Lumatone mapping for 100edo - Revision history

Lucius Chiaraviglio: /* Submerged-related rank-2 temperament */ Add the interval corresponding to the flat fourth

2026-09-23T14:27:17Z

Submerged-related rank-2 temperament: Add the interval corresponding to the flat fourth

← Older revision		Revision as of 14:27, 23 September 2026
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	== Submerged-related rank-2 temperament ==		== Submerged-related rank-2 temperament ==
	To maximize your range while covering the full gamut, use the [[3L 10s]] (10:7 step ratio) scale generated by a submajor third (in between ~[[5/4]] and ~[[16/13]]) of 31/100, which functions as a slightly sharp tridecimal submajor third ~[[26/21]] and a near-just (only slightly flat) tricesimoprimal submajor third ~[[31/25]]. The temperament is related to [[submerged]] in that 11 generators stack to make the flat ~[[4/3]] (corresponding to the sharp fifth of 100edo), but it misses most of the other intervals of submerged temperament. The range is just under 2½ octaves, which slope mildly upwards.		To maximize your range while covering the full gamut, use the [[3L 10s]] (10:7 step ratio) scale generated by a submajor third (in between ~[[5/4]] and ~[[16/13]]) of 31/100, which functions as a slightly sharp tridecimal submajor third ~[[26/21]] and a near-just (only slightly flat) tricesimoprimal submajor third ~[[31/25]]. The temperament is related to [[submerged]] in that 11 generators stack to make the flat ~[[4/3]] (41\100, corresponding to the sharp fifth ~[[5/3]] of 100edo), but it misses most of the other intervals of submerged temperament. The range is just under 2½ octaves, which slope mildly upwards.
	{{Lumatone EDO mapping\|n=100\|start=74\|xstep=7\|ystep=3}}		{{Lumatone EDO mapping\|n=100\|start=74\|xstep=7\|ystep=3}}

Lucius Chiaraviglio: /* Unnamed rank-2 temperament */ --> Submerged-related rank-2 temperament

2026-09-23T14:25:06Z

Unnamed rank-2 temperament: --> Submerged-related rank-2 temperament

← Older revision		Revision as of 14:25, 23 September 2026
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	{{Lumatone EDO mapping\|n=100\|start=12\|xstep=8\|ystep=-7}}		{{Lumatone EDO mapping\|n=100\|start=12\|xstep=8\|ystep=-7}}

	== ~~Unnamed~~ rank-2 temperament ==		== Submerged-related rank-2 temperament ==
	To maximize your range while covering the full gamut, use the [[3L 10s]] (10:7 step ratio) scale generated by a submajor third (in between ~[[5/4]] and ~[[16/13]]) of 31/100, which functions as a slightly sharp tridecimal submajor third ~[[26/21]] and a near-just (only slightly flat) tricesimoprimal submajor third ~[[31/25]]. The range is just under 2½ octaves, which slope mildly upwards.		To maximize your range while covering the full gamut, use the [[3L 10s]] (10:7 step ratio) scale generated by a submajor third (in between ~[[5/4]] and ~[[16/13]]) of 31/100, which functions as a slightly sharp tridecimal submajor third ~[[26/21]] and a near-just (only slightly flat) tricesimoprimal submajor third ~[[31/25]]. The temperament is related to [[submerged]] in that 11 generators stack to make the flat ~[[4/3]] (corresponding to the sharp fifth of 100edo), but it misses most of the other intervals of submerged temperament. The range is just under 2½ octaves, which slope mildly upwards.
	{{Lumatone EDO mapping\|n=100\|start=74\|xstep=7\|ystep=3}}		{{Lumatone EDO mapping\|n=100\|start=74\|xstep=7\|ystep=3}}

Lucius Chiaraviglio: /* Other Mappings */ --> Unnamed rank-2 temperament; flesh out description a bit; insert Bryan Deister's unnamed rank-3 temperament mapping after this

2026-09-23T14:13:14Z

Other Mappings: --> Unnamed rank-2 temperament; flesh out description a bit; insert Bryan Deister's unnamed rank-3 temperament mapping after this

← Older revision		Revision as of 14:13, 23 September 2026
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	{{Lumatone EDO mapping\|n=100\|start=12\|xstep=8\|ystep=-7}}		{{Lumatone EDO mapping\|n=100\|start=12\|xstep=8\|ystep=-7}}

	== ~~Other Mappings~~ ==		== Unnamed rank-2 temperament ==
	To ~~maximise~~ your range while covering the full gamut, use the [[3L 10s]] scale generated by a submajor third of 31/100.		To maximize your range while covering the full gamut, use the [[3L 10s]] (10:7 step ratio) scale generated by a submajor third (in between ~[[5/4]] and ~[[16/13]]) of 31/100, which functions as a slightly sharp tridecimal submajor third ~[[26/21]] and a near-just (only slightly flat) tricesimoprimal submajor third ~[[31/25]]. The range is just under 2½ octaves, which slope mildly upwards.
	{{Lumatone EDO mapping\|n=100\|start=74\|xstep=7\|ystep=3}}		{{Lumatone EDO mapping\|n=100\|start=74\|xstep=7\|ystep=3}}

			== Unnamed rank-3 temperament ==
			[[Bryan Deister]] has demonstrated a mapping for [[100edo]] that supports both a [[16L 4s]] scale (6:1 step ratio) and a flipped [[15L 2s]] scale (6:5 step ratio), in [https://www.youtube.com/shorts/gPbsSs4MFbQ ''100edo improv''] (2026). The rightward generator 6\100 functions as a near-just (only slightly flat) lesser vicesimotertial semitone ~[[24/23]] and a near-just (only slightly sharp) classic chromatic semitone ~[[25/24]]. Since 6 is not coprime with 100, an additional generator is required; since down-right 1\100 is used more often in the linked demonstration video, it can be considered the second generator; it functions as a sharp valinorsma ~[[176/175]] or a near-just (only slightly sharp major kirnbergerisma ~[[161/160]]. (Technically it could be used as a sole generator, but due to its small size, this would be very unwieldy. Also, technically the first generator 6\100 could be used as the sole generator for a rank-2 temperament with the octave divided into four parts, but this would be unwieldy for anything other than the aforementioned 16L 4s scale. The alternative upwards generator 5\100 is not co-prime with 100edo either, and would not work as the sole generator even with division of the octave into four parts.) The range (a bit over 1½ octaves) is even less than that of the [[12L 4s]] extra-expanded diatonic mapping, and the octaves slope upwards even more, but in exchange, this mapping enables easy fine adjustment of pitch and has a decent number of repeated notes to mitigate vertical wraparounds, while still having only a few notes of range chopped off in the corners.
			{{Lumatone EDO mapping\|n=100\|start=12\|xstep=6\|ystep=-5}}

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

Yourmusic Productions: Navbox.

2025-08-12T20:39:32Z

Navbox.

← Older revision		Revision as of 20:39, 12 August 2025
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	To maximise your range while covering the full gamut, use the [[3L 10s]] scale generated by a submajor third of 31/100.		To maximise your range while covering the full gamut, use the [[3L 10s]] scale generated by a submajor third of 31/100.
	{{Lumatone EDO mapping\|n=100\|start=74\|xstep=7\|ystep=3}}		{{Lumatone EDO mapping\|n=100\|start=74\|xstep=7\|ystep=3}}

			{{Navbox Lumatone}}

Yourmusic Productions: Expansion.

2025-08-12T20:35:14Z

Expansion.

← Older revision		Revision as of 20:35, 12 August 2025
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	== Diatonic ==		== Diatonic ==
	However, you can use the 100b val (using 59\100) to generate a hard diatonic (18:5 step size ratio. This will fail to cover the whole gamut due to the size of the edo.		However, you can use the 100b val (using 59\100) to generate a hard diatonic (18:5 step size ratio) that is a good tuning for [[quasisupra]]. This will fail to cover the whole gamut due to the size of the edo.
			{{Lumatone EDO mapping\|n=100\|start=16\|xstep=18\|ystep=-13}}

	{{Lumatone EDO mapping\|n=100\|start=16\|xstep=18\|ystep=-13}}		Since 50edo is already divisible by two, [[injera]] and its extensions also fail to cover all the notes in 100edo unless you divide the octave into four. The [[4L 8s]] mapping covers most of the notes with the occasional skip, while the [[12L 4s]] one does cover all the notes, but with very limited range and lopsided step size.
			=== 4L 8s ===
			{{Lumatone EDO mapping\|n=100\|start=80\|xstep=8\|ystep=1}}
			=== 12L 4s ===
			{{Lumatone EDO mapping\|n=100\|start=12\|xstep=8\|ystep=-7}}

			== Other Mappings ==
			To maximise your range while covering the full gamut, use the [[3L 10s]] scale generated by a submajor third of 31/100.
			{{Lumatone EDO mapping\|n=100\|start=74\|xstep=7\|ystep=3}}

MisterShafXen: Fixed a problem

2025-08-12T19:44:36Z

Fixed a problem

← Older revision		Revision as of 19:44, 12 August 2025
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	However, you can use the 100b val (using 59\100) to generate a hard diatonic (18:5 step size ratio. This will fail to cover the whole gamut due to the size of the edo.		However, you can use the 100b val (using 59\100) to generate a hard diatonic (18:5 step size ratio. This will fail to cover the whole gamut due to the size of the edo.

	~~(Note: When I ([[User:MisterShafXen]]) tried adding the~~ mapping ~~starting with 7 and steps xsteps~~=18 ~~ysteps~~=-13~~, it didn't work.)~~		{{Lumatone EDO mapping\|n=100\|start=16\|xstep=18\|ystep=-13}}

MisterShafXen: Created page with "{{Lumatone mapping intro}} == Diatonic == However, you can use the 100b val (using 59\100) to generate a hard diatonic (18:5 step size ratio. This will fail to cover the whole gamut due to the size of the edo. (Note: When I (User:MisterShafXen) tried adding the mapping starting with 7 and steps xsteps=18 ysteps=-13, it didn't work.)"

2025-08-12T19:35:35Z

Created page with "{{Lumatone mapping intro}} == Diatonic == However, you can use the 100b val (using 59\100) to generate a hard diatonic (18:5 step size ratio. This will fail to cover the whole gamut due to the size of the edo. (Note: When I (User:MisterShafXen) tried adding the mapping starting with 7 and steps xsteps=18 ysteps=-13, it didn't work.)"

New page

{{Lumatone mapping intro}}

== Diatonic ==
However, you can use the 100b val (using 59\100) to generate a hard diatonic (18:5 step size ratio. This will fail to cover the whole gamut due to the size of the edo.

(Note: When I ([[User:MisterShafXen]]) tried adding the mapping starting with 7 and steps xsteps=18 ysteps=-13, it didn't work.)