Lumatone mapping for 63edo: Difference between revisions

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== Diatonic ==

However, to the size of the edo, this mapping does not quite cover all the notes. In addition, the best approximation to [[5/4]] is the quadruply diminished or pentuply augmented 6th, which is extremely awkward to play with the root and 5th. The second best is shared with 12edo and is a triply augmented unison, which is slightly more ergonomic but still a tough stretch to play as a chord one-handed.

However, to the size of the edo, this mapping does not quite cover all the notes. In addition, the best approximation to [[5/4]] is the quadruply diminished or pentuply augmented 6th, which is extremely awkward to play with the root and 5th. The second best is shared with 12edo and is a triply augmented unison, which is slightly more ergonomic but still a tough stretch to play as a chord one-handed. Despite the missing notes, [[Bryan Deister]] has used this mapping, to make use of near-just ~[[14/11]] major thirds instead of ~5/4 major thirds, in [https://www.youtube.com/shorts/l-M2FZn2nC0 ''Venus as a Boy - Björk (microtonal cover in 63edo)''] (2025).

== Pseudo-Isomorphic Pseudo-Diatonic ==

[[Bryan Deister]] has used a pseudo-isomorphic pseudo-diatonic mapping laid out as for [[64edo]], but with note 63 actually being a duplicate of note 0 (but it is off the edge, so not visible unless this mapping would be used on a hypothetical XL-sized Lumatone). This is demonstrated in [https://www.youtube.com/shorts/EEAJ0AaWoJM ''63edo improv''] (2025), with a monochrome color scheme for additional challenge.

== Other Mappings ==

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== Pseudo-Meantone ==

== Aureus Pseudo-Meantone ==

[[Bryan Deister]] has demonstrated a [[6L 1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\93 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo 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.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals — for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.

[[Bryan Deister]] has demonstrated a [[6L 1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\63 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo 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.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals — for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.

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 == Diatonic ==
-However, to the size of the edo, this mapping does not quite cover all the notes. In addition, the best approximation to [[5/4]] is the quadruply diminished or pentuply augmented 6th, which is extremely awkward to play with the root and 5th. The second best is shared with 12edo and is a triply augmented unison, which is slightly more ergonomic but still a tough stretch to play as a chord one-handed.
+However, to the size of the edo, this mapping does not quite cover all the notes. In addition, the best approximation to [[5/4]] is the quadruply diminished or pentuply augmented 6th, which is extremely awkward to play with the root and 5th. The second best is shared with 12edo and is a triply augmented unison, which is slightly more ergonomic but still a tough stretch to play as a chord one-handed. Despite the missing notes, [[Bryan Deister]] has used this mapping, to make use of near-just ~[[14/11]] major thirds instead of ~5/4 major thirds, in [https://www.youtube.com/shorts/l-M2FZn2nC0 ''Venus as a Boy - Björk (microtonal cover in 63edo)''] (2025).
 {{Lumatone EDO mapping|n=63|start=6|xstep=11|ystep=-7}}
+== Pseudo-Isomorphic Pseudo-Diatonic ==
+[[Bryan Deister]] has used a pseudo-isomorphic pseudo-diatonic mapping laid out as for [[64edo]], but with note 63 actually being a duplicate of note 0 (but it is off the edge, so not visible unless this mapping would be used on a hypothetical XL-sized Lumatone). This is demonstrated in [https://www.youtube.com/shorts/EEAJ0AaWoJM ''63edo improv''] (2025), with a monochrome color scheme for additional challenge.
+{{Lumatone EDO mapping|n=64|start=56|xstep=10|ystep=-3}}
 == Other Mappings ==
@@ Line 26: / Line 30: @@
 {{Lumatone EDO mapping|n=63|start=13|xstep=3|ystep=11}}
-== Pseudo-Meantone ==
+== Aureus Pseudo-Meantone ==
-[[Bryan Deister]] has demonstrated a [[6L&nbsp;1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\93 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals &mdash; the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals &mdash; for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.
+[[Bryan Deister]] has demonstrated a [[6L&nbsp;1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\63 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals &mdash; the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals &mdash; for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.
 {{Lumatone EDO mapping|n=63|start=6|xstep=10|ystep=-7}}
 {{Navbox Lumatone}}