumatone EDO mapping\|n=34\|start=25\|xstep=5\|ystep=-1}}		{{Lumatone EDO mapping\|n=34\|start=25\|xstep=5\|ystep=-1}}

ArrowHead294 at 15:08, 16 May 2025

2025-05-16T15:08:06Z

← Older revision		Revision as of 15:08, 16 May 2025
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	== Mabila ==		== Mabila ==
	You can use the b val instead, which generates [[Mabila]].		You can use the b val instead, which generates [[Mabila]], but this puts the perfect fith in awkward places.
	{{Lumatone EDO mapping\|n=34\|start=14\|xstep=4\|ystep=3}}		{{Lumatone EDO mapping\|n=34\|start=14\|xstep=4\|ystep=3}}

	== Tetracot ==		== Tetracot ==
	~~However, this puts the perfect fith in awkward places.~~ The [[7L 6s]] [[Tetracot]] mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect 5th is in a straight line from the root, ~~while~~ single steps are neatly mapped to the vertical axis, ~~although it has less~~ range.		The [[6L 1s]] [[Tetracot]] mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect 5th is in a straight line from the root, 5-limit major and minor chords are very easily accessible, and single steps are neatly mapped to the vertical axis. However, the range is reduced to slightly over four octaves.
	{{Lumatone EDO mapping\|n=34\|start=25\|xstep=5\|ystep=-1}}		{{Lumatone EDO mapping\|n=34\|start=25\|xstep=5\|ystep=-1}}

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	== Hanson ==		== Hanson ==
	~~Or the~~ [[Hanson]] mapping, ~~although~~ the [[4L 3s]] ~~mapping does not quite cover the whole gamut~~.		The [[Hanson]] mapping also puts 5-limit consonances within easy reach of each other, but does not cover the full gamut unless expanded from the [[3L 1s]] mapping to [[4L 3s]].
	{{Lumatone EDO mapping\|n=34\|start=19\|xstep=9\|ystep=-2}}		{{Lumatone EDO mapping\|n=34\|start=19\|xstep=9\|ystep=-2}}


			{{Lumatone EDO mapping\|n=34\|start=3\|xstep=7\|ystep=-5}}

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

ArrowHead294 at 16:53, 26 March 2025

2025-03-26T16:53:31Z

← Older revision		Revision as of 16:53, 26 March 2025
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	== Mabila ==		== Mabila ==
	You can use the b val instead, which generates [[~~mabila~~]].		You can use the b val instead, which generates [[Mabila]].
	{{Lumatone EDO mapping\|n=34\|start=14\|xstep=4\|ystep=3}}		{{Lumatone EDO mapping\|n=34\|start=14\|xstep=4\|ystep=3}}

	== Tetracot ==		== Tetracot ==
	However, this puts the perfect ~~5th~~ in awkward places. The [[7L 6s]] [[Tetracot]] mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect 5th is in a straight line from the root, while single steps are neatly mapped to the vertical axis.		However, this puts the perfect fith in awkward places. The [[7L 6s]] [[Tetracot]] mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect 5th is in a straight line from the root, while single steps are neatly mapped to the vertical axis, although it has less range.
	{{Lumatone EDO mapping\|n=34\|start=25\|xstep=5\|ystep=-1}}		{{Lumatone EDO mapping\|n=34\|start=25\|xstep=5\|ystep=-1}}

ArrowHead294 at 15:02, 23 March 2025

2025-03-23T15:02:50Z

← Older revision		Revision as of 15:02, 23 March 2025
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	{{Lumatone mapping intro}} You can use the b val instead, which generates [[mabila]].		{{Lumatone mapping intro}}

			== Mabila ==
			You can use the b val instead, which generates [[mabila]].
	{{Lumatone EDO mapping\|n=34\|start=14\|xstep=4\|ystep=3}}		{{Lumatone EDO mapping\|n=34\|start=14\|xstep=4\|ystep=3}}

			== Tetracot ==
	However, this puts the perfect 5th in awkward places. The [[7L 6s]] [[Tetracot]] mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect 5th is in a straight line from the root, while single steps are neatly mapped to the vertical axis.		However, this puts the perfect 5th in awkward places. The [[7L 6s]] [[Tetracot]] mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect 5th is in a straight line from the root, while single steps are neatly mapped to the vertical axis.
	{{Lumatone EDO mapping\|n=34\|start=25\|xstep=5\|ystep=-1}}		{{Lumatone EDO mapping\|n=34\|start=25\|xstep=5\|ystep=-1}}

			== Semiquartal (Immunity) ==
	If you want greater range you can slice the perfect ~~4th~~ in two and use the [[~~immunity~~]] mapping. However, the resulting [[5L 4s]] MOS has a 6:1 step ratio, making it quite lopsided:		If you want greater range you can slice the perfect fourth in two and use the [[Immunity]] mapping. However, the resulting [[5L 4s]] MOS has a 6:1 step ratio, making it quite lopsided:
	{{Lumatone EDO mapping\|n=34\|start=19\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=34\|start=19\|xstep=7\|ystep=-1}}

			== Hanson ==
	Or the [[~~kleismic~~]] mapping, although the [[~~3L 1s~~]] mapping does not quite cover the whole gamut.		Or the [[Hanson]] mapping, although the [[4L 3s]] mapping does not quite cover the whole gamut.
	{{Lumatone EDO mapping\|n=34\|start=19\|xstep=9\|ystep=-2}}		{{Lumatone EDO mapping\|n=34\|start=19\|xstep=9\|ystep=-2}}

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

ArrowHead294 at 20:42, 21 March 2025

2025-03-21T20:42:47Z

← Older revision		Revision as of 20:42, 21 March 2025
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	{{Lumatone mapping intro}} You can use the b val instead, which generates [[mabila]].		{{Lumatone mapping intro}} You can use the b val instead, which generates [[mabila]].
	{{Lumatone EDO mapping\|n=34\|start=14\|xstep=4\|ystep=3}}		{{Lumatone EDO mapping\|n=34\|start=14\|xstep=4\|ystep=3}}

ArrowHead294 at 18:19, 14 March 2025

2025-03-14T18:19:06Z

← Older revision		Revision as of 18:19, 14 March 2025
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	~~34edo is an interesting case for [[Lumatone]] mappings, since ([[Lumatone mapping for 24edo\|like 24edo]]), it is not generated by fifths and octaves, so the [[Standard~~ Lumatone mapping ~~for Pythagorean]] only reaches [[17edo]] intervals unless you~~ use the b val instead, which generates [[mabila]].		{{Lumatone mapping intro}} You can use the b val instead, which generates [[mabila]].
	{{Lumatone EDO mapping\|n=34\|start=14\|xstep=4\|ystep=3}}		{{Lumatone EDO mapping\|n=34\|start=14\|xstep=4\|ystep=3}}