Lumatone mapping for 74edo - Revision history

Lucius Chiaraviglio: /* Cantonismic-Werckismic rank-3 temperament */ Add Bryan Deister's flipped version of this

2026-08-15T06:00:41Z

Cantonismic-Werckismic rank-3 temperament: Add Bryan Deister's flipped version of this

← Older revision		Revision as of 06:00, 15 August 2026
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	[[Bryan Deister]] has demonstrated the [[7L 6s]] (8:3 step ratio) mapping of [[74edo]] in [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025). The rightward generator (8\74) functions as a near-just tridecimal supraminor second ~[[14/13]]; three of them make a classic major third ~[[5/4]] (the [[cantonisma]] 10985/10976 is tempered out); five of them make an essentially-just undecimal subfifth ~[[16/11]]; and eight of them make a highly accurate undecimal supraminor seventh ~[[20/11]]. The upward generator (5\74) functions as ~[[21/20]] and ~[[22/21]] (the Werckisma ([[441/440]] is tempered out); two of these make ~[[11/10]]; five of these make ~[[24/19]] (which is distinguished from ~5/4); and eight of these make ~[[16/11]]. The range is just over 3 octaves with no missing notes, and the octaves slope down and wrap around vertically.		[[Bryan Deister]] has demonstrated the [[7L 6s]] (8:3 step ratio) mapping of [[74edo]] in [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025). The rightward generator (8\74) functions as a near-just tridecimal supraminor second ~[[14/13]]; three of them make a classic major third ~[[5/4]] (the [[cantonisma]] 10985/10976 is tempered out); five of them make an essentially-just undecimal subfifth ~[[16/11]]; and eight of them make a highly accurate undecimal supraminor seventh ~[[20/11]]. The upward generator (5\74) functions as ~[[21/20]] and ~[[22/21]] (the Werckisma ([[441/440]] is tempered out); two of these make ~[[11/10]]; five of these make ~[[24/19]] (which is distinguished from ~5/4); and eight of these make ~[[16/11]]. The range is just over 3 octaves with no missing notes, and the octaves slope down and wrap around vertically.
	{{Lumatone EDO mapping\|n=74\|start=4\|xstep=8\|ystep=-5}}		{{Lumatone EDO mapping\|n=74\|start=4\|xstep=8\|ystep=-5}}

			==== Flipped version with divided octave ====
			If the above mapping is flipped (so that what was the upwards generator is now the down-right generator), the scale becomes [[8L 2s]] (8:5 step ratio, now dividing the octave in half), as demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/shorts/TKZ05H4jYGc ''<nowiki>Waltz in 74edo [short clip]</nowiki>''] (2026). The octaves are closer to level (now sloping mildly upwards), and the range is actually slightly extended to 3¼ octaves, while still having a few repeated notes to mitigate vertical wraparounds.
			{{Lumatone EDO mapping\|n=74\|start=70\|xstep=8\|ystep=-3}}

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

Lucius Chiaraviglio: /* Cantonismic-Werckismic rank-3 temperament */ Adjust wording, including adding scale step ratio

2026-08-12T06:28:56Z

Cantonismic-Werckismic rank-3 temperament: Adjust wording, including adding scale step ratio

← Older revision		Revision as of 06:28, 12 August 2026
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	== Cantonismic-Werckismic rank-3 temperament ==		== Cantonismic-Werckismic rank-3 temperament ==
	[[Bryan Deister]] has demonstrated the [[7L 6s]] mapping of [[74edo]] in [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025). The rightward generator (8\74) functions as ~[[14/13]]; three of them make a classic major third ~[[5/4]] (the [[cantonisma]] 10985/10976 is tempered out); five of them make an essentially-just undecimal subfifth ~[[16/11]]; and eight of them make a highly accurate undecimal supraminor seventh ~[[20/11]]. The upward generator (5\74) functions as ~[[21/20]] and ~[[22/21]] (the Werckisma ([[441/440]] is tempered out); two of these make ~[[11/10]]; five of these make ~[[24/19]] (which is distinguished from ~5/4); and eight of these make ~[[16/11]]. The range is ~~about~~ just over 3 octaves with no missing notes, and the octaves slope down and wrap around vertically.		[[Bryan Deister]] has demonstrated the [[7L 6s]] (8:3 step ratio) mapping of [[74edo]] in [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025). The rightward generator (8\74) functions as a near-just tridecimal supraminor second ~[[14/13]]; three of them make a classic major third ~[[5/4]] (the [[cantonisma]] 10985/10976 is tempered out); five of them make an essentially-just undecimal subfifth ~[[16/11]]; and eight of them make a highly accurate undecimal supraminor seventh ~[[20/11]]. The upward generator (5\74) functions as ~[[21/20]] and ~[[22/21]] (the Werckisma ([[441/440]] is tempered out); two of these make ~[[11/10]]; five of these make ~[[24/19]] (which is distinguished from ~5/4); and eight of these make ~[[16/11]]. The range is just over 3 octaves with no missing notes, and the octaves slope down and wrap around vertically.
	{{Lumatone EDO mapping\|n=74\|start=4\|xstep=8\|ystep=-5}}		{{Lumatone EDO mapping\|n=74\|start=4\|xstep=8\|ystep=-5}}

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

Lucius Chiaraviglio: /* Diatonic */ Add Bryan Deister's flipped/rotated diatonic mapping

2026-07-02T03:00:42Z

Diatonic: Add Bryan Deister's flipped/rotated diatonic mapping

← Older revision		Revision as of 03:00, 2 July 2026
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	Despite the missing notes, [[Bryan Deister]] has used the diatonic mapping in [https://www.youtube.com/shorts/dB9_3TC3yPo ''Resonance - Home (microtonal cover in 74edo)''] (2026).		Despite the missing notes, [[Bryan Deister]] has used the diatonic mapping in [https://www.youtube.com/shorts/dB9_3TC3yPo ''Resonance - Home (microtonal cover in 74edo)''] (2026).
	{{Lumatone EDO mapping\|n=74\|start=70\|xstep=12\|ystep=-5}}		{{Lumatone EDO mapping\|n=74\|start=70\|xstep=12\|ystep=-5}}

			=== Flipped/Rotated version ===
			One option for dealing with the large gamut of [[74edo]] on a standard-sized Lumatone is to flip and rotate the diatonic mapping, as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/shorts/vi-KljzPkGs ''74edo improv''] (2026). The scale is still [[5L 2s]] with a 12:7 step ratio, but now the whole tones proceed down-right while the diatonic semitones proceed right. Each octave is still missing some notes, but due to the octave slope, they are different missing notes in each octave (other than the octaves chopped off by the upper left and lower right corners); the range is three mostly-complete octaves plus a bass octave of full compass but severely truncated gamut, plus a partial treble octave.
			{{Lumatone EDO mapping\|n=74\|start=0\|xstep=7\|ystep=5}}

	== Semimeantone ==		== Semimeantone ==

Lucius Chiaraviglio: /* Diatonic */ Add demo video

2026-03-15T01:00:40Z

Diatonic: Add demo video

← Older revision		Revision as of 01:00, 15 March 2026
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	{{Lumatone mapping intro}} However, due to its size, this mapping does not cover all the notes, although this does not matter in many keys because lower limit harmonics are relatively close together, which opens the possibility that even modulation to remote keys might be accommodated in some cases by the use of Lumatone presets mapping different diatonic subsets of 74edo.		{{Lumatone mapping intro}} However, due to its size, this mapping does not cover all the notes, although this does not matter in many keys because lower limit harmonics are relatively close together, which opens the possibility that even modulation to remote keys might be accommodated in some cases by the use of Lumatone presets mapping different diatonic subsets of 74edo.
	== Diatonic ==		== Diatonic ==
			Despite the missing notes, [[Bryan Deister]] has used the diatonic mapping in [https://www.youtube.com/shorts/dB9_3TC3yPo ''Resonance - Home (microtonal cover in 74edo)''] (2026).
	{{Lumatone EDO mapping\|n=74\|start=70\|xstep=12\|ystep=-5}}		{{Lumatone EDO mapping\|n=74\|start=70\|xstep=12\|ystep=-5}}

Lucius Chiaraviglio: Add Bryan Deister's Cantonismic-Werkicsmic rank-3 temperament mapping

2025-07-26T06:40:38Z

Add Bryan Deister's Cantonismic-Werkicsmic rank-3 temperament mapping

← Older revision		Revision as of 06:40, 26 July 2025
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	The [[2L 9s]] mapping is another option, especially if you don't mind using the second best mapping for some notes in larger chords; however, it skips some notes in all octaves, exacerbated in the lower and upper full octaves by the shear inherent in this layout.		The [[2L 9s]] mapping is another option, especially if you don't mind using the second best mapping for some notes in larger chords; however, it skips some notes in all octaves, exacerbated in the lower and upper full octaves by the shear inherent in this layout.
	{{Lumatone EDO mapping\|n=74\|start=27\|xstep=4\|ystep=15}}		{{Lumatone EDO mapping\|n=74\|start=27\|xstep=4\|ystep=15}}

			== Cantonismic-Werckismic rank-3 temperament ==
			[[Bryan Deister]] has demonstrated the [[7L 6s]] mapping of [[74edo]] in [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025). The rightward generator (8\74) functions as ~[[14/13]]; three of them make a classic major third ~[[5/4]] (the [[cantonisma]] 10985/10976 is tempered out); five of them make an essentially-just undecimal subfifth ~[[16/11]]; and eight of them make a highly accurate undecimal supraminor seventh ~[[20/11]]. The upward generator (5\74) functions as ~[[21/20]] and ~[[22/21]] (the Werckisma ([[441/440]] is tempered out); two of these make ~[[11/10]]; five of these make ~[[24/19]] (which is distinguished from ~5/4); and eight of these make ~[[16/11]]. The range is about just over 3 octaves with no missing notes, and the octaves slope down and wrap around vertically.
			{{Lumatone EDO mapping\|n=74\|start=4\|xstep=8\|ystep=-5}}

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

Lucius Chiaraviglio: Possible way to get all of the notes in the diatonic mapping, just not all at once.

2025-06-09T02:05:40Z

Possible way to get all of the notes in the diatonic mapping, just not all at once.

← Older revision		Revision as of 02:05, 9 June 2025
Line 1:		Line 1:
	{{Lumatone mapping intro}} However, due to its size, this mapping does not cover all the notes, although this does not matter in many keys because lower limit harmonics are relatively close together.		{{Lumatone mapping intro}} However, due to its size, this mapping does not cover all the notes, although this does not matter in many keys because lower limit harmonics are relatively close together, which opens the possibility that even modulation to remote keys might be accommodated in some cases by the use of Lumatone presets mapping different diatonic subsets of 74edo.
	== Diatonic ==		== Diatonic ==
	{{Lumatone EDO mapping\|n=74\|start=70\|xstep=12\|ystep=-5}}		{{Lumatone EDO mapping\|n=74\|start=70\|xstep=12\|ystep=-5}}

Lucius Chiaraviglio: Fix comma splice

2025-06-08T20:30:54Z

Fix comma splice

← Older revision		Revision as of 20:30, 8 June 2025
Line 4:		Line 4:

	== Semimeantone ==		== Semimeantone ==
	The [[2L 8s]] mapping covers the whole gamut as efficiently as possible in a span of three octaves, although notes 52, 58, 65 & 71-72 are missing from the otherwise full upper octave, octaves slope slightly upward.		The [[2L 8s]] mapping covers the whole gamut as efficiently as possible in a span of three octaves, although notes 52, 58, 65 & 71-72 are missing from the otherwise full upper octave; octaves slope slightly upward.
	{{Lumatone EDO mapping\|n=74\|start=68\|xstep=6\|ystep=7}}		{{Lumatone EDO mapping\|n=74\|start=68\|xstep=6\|ystep=7}}

Yourmusic Productions: Shifting zero point to give two complete octaves and amend description appropriately.

2025-06-08T09:29:14Z

Shifting zero point to give two complete octaves and amend description appropriately.

← Older revision		Revision as of 09:29, 8 June 2025
Line 4:		Line 4:

	== Semimeantone ==		== Semimeantone ==
	The [[2L 8s]] mapping covers the whole gamut as efficiently as possible in a span of three octaves, although ~~one note 1 is missing from the lower otherwise full octave~~, ~~and one each of notes 59~~, 65~~, and~~ 72 is missing from the ~~upper~~ otherwise full octave ~~(so that only the middle octave is truly complete);~~ octaves slope slightly upward.		The [[2L 8s]] mapping covers the whole gamut as efficiently as possible in a span of three octaves, although notes 52, 58, 65 & 71-72 are missing from the otherwise full upper octave, octaves slope slightly upward.
	{{Lumatone EDO mapping\|n=74\|start=1\|xstep=6\|ystep=7}}		{{Lumatone EDO mapping\|n=74\|start=68\|xstep=6\|ystep=7}}

	== Liese ==		== Liese ==

Lucius Chiaraviglio: /* Semimean and Liese */ Missing notes

2025-06-08T09:16:00Z

Semimean and Liese: Missing notes

← Older revision		Revision as of 09:16, 8 June 2025
Line 4:		Line 4:

	== Semimeantone ==		== Semimeantone ==
	The [[2L 8s]] mapping covers the whole gamut as efficiently as possible, although octaves slope slightly upward.		The [[2L 8s]] mapping covers the whole gamut as efficiently as possible in a span of three octaves, although one note 1 is missing from the lower otherwise full octave, and one each of notes 59, 65, and 72 is missing from the upper otherwise full octave (so that only the middle octave is truly complete); octaves slope slightly upward.
	{{Lumatone EDO mapping\|n=74\|start=1\|xstep=6\|ystep=7}}		{{Lumatone EDO mapping\|n=74\|start=1\|xstep=6\|ystep=7}}

	== Liese ==		== Liese ==
	The [[2L 9s]] mapping is ~~also quite effective at covering all the notes~~, especially if you don't mind using the second best mapping for some notes in larger chords.		The [[2L 9s]] mapping is another option, especially if you don't mind using the second best mapping for some notes in larger chords; however, it skips some notes in all octaves, exacerbated in the lower and upper full octaves by the shear inherent in this layout.
	{{Lumatone EDO mapping\|n=74\|start=27\|xstep=4\|ystep=15}}		{{Lumatone EDO mapping\|n=74\|start=27\|xstep=4\|ystep=15}}

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

Yourmusic Productions: Create Page.

2025-06-07T23:11:35Z

Create Page.

New page

{{Lumatone mapping intro}} However, due to its size, this mapping does not cover all the notes, although this does not matter in many keys because lower limit harmonics are relatively close together.
== Diatonic ==
{{Lumatone EDO mapping|n=74|start=70|xstep=12|ystep=-5}}

== Semimeantone ==
The [[2L 8s]] mapping covers the whole gamut as efficiently as possible, although octaves slope slightly upward.
{{Lumatone EDO mapping|n=74|start=1|xstep=6|ystep=7}}

== Liese ==
The [[2L 9s]] mapping is also quite effective at covering all the notes, especially if you don't mind using the second best mapping for some notes in larger chords.
{{Lumatone EDO mapping|n=74|start=27|xstep=4|ystep=15}}

{{Navbox Lumatone}}