Lumatone mapping for 68edo - Revision history

ArrowHead294: Whoops

2025-09-29T18:22:52Z

Whoops

← Older revision		Revision as of 18:22, 29 September 2025
Line 4:		Line 4:
	You can use the b val, but it is very flat. On the plus side, the patent 5th is directly above the flat one, so you can also use this mapping as a split-chroma relative of [[tetracot]] that requires larger vertical stretches to hit familiar chords.		You can use the b val, but it is very flat. On the plus side, the patent 5th is directly above the flat one, so you can also use this mapping as a split-chroma relative of [[tetracot]] that requires larger vertical stretches to hit familiar chords.
	{{Lumatone EDO mapping\|n=68\|start=52\|xstep=10\|ystep=-1}}		{{Lumatone EDO mapping\|n=68\|start=52\|xstep=10\|ystep=-1}}

	~~== Diaschismic ==~~
	The [[diaschismic]] mapping would hit harmonics with greater efficiency than the diatonic mapping, but this also has multiple unconnected rings in 68edo, requiring splitting of either the period or generator to hit all the notes. The most obvious of these would be [[Shrutar]], but this results in either a very lopsided step size or a lot of repeated notes, making it not actually the optimal mapping for an edo of this size.

	== Octacot ==		== Octacot ==
	The [[octacot]] mapping is also another option, but has only two octaves of range.		The [[octacot]] mapping is also another option, but has only two octaves of range.
	{{Lumatone EDO mapping\|n=68\|start=65\|xstep=5\|ystep=-2}}		{{Lumatone EDO mapping\|n=68\|start=65\|xstep=5\|ystep=-2}}

			== Diaschismic ==
			The [[diaschismic]] mapping would hit harmonics with greater efficiency than the diatonic mapping, but this also has multiple unconnected rings in 68edo, requiring splitting of either the period or generator to hit all the notes. The most obvious of these would be [[Shrutar]], but this results in either a very lopsided step size or a lot of repeated notes, making it not actually the optimal mapping for an edo of this size.

	=== Bidia ===		=== Bidia ===

ArrowHead294 at 18:22, 29 September 2025

2025-09-29T18:22:17Z

← Older revision		Revision as of 18:22, 29 September 2025
Line 7:		Line 7:
	== Diaschismic ==		== Diaschismic ==
	The [[diaschismic]] mapping would hit harmonics with greater efficiency than the diatonic mapping, but this also has multiple unconnected rings in 68edo, requiring splitting of either the period or generator to hit all the notes. The most obvious of these would be [[Shrutar]], but this results in either a very lopsided step size or a lot of repeated notes, making it not actually the optimal mapping for an edo of this size.		The [[diaschismic]] mapping would hit harmonics with greater efficiency than the diatonic mapping, but this also has multiple unconnected rings in 68edo, requiring splitting of either the period or generator to hit all the notes. The most obvious of these would be [[Shrutar]], but this results in either a very lopsided step size or a lot of repeated notes, making it not actually the optimal mapping for an edo of this size.

			== Octacot ==
			The [[octacot]] mapping is also another option, but has only two octaves of range.
			{{Lumatone EDO mapping\|n=68\|start=65\|xstep=5\|ystep=-2}}

	=== Bidia ===		=== Bidia ===
	The next option is slicing the period in 4, which produces [[bidia]]. The [[4L 4s]] mapping covers the full gamut in the middle octaves with a minimum of repeated notes, but skips quite a few at the edges and has a strong downward slope. The [[8L 4s]] mapping covers all the notes with a mild slope and a moderate amount of repeated notes, but with a smaller range.		The next option is slicing the period in 4, which produces [[bidia]]. The [[4L 4s]] mapping covers the full gamut in the middle octaves with a minimum of repeated notes, but skips quite a few at the edges and has a strong downward slope. The [[8L 4s]] mapping covers all the notes with a mild slope and a moderate amount of repeated notes, but with a smaller range.
	{{Lumatone EDO mapping\|n=68\|start=0\|xstep=6\|ystep=5}}		{{Lumatone EDO mapping\|n=68\|start=0\|xstep=6\|ystep=5}}
	{{Lumatone EDO mapping\|n=68\|start=60\|xstep=6\|ystep=-1}}		{{Lumatone EDO mapping\|n=68\|start=60\|xstep=6\|ystep=-1}}

	=== Quadrasruta ===		=== Quadrasruta ===
	Another option is the [[8L 2s]] [[Quadrasruta]] mapping, which gives you more than three octaves with no missed notes and only a mild upward octave slant, making all harmonics except for the 11th & 19th easy to play together.		Another option is the [[8L 2s]] [[Quadrasruta]] mapping, which gives you more than three octaves with no missed notes and only a mild upward octave slant, making all harmonics except for the 11th and 19th easy to play together.
	{{Lumatone EDO mapping\|n=68\|start=53\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=68\|start=53\|xstep=7\|ystep=-1}}

	== Antidiatonic ==		== Antidiatonic ==
	To give you a little more range while keeping octaves fairly near horizontal, the [[2L 7s]] mapping generated by 31/68 works decently, especially if you favor using the 11th harmonic in compositions.		To give you a little more range while keeping octaves fairly near horizontal, the [[2L 7s]] mapping generated by 31/68 works decently, especially if you favor using the 11th harmonic in compositions.
	{{Lumatone EDO mapping\|n=68\|start=57\|xstep=6\|ystep=7}}		{{Lumatone EDO mapping\|n=68\|start=57\|xstep=6\|ystep=7}}

Lucius Chiaraviglio: /* Antidiatonic */ Insert Bryan Deister's Biyatismic (Zeus) mapping after this

2025-08-01T05:56:27Z

Antidiatonic: Insert Bryan Deister's Biyatismic (Zeus) mapping after this

← Older revision		Revision as of 05:56, 1 August 2025
Line 19:		Line 19:
	To give you a little more range while keeping octaves fairly near horizontal, the [[2L 7s]] mapping generated by 31/68 works decently, especially if you favor using the 11th harmonic in compositions.		To give you a little more range while keeping octaves fairly near horizontal, the [[2L 7s]] mapping generated by 31/68 works decently, especially if you favor using the 11th harmonic in compositions.
	{{Lumatone EDO mapping\|n=68\|start=57\|xstep=6\|ystep=7}}		{{Lumatone EDO mapping\|n=68\|start=57\|xstep=6\|ystep=7}}

			== Biyatismic (Zeus) ==
			[[Bryan Deister]] has used a [[Biyatismic clan#Zeus\|Biyatismic (Zeus)]] layout with a [[7L 1s]] scale (9:5 step ratio) for [[68edo]], as demonstrated in [https://www.youtube.com/shorts/CO1AslAu9E0 ''microtonal improvisation in 68edo''] (2025). The rightward generator 9\68 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. The chroma of the scale (4\68, upwards on this layout) is the near-just diptolemaic chromatic semitone ~[[25/24]], and is convenient to use as a second generator (even though such is not required to avoid [[contorsion]]) to access other consonant intervals quickly, although sometimes with strange preferences built in — for instance, the septimal whole tone ~[[8/7]] is much easier to reach (at 13\68) than the Pythagorean whole tone ~[[9/8]] (which requires a substantial vertical reach at 12\68), while the septimal minor third ~[[7/6]] (at 15\18) is a much longer vertical reach than the classic minor third ~6/5 (at 18\68), and the septimal major third ~[[9/7]] is a much longer vertical reach (at 25\68) than the classic major third ~[[5/4]] (at 22\68). Fortunately the fourth (~[[4/3]], at 28\68), the Axirabian paramajor fourth (~[[11/8]], at 31\68), the Axirabian paraminor fifth (~[[16/11]], at 37\68) and fifth (~[[3/2]], at 40\68) are all easy to reach as long as they do not go through a vertical wraparound (as happens to the fourth in the bass octave). The range is four octaves plus two notes, and octaves slope upwards — not severely, but a vertical wraparound is unavoidable if note 0 is placed to get complete octaves as defined to reach from note 0 to note 0.
			{{Lumatone EDO mapping\|n=68\|start=0\|xstep=9\|ystep=-4}}

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

Yourmusic Productions: Tweaking.

2025-07-16T11:27:45Z

Tweaking.

← Older revision		Revision as of 11:27, 16 July 2025
Line 3:		Line 3:
	== Diatonic ==		== Diatonic ==
	You can use the b val, but it is very flat. On the plus side, the patent 5th is directly above the flat one, so you can also use this mapping as a split-chroma relative of [[tetracot]] that requires larger vertical stretches to hit familiar chords.		You can use the b val, but it is very flat. On the plus side, the patent 5th is directly above the flat one, so you can also use this mapping as a split-chroma relative of [[tetracot]] that requires larger vertical stretches to hit familiar chords.
	{{Lumatone EDO mapping\|n=68\|start=4\|xstep=10\|ystep=-1}}		{{Lumatone EDO mapping\|n=68\|start=52\|xstep=10\|ystep=-1}}

	== Diaschismic ==		== Diaschismic ==
Line 13:		Line 13:

	=== Quadrasruta ===		=== Quadrasruta ===
	Another option is the [[8L 2s]] [[Quadrasruta]] mapping, which gives you more than three octaves with no missed notes and only a mild upward octave slant.		Another option is the [[8L 2s]] [[Quadrasruta]] mapping, which gives you more than three octaves with no missed notes and only a mild upward octave slant, making all harmonics except for the 11th & 19th easy to play together.
	{{Lumatone EDO mapping\|n=68\|start=53\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=68\|start=53\|xstep=7\|ystep=-1}}

	== Antidiatonic ==		== Antidiatonic ==
	To give you a little more range while keeping octaves fairly near horizontal, the [[2L 7s]] mapping generated by 31/68 works decently, especially if you favor using the 11th harmonic in compositions.		To give you a little more range while keeping octaves fairly near horizontal, the [[2L 7s]] mapping generated by 31/68 works decently, especially if you favor using the 11th harmonic in compositions.
	{{Lumatone EDO mapping\|n=68\|start=34\|xstep=6\|ystep=7}}		{{Lumatone EDO mapping\|n=68\|start=57\|xstep=6\|ystep=7}}

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

Yourmusic Productions: Create Page.

2025-07-16T11:09:04Z

Create Page.

New page

{{Lumatone mapping intro}} In addition, due to its size, it would not cover all the notes even if it was.

== Diatonic ==
You can use the b val, but it is very flat. On the plus side, the patent 5th is directly above the flat one, so you can also use this mapping as a split-chroma relative of [[tetracot]] that requires larger vertical stretches to hit familiar chords.
{{Lumatone EDO mapping|n=68|start=4|xstep=10|ystep=-1}}

== Diaschismic ==
The [[diaschismic]] mapping would hit harmonics with greater efficiency than the diatonic mapping, but this also has multiple unconnected rings in 68edo, requiring splitting of either the period or generator to hit all the notes. The most obvious of these would be [[Shrutar]], but this results in either a very lopsided step size or a lot of repeated notes, making it not actually the optimal mapping for an edo of this size.
=== Bidia ===
The next option is slicing the period in 4, which produces [[bidia]]. The [[4L 4s]] mapping covers the full gamut in the middle octaves with a minimum of repeated notes, but skips quite a few at the edges and has a strong downward slope. The [[8L 4s]] mapping covers all the notes with a mild slope and a moderate amount of repeated notes, but with a smaller range.
{{Lumatone EDO mapping|n=68|start=0|xstep=6|ystep=5}}
{{Lumatone EDO mapping|n=68|start=60|xstep=6|ystep=-1}}

=== Quadrasruta ===
Another option is the [[8L 2s]] [[Quadrasruta]] mapping, which gives you more than three octaves with no missed notes and only a mild upward octave slant.
{{Lumatone EDO mapping|n=68|start=53|xstep=7|ystep=-1}}

== Antidiatonic ==
To give you a little more range while keeping octaves fairly near horizontal, the [[2L 7s]] mapping generated by 31/68 works decently, especially if you favor using the 11th harmonic in compositions.
{{Lumatone EDO mapping|n=68|start=34|xstep=6|ystep=7}}

{{Navbox Lumatone}}