Lumatone mapping for 87edo - Revision history

Lucius Chiaraviglio: /* Aureus Pseudo-Meantone */ Fix typo

2026-05-03T23:48:20Z

Aureus Pseudo-Meantone: Fix typo

← Older revision		Revision as of 23:48, 3 May 2026
Line 12:		Line 12:

	== Aureus Pseudo-Meantone ==		== Aureus Pseudo-Meantone ==
	[[Bryan Deister]] has demonstrated a [[11L 5s]] (7:2 step ratio) mapping for [[87edo]] in [[https://www.youtube.com/shorts/rINJKiMQE78 ''Circuit Bent - Stomach Book (microtonal cover in 87edo)''] (2025). The generator 14\87, which is two keys right from the root note, is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it near-just; two of them make an essentially just classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 87edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals — the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) Since this interval is two keys right instead of just one (as needed to avoid missing notes), this version of the temperament can be viewed as a split generator version, in which each ~19/17 is split into two equal intervals that function as both a small septendecimal semitone ~[[18/17]] and a large undevicesimal semitone ~[[19/18]], both being close to just (and the photisma [[324/323]] is tempered out). Although no second generator is needed to reach all of the notes, for convenience, down-right by one key (2\87) can be used for convenience as a second generator that functions as ~[[49/48]] (inconsistently mapped), ~[[55/54]], ~[[64/63]], ~[[65/64]], and ~[[81/80]], of which the septimal chroma ~64/63 is near-just, and four of these make a near-just classic diatonic semitone ~[[16/15]] (the currently unnamed unnoticeable comma [[5250987/5242880]] is tempered out). The range is somewhat over two octaves (which slant very slightly downwards) with no missed notes and some repeated notes to mitigate vertical wraparounds.		[[Bryan Deister]] has demonstrated a [[11L 5s]] (7:2 step ratio) mapping for [[87edo]] in [https://www.youtube.com/shorts/rINJKiMQE78 ''Circuit Bent - Stomach Book (microtonal cover in 87edo)''] (2025). The generator 14\87, which is two keys right from the root note, is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it near-just; two of them make an essentially just classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 87edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals — the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) Since this interval is two keys right instead of just one (as needed to avoid missing notes), this version of the temperament can be viewed as a split generator version, in which each ~19/17 is split into two equal intervals that function as both a small septendecimal semitone ~[[18/17]] and a large undevicesimal semitone ~[[19/18]], both being close to just (and the photisma [[324/323]] is tempered out). Although no second generator is needed to reach all of the notes, for convenience, down-right by one key (2\87) can be used for convenience as a second generator that functions as ~[[49/48]] (inconsistently mapped), ~[[55/54]], ~[[64/63]], ~[[65/64]], and ~[[81/80]], of which the septimal chroma ~64/63 is near-just, and four of these make a near-just classic diatonic semitone ~[[16/15]] (the currently unnamed unnoticeable comma [[5250987/5242880]] is tempered out). The range is somewhat over two octaves (which slant very slightly downwards) with no missed notes and some repeated notes to mitigate vertical wraparounds.

	{{Lumatone EDO mapping\|n=87\|start=6\|xstep=7\|ystep=-5}}		{{Lumatone EDO mapping\|n=87\|start=6\|xstep=7\|ystep=-5}}

Lucius Chiaraviglio: /* Pseudo-Isomorphic Quasi-Diatonic */ Insert Bryan Deister's Aureus Pseudo-Meantone after this

2025-11-18T10:23:49Z

Pseudo-Isomorphic Quasi-Diatonic: Insert Bryan Deister's Aureus Pseudo-Meantone after this

← Older revision		Revision as of 10:23, 18 November 2025
Line 10:		Line 10:
	For those who do not want the octave stretch, [[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for [[87edo]] in [https://www.youtube.com/shorts/5OH9OOGeuX4 ''87edo waltz''] (2025). This mapping retains a diatonic-style layout for ease of access to common consonant intervals, although it does not include all the notes of the tuning system. Each note 87 is actually another note 0, so as to reset octave pitch down by half of ~[[81/80]] (moderately inflated).		For those who do not want the octave stretch, [[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for [[87edo]] in [https://www.youtube.com/shorts/5OH9OOGeuX4 ''87edo waltz''] (2025). This mapping retains a diatonic-style layout for ease of access to common consonant intervals, although it does not include all the notes of the tuning system. Each note 87 is actually another note 0, so as to reset octave pitch down by half of ~[[81/80]] (moderately inflated).
	{{Lumatone EDO mapping\|n=88\|start=80\|xstep=14\|ystep=-5}}		{{Lumatone EDO mapping\|n=88\|start=80\|xstep=14\|ystep=-5}}

			== Aureus Pseudo-Meantone ==
			[[Bryan Deister]] has demonstrated a [[11L 5s]] (7:2 step ratio) mapping for [[87edo]] in [[https://www.youtube.com/shorts/rINJKiMQE78 ''Circuit Bent - Stomach Book (microtonal cover in 87edo)''] (2025). The generator 14\87, which is two keys right from the root note, is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it near-just; two of them make an essentially just classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 87edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals — the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) Since this interval is two keys right instead of just one (as needed to avoid missing notes), this version of the temperament can be viewed as a split generator version, in which each ~19/17 is split into two equal intervals that function as both a small septendecimal semitone ~[[18/17]] and a large undevicesimal semitone ~[[19/18]], both being close to just (and the photisma [[324/323]] is tempered out). Although no second generator is needed to reach all of the notes, for convenience, down-right by one key (2\87) can be used for convenience as a second generator that functions as ~[[49/48]] (inconsistently mapped), ~[[55/54]], ~[[64/63]], ~[[65/64]], and ~[[81/80]], of which the septimal chroma ~64/63 is near-just, and four of these make a near-just classic diatonic semitone ~[[16/15]] (the currently unnamed unnoticeable comma [[5250987/5242880]] is tempered out). The range is somewhat over two octaves (which slant very slightly downwards) with no missed notes and some repeated notes to mitigate vertical wraparounds.

			{{Lumatone EDO mapping\|n=87\|start=6\|xstep=7\|ystep=-5}}

	== Rodan ==		== Rodan ==

Lucius Chiaraviglio: /* Diatonic */ Insert Bryan Deister's Pseudo-Isomorphic Quasi-Diatonic mapping after this

2025-09-21T07:01:46Z

Diatonic: Insert Bryan Deister's Pseudo-Isomorphic Quasi-Diatonic mapping after this

← Older revision		Revision as of 07:01, 21 September 2025
Line 6:		Line 6:
	There is an alternate diatonic scale that makes 5-limit chords easy to play, but it has a slight octave stretch. Since every note is available in at least some of the octaves, this may actually be advantageous.		There is an alternate diatonic scale that makes 5-limit chords easy to play, but it has a slight octave stretch. Since every note is available in at least some of the octaves, this may actually be advantageous.
	{{Lumatone EDO mapping\|n=87\|start=79\|xstep=14\|ystep=-5}}		{{Lumatone EDO mapping\|n=87\|start=79\|xstep=14\|ystep=-5}}

			== Pseudo-Isomorphic Quasi-Diatonic ==
			For those who do not want the octave stretch, [[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for [[87edo]] in [https://www.youtube.com/shorts/5OH9OOGeuX4 ''87edo waltz''] (2025). This mapping retains a diatonic-style layout for ease of access to common consonant intervals, although it does not include all the notes of the tuning system. Each note 87 is actually another note 0, so as to reset octave pitch down by half of ~[[81/80]] (moderately inflated).
			{{Lumatone EDO mapping\|n=88\|start=80\|xstep=14\|ystep=-5}}

	== Rodan ==		== Rodan ==

Lucius Chiaraviglio: /* Misty */ Add demo video, and move note 0 to match the demo video and avoid a missed note 1 in the first octave

2025-07-28T11:41:50Z

Misty: Add demo video, and move note 0 to match the demo video and avoid a missed note 1 in the first octave

← Older revision		Revision as of 11:41, 28 July 2025
Line 21:		Line 21:
	{{Lumatone EDO mapping\|n=87\|start=53\|xstep=5\|ystep=8}}		{{Lumatone EDO mapping\|n=87\|start=53\|xstep=5\|ystep=8}}
	== Misty ==		== Misty ==
	The [[3L 9s]] [[Misty]] mapping is quite efficient at making harmonics easy to play together, gives you a relatively 12edo-like experience and keeps octaves near horizontal, but has a slightly smaller range.		The [[3L 9s]] [[Misty]] mapping is quite efficient at making harmonics easy to play together, gives you a relatively 12edo-like experience and keeps octaves near horizontal, but has a slightly smaller range. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/ecxELXmkYAs ''microtonal improvisation in 87edo''] (2025).
	{{Lumatone EDO mapping\|n=87\|start=60\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=87\|start=54\|xstep=7\|ystep=1}}

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

Yourmusic Productions: Create Page.

2025-07-10T11:55:50Z

Create Page.

New page

{{Lumatone mapping intro}} Due to the edos size, it would not cover the whole gamut even if it was.

== Diatonic ==
You can use the b val, which is at least a near perfect tuning for [[deeptone]].
{{Lumatone EDO mapping|n=87|start=69|xstep=13|ystep=-2}}
There is an alternate diatonic scale that makes 5-limit chords easy to play, but it has a slight octave stretch. Since every note is available in at least some of the octaves, this may actually be advantageous.
{{Lumatone EDO mapping|n=87|start=79|xstep=14|ystep=-5}}

== Rodan ==
The [[Rodan]] mapping is quite efficient and 87edo is an essentially perfect tuning for the temperament, which makes it a good option. However, the [[1L 4s]] and [[5L 1s]] mappings only cover about half the notes and the [[5L 6s]] one has heavily sloped octaves whichever direction you put the chroma. The reverse chroma one is the only one of these that covers the full gamut in the central octave.
=== 1L 4s ===
{{Lumatone EDO mapping|n=87|start=24|xstep=17|ystep=2}}
=== 5L 1s ===
{{Lumatone EDO mapping|n=87|start=39|xstep=17|ystep=-15}}
=== 5L 6s ===
{{Lumatone EDO mapping|n=87|start=11|xstep=15|ystep=-13}}
{{Lumatone EDO mapping|n=87|start=31|xstep=2|ystep=13}}

== Kleismic ==
The [[4L 7s]] mapping covers the full gamut and keeps octaves fairly horizontal when the small step goes rightward.
{{Lumatone EDO mapping|n=87|start=53|xstep=5|ystep=8}}
== Misty ==
The [[3L 9s]] [[Misty]] mapping is quite efficient at making harmonics easy to play together, gives you a relatively 12edo-like experience and keeps octaves near horizontal, but has a slightly smaller range.
{{Lumatone EDO mapping|n=87|start=60|xstep=7|ystep=1}}

{{Navbox Lumatone}}