Lumatone mapping for 39edo - Revision history

Lucius Chiaraviglio: /* Semiquartal (immunity) */ Add Bryan Deister's Biyatismic mapping

2026-01-13T08:18:57Z

Semiquartal (immunity): Add Bryan Deister's Biyatismic mapping

← Older revision		Revision as of 08:18, 13 January 2026
Line 26:		Line 26:
	The [[immunity]] mapping gives excellent range (over 6⅓ octaves), but the resulting [[5L 4s]] scale has a 7:1 step ratio, which makes it very lopsided; on the other hand, the octaves slope up in this mapping more gently than they slope down on the previous four mappings.		The [[immunity]] mapping gives excellent range (over 6⅓ octaves), but the resulting [[5L 4s]] scale has a 7:1 step ratio, which makes it very lopsided; on the other hand, the octaves slope up in this mapping more gently than they slope down on the previous four mappings.
	{{Lumatone EDO mapping\|n=39\|start=21\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=39\|start=21\|xstep=8\|ystep=-1}}

			== Biyatismic ==
			[[Bryan Deister]] has used a [[Biyatismic_clan\|biyatismic]] layout with a [[7L 1s]] scale (5:4 step ratio) for [[39edo]], as demonstrated in [https://www.youtube.com/shorts/Tf812DJzoEA ''<nowiki>Tilt Your Head Down - 39edo [short]</nowiki>''] (2026). The rightward generator 4\39 is a combination of the Alpharabian tendoneutral second ~[[12/11]] and the undecimal submajor second ~[[11/10]], and two of these make a near-just classic minor third ~[[6/5]], with the biyatisma ([[121/120]]) being tempered out. Although biyatismic is technically rank-3 or rank-4, it functions here as a rank-2 temperament, filling in several useful intervals by rightward progression and octave-reduction: four of these generators make a near-just septimal tritone ~[[10/7]]; five of them make a flat pentacircle minor sixth ~[[11/7]] or a somewhat sharp septimal minor sixth ~[[14/9]]; and six of them make a flat septimal major sixth ~[[12/7]]. After octave-reduction, nine of them make a slightly sharp classic whole tone ~[[10/9]]; ten of them make a flat Alpharabian artoneutral third ~[[11/9]]; eleven of them make a flat fourth ~[[4/3]]; twelve of them make a slightly flat Axirabian paraminor fifth ~[[16/11]]; and thirteen of them make a flat classic minor sixth ~[[8/5]]. The range is just under four octaves, and the octaves slant up.
			{{Lumatone EDO mapping\|n=39\|start=27\|xstep=5\|ystep=-1}}

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

Lucius Chiaraviglio: /* Familia */ Add diatonic semitone

2025-10-12T06:03:19Z

Familia: Add diatonic semitone

← Older revision		Revision as of 06:03, 12 October 2025
Line 20:		Line 20:

	== Familia ==		== Familia ==
	Related to amity is [[Amity_family#Familia\|familia]]. [[Bryan Deister]] has demonstrated a [[3L 4s]] (10:3 step ratio) layout for this, in [https://www.youtube.com/shorts/1T_xrZpUslQ ''39edo improv''] (2025). Right by 1 key (10\39) is a somewhat flat classic minor third ~[[6/5]], while down-right by 1 key (3\39) is an inconsistently mapped sharp diptolmeic chromatic semitone (~[[25/24]]), which means that right 1 key + down-right 1 key (total 13\39) yields a sharp (400{{c}}) classic major third ~[[5/4]]). The range is six octaves, although the octaves slope down enough to cause a vertical wraparound.		Related to amity is [[Amity_family#Familia\|familia]]. [[Bryan Deister]] has demonstrated a [[3L 4s]] (10:3 step ratio) layout for this, in [https://www.youtube.com/shorts/1T_xrZpUslQ ''39edo improv''] (2025). Right by 1 key (10\39) is a somewhat flat classic minor third ~[[6/5]], while down-right by 1 key (3\39) functions both as an inconsistently mapped sharp diptolmeic chromatic semitone (~[[25/24]]) and an inconsistently mapped flat ptolemaic diatonic semitone (~[[16/15]]), which means that right 1 key + down-right 1 key (total 13\39) yields a sharp (400{{c}}) classic major third ~[[5/4]]). The range is six octaves, although the octaves slope down enough to cause a vertical wraparound.
	{{Lumatone EDO mapping\|n=39\|start=0\|xstep=10\|ystep=-7}}		{{Lumatone EDO mapping\|n=39\|start=0\|xstep=10\|ystep=-7}}

Lucius Chiaraviglio: Add Bryan Deister's Familia mapping

2025-10-12T05:59:48Z

Add Bryan Deister's Familia mapping

← Older revision		Revision as of 05:59, 12 October 2025
Line 18:		Line 18:
	The [[Lumatone mapping for amity]] is also above average at putting good intervals close together, and makes chromatic runs much easier than the previous two layouts.		The [[Lumatone mapping for amity]] is also above average at putting good intervals close together, and makes chromatic runs much easier than the previous two layouts.
	{{Lumatone EDO mapping\|n=39\|start=0\|xstep=6\|ystep=-1}}		{{Lumatone EDO mapping\|n=39\|start=0\|xstep=6\|ystep=-1}}

			== Familia ==
			Related to amity is [[Amity_family#Familia\|familia]]. [[Bryan Deister]] has demonstrated a [[3L 4s]] (10:3 step ratio) layout for this, in [https://www.youtube.com/shorts/1T_xrZpUslQ ''39edo improv''] (2025). Right by 1 key (10\39) is a somewhat flat classic minor third ~[[6/5]], while down-right by 1 key (3\39) is an inconsistently mapped sharp diptolmeic chromatic semitone (~[[25/24]]), which means that right 1 key + down-right 1 key (total 13\39) yields a sharp (400{{c}}) classic major third ~[[5/4]]). The range is six octaves, although the octaves slope down enough to cause a vertical wraparound.
			{{Lumatone EDO mapping\|n=39\|start=0\|xstep=10\|ystep=-7}}

	== Semiquartal (immunity) ==		== Semiquartal (immunity) ==
	The [[immunity]] mapping gives excellent range, but the resulting [[5L 4s]] scale has a 7:1 step ratio, which makes it very lopsided.		The [[immunity]] mapping gives excellent range (over 6⅓ octaves), but the resulting [[5L 4s]] scale has a 7:1 step ratio, which makes it very lopsided; on the other hand, the octaves slope up in this mapping more gently than they slope down on the previous four mappings.
	{{Lumatone EDO mapping\|n=39\|start=21\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=39\|start=21\|xstep=8\|ystep=-1}}

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

FloraC: Cleanup

2025-09-11T06:00:35Z

Cleanup

← Older revision		Revision as of 06:00, 11 September 2025
Line 6:		Line 6:
	{{Lumatone EDO mapping\|n=39\|start=6\|xstep=7\|ystep=-5}}		{{Lumatone EDO mapping\|n=39\|start=6\|xstep=7\|ystep=-5}}

	== Augmented + ~~Immunity~~ ==		== Augmented + immunity ==
			[[Bryan Deister]] has used a [[porcupine]]-inspired layout for [[39edo]], as demonstrated in [https://www.youtube.com/watch?v=XLRaG_pBN7k&lc=UgwfjZwncsryQjeNUg14AaABAg.AHVkw8aNSEGAHZU_J2qOPM ''39edo jam''] (2025). To take advantage of the fact that 39edo is at the intersection of [[augmented (temperament)\|augmented]] and [[immunity]], the rightward generator is 5\39, half of a [[6/5]] minor third as [[12/11]]~[[11/10]] (but much closer to 12/11). This enables a modmos derived from [[1L 6s]] by shrinking the large step from 9\39 to 8\39 and expanding one of the small steps from 5\39 to 6\39, to enable chords such as 12/11 (somewhat sharp, at 5\39) – 6/5 (slightly flat, at 10\39) – [[11/8]] (near-just, at 18\39) – [[3/2]] (mildly sharp, 23\39) – [[18/11]] (moderately sharp, at 28\39) – [[9/5]] (near-just, at 33\39). Playing this chord uses almost the same geometry of depressed keys as that for playing a diatonic scale in a diatonic mapping (but has a very different sound effect), save when proceeding to the next octave. The range is slightly over 6 octaves overall (which slant moderately downwards), but with the first and last octaves missing some notes due to clipping in the upper left and lower right corners of the layout.
	[[Bryan Deister]] has used a [[~~Porcupine~~]]-inspired layout for [[39edo]], as demonstrated in [https://www.youtube.com/watch?v=XLRaG_pBN7k&lc=UgwfjZwncsryQjeNUg14AaABAg.AHVkw8aNSEGAHZU_J2qOPM ''39edo jam''] (2025). To take advantage of the fact that 39edo is at the intersection of [[~~Augmented~~]] and [[~~Immunity~~]], the rightward generator is 5\39, half of a [[6/5]] minor third as [[12/11]] ~ [[11/10]] (but much closer to 12/11). This enables a ~~MODMOS~~ derived from [[1L 6s]] by shrinking the large step from 9\39 to 8\39 and expanding one of the small steps from 5\39 to 6\39, to enable chords such as 12/11 (somewhat sharp, at 5\39) - 6/5 (slightly flat, at 10\39) - [[11/8]] (near-just, at 18\39) - [[3/2]] (mildly sharp, 23\39) - [[18/11]] (moderately sharp, at 28\39) - [[9/5]] (near-just, at 33\39). Playing this chord uses almost the same geometry of depressed keys as that for playing a diatonic scale in a diatonic mapping (but has a very different sound effect), save when proceeding to the next octave. The range is slightly over 6 octaves overall (which slant moderately downwards), but with the first and last octaves missing some notes due to clipping in the upper left and lower right corners of the layout.

	{{Lumatone EDO mapping\|n=39\|start=34\|xstep=5\|ystep=3}}		{{Lumatone EDO mapping\|n=39\|start=34\|xstep=5\|ystep=3}}
Line 17:		Line 16:

	== Amity ==		== Amity ==
	The [[Lumatone mapping for ~~Amity~~]] is also above average at putting good intervals close together, and makes chromatic runs much easier than the previous two layouts.		The [[Lumatone mapping for amity]] is also above average at putting good intervals close together, and makes chromatic runs much easier than the previous two layouts.
	{{Lumatone EDO mapping\|n=39\|start=0\|xstep=6\|ystep=-1}}		{{Lumatone EDO mapping\|n=39\|start=0\|xstep=6\|ystep=-1}}

	== Semiquartal (~~Immunity~~) ==		== Semiquartal (immunity) ==
	The [[~~Immunity~~]] mapping gives excellent range, but the resulting [[5L 4s]] scale has a 7:1 step ratio, which makes it very lopsided.		The [[immunity]] mapping gives excellent range, but the resulting [[5L 4s]] scale has a 7:1 step ratio, which makes it very lopsided.
	{{Lumatone EDO mapping\|n=39\|start=21\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=39\|start=21\|xstep=8\|ystep=-1}}

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

Lucius Chiaraviglio: Add Bryan Deister's 39edo Lumatone mapping; also add text for the diatonic mapping

2025-05-02T06:36:27Z

Add Bryan Deister's 39edo Lumatone mapping; also add text for the diatonic mapping

← Older revision		Revision as of 06:36, 2 May 2025
Line 1:		Line 1:
	{{Lumatone mapping intro}}		{{Lumatone mapping intro}}
	== Diatonic ==		== Diatonic ==

			Although not as imbalanced as the diatonic scale for [[37edo]] (step ratio 7:1), the diatonic scale for 39edo is still fairly imbalanced (step ratio 7:2).

	{{Lumatone EDO mapping\|n=39\|start=6\|xstep=7\|ystep=-5}}		{{Lumatone EDO mapping\|n=39\|start=6\|xstep=7\|ystep=-5}}

			== Augmented + Immunity ==

			[[Bryan Deister]] has used a [[Porcupine]]-inspired layout for [[39edo]], as demonstrated in [https://www.youtube.com/watch?v=XLRaG_pBN7k&lc=UgwfjZwncsryQjeNUg14AaABAg.AHVkw8aNSEGAHZU_J2qOPM ''39edo jam''] (2025). To take advantage of the fact that 39edo is at the intersection of [[Augmented]] and [[Immunity]], the rightward generator is 5\39, half of a [[6/5]] minor third as [[12/11]] ~ [[11/10]] (but much closer to 12/11). This enables a MODMOS derived from [[1L 6s]] by shrinking the large step from 9\39 to 8\39 and expanding one of the small steps from 5\39 to 6\39, to enable chords such as 12/11 (somewhat sharp, at 5\39) - 6/5 (slightly flat, at 10\39) - [[11/8]] (near-just, at 18\39) - [[3/2]] (mildly sharp, 23\39) - [[18/11]] (moderately sharp, at 28\39) - [[9/5]] (near-just, at 33\39). Playing this chord uses almost the same geometry of depressed keys as that for playing a diatonic scale in a diatonic mapping (but has a very different sound effect), save when proceeding to the next octave. The range is slightly over 6 octaves overall (which slant moderately downwards), but with the first and last octaves missing some notes due to clipping in the upper left and lower right corners of the layout.

			{{Lumatone EDO mapping\|n=39\|start=34\|xstep=5\|ystep=3}}

	== Triforce ==		== Triforce ==

ArrowHead294: /* Amity */

2025-03-23T15:08:43Z

Amity

← Older revision		Revision as of 15:08, 23 March 2025
Line 8:		Line 8:

	== Amity ==		== Amity ==
	The [[Lumatone mapping for ~~Amit~~]] is also above average at putting good intervals close together, and makes chromatic runs much easier than the previous two layouts.		The [[Lumatone mapping for Amity]] is also above average at putting good intervals close together, and makes chromatic runs much easier than the previous two layouts.
	{{Lumatone EDO mapping\|n=39\|start=0\|xstep=6\|ystep=-1}}		{{Lumatone EDO mapping\|n=39\|start=0\|xstep=6\|ystep=-1}}

ArrowHead294 at 15:08, 23 March 2025

2025-03-23T15:08:34Z

← Older revision		Revision as of 15:08, 23 March 2025
Line 1:		Line 1:
	{{Lumatone mapping intro}}		{{Lumatone mapping intro}}
			== Diatonic ==
	{{Lumatone EDO mapping\|n=39\|start=6\|xstep=7\|ystep=-5}}		{{Lumatone EDO mapping\|n=39\|start=6\|xstep=7\|ystep=-5}}

			== Triforce ==
	Since it is ~~it's~~ optimal patent val, the [[triforce]] mapping is also a particularly good way to organise the intervals of 39edo.		Since it is its optimal patent val, the [[triforce]] mapping is also a particularly good way to organise the intervals of 39edo.
	{{Lumatone EDO mapping\|n=39\|start=0\|xstep=8\|ystep=-3}}		{{Lumatone EDO mapping\|n=39\|start=0\|xstep=8\|ystep=-3}}

			== Amity ==
	The [[~~amity~~]] ~~mapping~~ is also above average at putting good intervals close together, and makes chromatic runs much easier than the previous two layouts.		The [[Lumatone mapping for Amit]] is also above average at putting good intervals close together, and makes chromatic runs much easier than the previous two layouts.
	{{Lumatone EDO mapping\|n=39\|start=0\|xstep=6\|ystep=-1}}		{{Lumatone EDO mapping\|n=39\|start=0\|xstep=6\|ystep=-1}}

			== Semiquartal (Immunity) ==
	The [[~~immunity~~]] mapping ~~is also another option~~, but the resulting [[5L 4s]] scale has a 7:1 step ratio which makes it very lopsided.		The [[Immunity]] mapping gives excellent range, but the resulting [[5L 4s]] scale has a 7:1 step ratio, which makes it very lopsided.
	{{Lumatone EDO mapping\|n=39\|start=21\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=39\|start=21\|xstep=8\|ystep=-1}}

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

ArrowHead294 at 18:20, 14 March 2025

2025-03-14T18:20:36Z

← Older revision		Revision as of 18:20, 14 March 2025
Line 1:		Line 1:
	~~There are many conceivable ways to map [[39edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard~~ Lumatone mapping ~~for Pythagorean]].~~		{{Lumatone mapping intro}}
	{{Lumatone EDO mapping\|n=39\|start=6\|xstep=7\|ystep=-5}}		{{Lumatone EDO mapping\|n=39\|start=6\|xstep=7\|ystep=-5}}

ArrowHead294 at 13:04, 8 March 2025

2025-03-08T13:04:53Z

← Older revision		Revision as of 13:04, 8 March 2025
Line 1:		Line 1:
	There are many conceivable ways to map [[39edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]].		There are many conceivable ways to map [[39edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]].
			{{Lumatone EDO mapping\|n=39\|start=6\|xstep=7\|ystep=-5}}

	~~{{Lumatone EDO mapping\|n=39\|start=6\|xstep=7\|ystep=-5}}~~

	Since it is it's optimal patent val, the [[triforce]] mapping is also a particularly good way to organise the intervals of 39edo.		Since it is it's optimal patent val, the [[triforce]] mapping is also a particularly good way to organise the intervals of 39edo.
	{{Lumatone EDO mapping\|n=39\|start=0\|xstep=8\|ystep=-3}}		{{Lumatone EDO mapping\|n=39\|start=0\|xstep=8\|ystep=-3}}

	~~The [[immunity]] and [[amity]] mappings are also above average at putting good intervals close together, and make chromatic runs much easier than the previous two layouts.~~
	~~{{Lumatone EDO mapping\|n=39\|start=21\|xstep=8\|ystep=-1}}~~

			The [[amity]] mapping is also above average at putting good intervals close together, and makes chromatic runs much easier than the previous two layouts.
	{{Lumatone EDO mapping\|n=39\|start=0\|xstep=6\|ystep=-1}}		{{Lumatone EDO mapping\|n=39\|start=0\|xstep=6\|ystep=-1}}


			The [[immunity]] mapping is also another option, but the resulting [[5L 4s]] scale has a 7:1 step ratio which makes it very lopsided.
			{{Lumatone EDO mapping\|n=39\|start=21\|xstep=8\|ystep=-1}}

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

ArrowHead294 at 16:51, 11 February 2025

2025-02-11T16:51:25Z

← Older revision		Revision as of 16:51, 11 February 2025
Line 11:		Line 11:
	{{Lumatone EDO mapping\|n=39\|start=0\|xstep=6\|ystep=-1}}		{{Lumatone EDO mapping\|n=39\|start=0\|xstep=6\|ystep=-1}}

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