Lumatone mapping for 42edo - Revision history

Lucius Chiaraviglio: /* Whitewood + Qeema/Tritikleismic */ Reorganize and add another version from Bryan Deister; also fix mistake in the mapping (42edo is a minefield)

2026-03-04T10:03:08Z

Whitewood + Qeema/Tritikleismic: Reorganize and add another version from Bryan Deister; also fix mistake in the mapping (42edo is a minefield)

← Older revision		Revision as of 10:03, 4 March 2026
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	== Whitewood + Qeema/Tritikleismic ==		== Whitewood + Qeema/Tritikleismic ==
	Since [[42edo]] is a multiple of [[7edo]], and not far beyond the last diatonic-incapable tuning [[35edo]], [[whitewood]] is still a legitimate mapping for it; since the 5th harmonic is also close to maximally far from just, this suggests [[qeema]]/[[tritikleismic]] temperament, using the 42bc [[val]] (42bcd if using the 7-limit), for which the generator is a near-just classic minor third ~[[6/5]] (with the very large errors in the 3rd and 5th harmonics canceling each other almost perfectly)~~; this generator~~ corresponds to one key right ~~(which itself~~ is the very flatly approximated ~~major second~~ ~[[9/8]]) ~~plus~~ one key down-right. ~~Use of this~~ generator plus some extra down-right key movements as needed gives rise to the scales [[2L 6s]] (6:5 step ratio) and [[2L 4s]] (11:5 step ratio). [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/B90JT_SxSSE ''<nowiki>A Hunger Awakes - 42edo [short]</nowiki>''] (2026), although with different placement of MIDI note 0. The range is about 4¾ octaves, which slant up with the rows (as normal for whitewood mappings).		Since [[42edo]] is a multiple of [[7edo]], and not far beyond the last diatonic-incapable tuning [[35edo]], [[whitewood]] is still a legitimate mapping for it; since the 5th harmonic is also close to maximally far from just, this suggests [[qeema]]/[[tritikleismic]] temperament, using the 42bc [[val]] (42bcd if using the 7-limit), for which the generator 11\42 is a near-just classic minor third ~[[6/5]] (with the very large errors in the 3rd and 5th harmonics canceling each other almost perfectly), and corresponds to one key right plus one key down-right, although the two mappings below differ in how the generator is constituted.

			==== 2L 6s + 2L 4s version ====
			On one version of the mapping, one key right 6\42 corresponds to the very flatly approximated ptolemaic whole tone ~[[10/9]]), and one key down-right 5\42 is a neutral second close to ~[[25/23]] by direct approximation (which, however, does not map to this interval by [[patent val]] [[mapping]]). Combining these to form the generator plus some extra down-right key movements as needed gives rise to the scales [[2L 6s]] (6:5 step ratio) and [[2L 4s]] (11:5 step ratio). [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/B90JT_SxSSE ''<nowiki>A Hunger Awakes - 42edo [short]</nowiki>''] (2026), although with different placement of MIDI note 0. The range is about 4¾ octaves, which slant up with the rows (as normal for whitewood mappings).
	{{Lumatone EDO mapping\|n=42\|start=34\|xstep=6\|ystep=-1}}		{{Lumatone EDO mapping\|n=42\|start=34\|xstep=6\|ystep=-1}}

			==== 2L 7s + 2L 5s version ====
			In an alternate version of the above mapping, one key right 7\42 corresponds to the werckismic tone ~[[55/49]] (since the similar ~[[9/8]] maps inconsistently to another interval), and one key down-right 4\42 corresponds to a sharp large septendecimal semitone ~[[17/16]]. Combining these to form the generator generator plus some extra down-right key movements as needed gives rise to the scales [[2L 7s]] (7:4 step ratio) and [[2L 5s]] (11:4 step ratio). [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/D_YgzRJFg8I ''<nowiki>Waltz in 42edo [short]</nowiki>''] (2026). The range is a bit over five octaves, which slant up with the rows (as normal for whitewood mappings).
			{{Lumatone EDO mapping\|n=42\|start=0\|xstep=7\|ystep=-3}}

	== Lemba ==		== Lemba ==

Lucius Chiaraviglio: /* Whitewood + Qeema/Tritikleismic */ Add another sscale and step ratios

2026-02-25T08:11:22Z

Whitewood + Qeema/Tritikleismic: Add another sscale and step ratios

← Older revision		Revision as of 08:11, 25 February 2026
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	== Whitewood + Qeema/Tritikleismic ==		== Whitewood + Qeema/Tritikleismic ==
	Since [[42edo]] is a multiple of [[7edo]], and not far beyond the last diatonic-incapable tuning [[35edo]], [[whitewood]] is still a legitimate mapping for it; since the 5th harmonic is also close to maximally far from just, this suggests [[qeema]]/[[tritikleismic]] temperament, using the 42bc [[val]] (42bcd if using the 7-limit), for which the generator is a near-just classic minor third ~[[6/5]] (with the very large errors in the 3rd and 5th harmonics canceling each other almost perfectly); this generator corresponds to one key right (which itself is the very flatly approximated major second ~[[9/8]]) plus one key down-right. Use of this generator plus some extra down-right key movements as needed gives rise to the ~~scale~~ [[2L 6s]]. [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/B90JT_SxSSE ''<nowiki>A Hunger Awakes - 42edo [short]</nowiki>''] (2026), although with different placement of MIDI note 0. The range is about 4¾ octaves, which slant up with the rows (as normal for whitewood mappings).		Since [[42edo]] is a multiple of [[7edo]], and not far beyond the last diatonic-incapable tuning [[35edo]], [[whitewood]] is still a legitimate mapping for it; since the 5th harmonic is also close to maximally far from just, this suggests [[qeema]]/[[tritikleismic]] temperament, using the 42bc [[val]] (42bcd if using the 7-limit), for which the generator is a near-just classic minor third ~[[6/5]] (with the very large errors in the 3rd and 5th harmonics canceling each other almost perfectly); this generator corresponds to one key right (which itself is the very flatly approximated major second ~[[9/8]]) plus one key down-right. Use of this generator plus some extra down-right key movements as needed gives rise to the scales [[2L 6s]] (6:5 step ratio) and [[2L 4s]] (11:5 step ratio). [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/B90JT_SxSSE ''<nowiki>A Hunger Awakes - 42edo [short]</nowiki>''] (2026), although with different placement of MIDI note 0. The range is about 4¾ octaves, which slant up with the rows (as normal for whitewood mappings).
	{{Lumatone EDO mapping\|n=42\|start=34\|xstep=6\|ystep=-1}}		{{Lumatone EDO mapping\|n=42\|start=34\|xstep=6\|ystep=-1}}

Lucius Chiaraviglio: /* Lemba */ Experimented with moving note 0 — rejected because of potential vertical wraparound problems, but found that range is almost six octaves

2026-01-17T02:44:55Z

Lemba: Experimented with moving note 0 — rejected because of potential vertical wraparound problems, but found that range is almost six octaves

← Older revision		Revision as of 02:44, 17 January 2026
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	== Lemba ==		== Lemba ==
	The [[Lemba]] mapping is also of particular interest despite using a non-patent val. It achieves a range of ~~somewhat under~~ six octaves, with only a slight downwards slope.		The [[Lemba]] mapping is also of particular interest despite using a non-patent val. It achieves a range of almost six octaves, with only a slight downwards slope.
	{{Lumatone EDO mapping\|n=42\|start=40\|xstep=8\|ystep=-3}}		{{Lumatone EDO mapping\|n=42\|start=40\|xstep=8\|ystep=-3}}

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

Lucius Chiaraviglio: /* Lemba */ Fix number

2026-01-17T02:41:25Z

Lemba: Fix number

← Older revision		Revision as of 02:41, 17 January 2026
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	== Lemba ==		== Lemba ==
	The [[Lemba]] mapping is also of particular interest despite using a non-patent val. It achieves a range of somewhat under ~~five~~ octaves, with only a slight downwards slope.		The [[Lemba]] mapping is also of particular interest despite using a non-patent val. It achieves a range of somewhat under six octaves, with only a slight downwards slope.
	{{Lumatone EDO mapping\|n=42\|start=40\|xstep=8\|ystep=-3}}		{{Lumatone EDO mapping\|n=42\|start=40\|xstep=8\|ystep=-3}}

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

Lucius Chiaraviglio: /* Lemba */ Add a reason for it to be of interest

2026-01-17T02:40:57Z

Lemba: Add a reason for it to be of interest

← Older revision		Revision as of 02:40, 17 January 2026
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	== Lemba ==		== Lemba ==
	The [[Lemba]] mapping is also of particular interest despite using a non-patent val.		The [[Lemba]] mapping is also of particular interest despite using a non-patent val. It achieves a range of somewhat under five octaves, with only a slight downwards slope.
	{{Lumatone EDO mapping\|n=42\|start=40\|xstep=8\|ystep=-3}}		{{Lumatone EDO mapping\|n=42\|start=40\|xstep=8\|ystep=-3}}

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

Lucius Chiaraviglio: /* Pseudo-Isomorphic Pseudo-Diatonic */ Insert Bryan Deister's Whitewood + Qeema/Tritikleismic mapping after this

2026-01-17T02:39:31Z

Pseudo-Isomorphic Pseudo-Diatonic: Insert Bryan Deister's Whitewood + Qeema/Tritikleismic mapping after this

← Older revision		Revision as of 02:39, 17 January 2026
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	A pseudo-isomorphic pseudo-diatonic mapping for [[42edo]] that duplicates note 0 (as note 18) enables diatonic playing while keeping octaves level — it is the [[43edo]] diatonic layout, but with only 42 unique notes per octave. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/watch?v=cL6CY3U9mHM ''42edo groove''] (2025).		A pseudo-isomorphic pseudo-diatonic mapping for [[42edo]] that duplicates note 0 (as note 18) enables diatonic playing while keeping octaves level — it is the [[43edo]] diatonic layout, but with only 42 unique notes per octave. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/watch?v=cL6CY3U9mHM ''42edo groove''] (2025).
	{{Lumatone EDO mapping\|n=43\|start=41\|xstep=7\|ystep=-3}}		{{Lumatone EDO mapping\|n=43\|start=41\|xstep=7\|ystep=-3}}

			== Whitewood + Qeema/Tritikleismic ==
			Since [[42edo]] is a multiple of [[7edo]], and not far beyond the last diatonic-incapable tuning [[35edo]], [[whitewood]] is still a legitimate mapping for it; since the 5th harmonic is also close to maximally far from just, this suggests [[qeema]]/[[tritikleismic]] temperament, using the 42bc [[val]] (42bcd if using the 7-limit), for which the generator is a near-just classic minor third ~[[6/5]] (with the very large errors in the 3rd and 5th harmonics canceling each other almost perfectly); this generator corresponds to one key right (which itself is the very flatly approximated major second ~[[9/8]]) plus one key down-right. Use of this generator plus some extra down-right key movements as needed gives rise to the scale [[2L 6s]]. [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/B90JT_SxSSE ''<nowiki>A Hunger Awakes - 42edo [short]</nowiki>''] (2026), although with different placement of MIDI note 0. The range is about 4¾ octaves, which slant up with the rows (as normal for whitewood mappings).
			{{Lumatone EDO mapping\|n=42\|start=34\|xstep=6\|ystep=-1}}

	== Lemba ==		== Lemba ==

Lucius Chiaraviglio: /* Diatonic */ Add Bryan Deister's pseudo-diatonic pseudo-isomorphic mapping

2025-10-01T20:56:25Z

Diatonic: Add Bryan Deister's pseudo-diatonic pseudo-isomorphic mapping

← Older revision		Revision as of 20:56, 1 October 2025
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	The flat fifth is the same as that of [[7edo]], which if used would result in six mutually-exclusive rings of fifths, so to cycle through all notes using the [[circle of fifths]] you need to use the sharp fifth instead, which gives [[ultrapyth]].		The flat fifth is the same as that of [[7edo]], which if used would result in six mutually-exclusive rings of fifths, so to cycle through all notes using the [[circle of fifths]] you need to use the sharp fifth instead, which gives [[ultrapyth]].
	{{Lumatone EDO mapping\|n=42\|start=12\|xstep=8\|ystep=-7}}		{{Lumatone EDO mapping\|n=42\|start=12\|xstep=8\|ystep=-7}}

			== Pseudo-Isomorphic Pseudo-Diatonic ==
			A pseudo-isomorphic pseudo-diatonic mapping for [[42edo]] that duplicates note 0 (as note 18) enables diatonic playing while keeping octaves level — it is the [[43edo]] diatonic layout, but with only 42 unique notes per octave. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/watch?v=cL6CY3U9mHM ''42edo groove''] (2025).
			{{Lumatone EDO mapping\|n=43\|start=41\|xstep=7\|ystep=-3}}

	== Lemba ==		== Lemba ==

ArrowHead294 at 15:11, 23 March 2025

2025-03-23T15:11:04Z

← Older revision		Revision as of 15:11, 23 March 2025
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	{{Lumatone mapping intro}} The flat fifth is the same as that of [[7edo]], which if used would result in six mutually-exclusive rings of fifths, so to cycle through all notes using the [[~~chain-of-fifths notation\|~~circle of fifths]] you need to use the sharp fifth instead, which gives [[ultrapyth]].		{{Lumatone mapping intro}}

			== Diatonic ==
			The flat fifth is the same as that of [[7edo]], which if used would result in six mutually-exclusive rings of fifths, so to cycle through all notes using the [[circle of fifths]] you need to use the sharp fifth instead, which gives [[ultrapyth]].
	{{Lumatone EDO mapping\|n=42\|start=12\|xstep=8\|ystep=-7}}		{{Lumatone EDO mapping\|n=42\|start=12\|xstep=8\|ystep=-7}}

			== Lemba ==
	The [[Lemba]] mapping is also of particular interest despite using a non patent val.		The [[Lemba]] mapping is also of particular interest despite using a non-patent val.
	{{Lumatone EDO mapping\|n=42\|start=40\|xstep=8\|ystep=-3}}		{{Lumatone EDO mapping\|n=42\|start=40\|xstep=8\|ystep=-3}}

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

ArrowHead294 at 04:30, 15 March 2025

2025-03-15T04:30:57Z

← Older revision		Revision as of 04:30, 15 March 2025
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	{{Lumatone mapping intro}} The ~~patent val~~ is ~~slightly better~~, which gives [[ultrapyth]].		{{Lumatone mapping intro}} The flat fifth is the same as that of [[7edo]], which if used would result in six mutually-exclusive rings of fifths, so to cycle through all notes using the [[chain-of-fifths notation\|circle of fifths]] you need to use the sharp fifth instead, which gives [[ultrapyth]].
	{{Lumatone EDO mapping\|n=42\|start=12\|xstep=8\|ystep=-7}}		{{Lumatone EDO mapping\|n=42\|start=12\|xstep=8\|ystep=-7}}

ArrowHead294 at 19:01, 14 March 2025

2025-03-14T19:01:18Z

← Older revision		Revision as of 19:01, 14 March 2025
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	{{Lumatone mapping intro}}		{{Lumatone mapping intro}} The patent val is slightly better, which gives [[ultrapyth]].
	{{Lumatone EDO mapping\|n=42\|start=12\|xstep=8\|ystep=-7}}		{{Lumatone EDO mapping\|n=42\|start=12\|xstep=8\|ystep=-7}}