Lumatone mapping for 23edo: Difference between revisions

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~~There are many conceivable ways to map [[23edo]] onto the [[~~Lumatone~~]] keyboard. Only one~~, however, ~~agrees with~~ the [[~~Standard Lumatone mapping for Pythagorean~~]].

== Antidiatonic ==

The flat fifth is slightly closer, however, which produces the following layout. However, as 23edo is a [[mavila]] temperament, its best fifths are both quite dissonant and the chromatic semitone goes in the opposite direction to usual. In fact, all 4 of its first prime harmonics are tuned almost as badly as is possible with its step size.

~~However~~, ~~as 23edo~~ is a [[~~mavila~~]] ~~temperament~~, it's ~~best fifths are quite dissonant~~ and the ~~chromatic semitone goes in~~ the ~~opposite direction~~ to ~~usual~~. ~~In fact~~, ~~all 4 of its first prime harmonics are tuned almost~~ as ~~badly~~ as is ~~possible~~ with ~~its step size~~. The first harmonics that are decently tuned are 9, 13, 15, 17 & 21. The most efficient way to reach these is the [[sephiroth]] mapping, which forms a neat 16:17:21:26:32 chord with -3 generators.

== Mavila (Superdiatonic) + Baldy (Amsochromic) ==

Still using the [[23edo]] flat fifth ~[[3/2]] for [[mavila]] temperament, an alternative to the antidiatonic mapping is the superdiatonic mapping, having a [[7L 2s]] scale (3:1 step ratio), with the generator 13\23 being reached by moving four keys right plus one key down-right. This reduces the range from just under five octaves to about 3½ octaves, although it keeps them nearly level — rising gently enough to support division into multiple manuals. It also supports a [[6L 5s]] scale (3:1 step ratio) if the mildly sharp directly-approximated Pythagorean whole tone ~[[9/8]] is used as a generator instead, although this causes the octaves to slope down enough to prevent vertical division into two contiguous manuals; this generator (4\23) is reached by moving one key right plus one key down-right, which is easier than reaching the mavila generator. This mapping is demonstrated on the left Lumatone in {{W|David Wise}}'s [https://www.youtube.com/watch?v=joi8vyChSy4&list=WL&index=266 ''Aquatic Ambience''] (1993 via {{W|Donkey Kong Country}} (1994) – microtonal cover in 23edo by [[Stephen Weigel]] (right) and [[Vito Sicurella]] (left) on Lumatones (2026, from UnTwelve 2025); the color scheme is for the superdiatonic scale, but different between the left and right halves of the layout to represent division into two horizontal zones for different soft synthesizers. This layout is used on the left Lumatone; for the right Lumatone layout, see Oolong (Smitonic) below.

== Oolong (Smitonic) ==

An alternative for [[23edo]] to using either (highly inaccurate) fifth as a generator is stacking the much more accurate (only slightly flat) classic minor third ~[[6/5]], as in [[oolong]] temperament, having a [[4L 3s]] scale (5:1 step ratio); the generator 6\23 is reached by moving one key right plus one key down-right. This results in a moderate downwards slope of the octaves, but the range is 5¾ octaves, still with a generous allocation of repeated notes to mitigate vertical wraparounds. This mapping is demonstrated on the right Lumatone in {{W|David Wise}}'s [https://www.youtube.com/watch?v=joi8vyChSy4&list=WL&index=266 ''Aquatic Ambience''] (1993 via {{W|Donkey Kong Country}} (1994) – microtonal cover in 23edo by [[Stephen Weigel]] (right) and [[Vito Sicurella]] (left) on Lumatones (2026, from UnTwelve 2025). This layout is used on the right Lumatone; for the left Lumatone layout, see Mavila (Superdiatonic) + Baldy (Amsochromic) above.

== Sephiroth ==

The first harmonics that are decently tuned are 9, 13, 15, 17, and 21. The most efficient way to reach these is the [[sephiroth]] mapping, which forms a neat 16:17:21:26:32 chord with −3 generators.

Also quite effective is the [[Subgroup_temperaments#A-team|A-~~team~~]] mapping, which turns the harmonic sequence 16:18:21 and ~~it's~~ inversion into easy to play consonant cluster chords.

== A-Team ==

Also quite effective is the [[Subgroup_temperaments#A-team|A-Team]] mapping, which turns the harmonic sequence 16:18:21 and its inversion into easy to play consonant cluster chords that only require a single finger to hit all three notes.

== Didacus/Isra-related Machinoid ==

[[Bryan Deister]] has demonstrated a [[5L 1s]] (4:3 step ratio) mapping for [[23edo]] in [https://www.youtube.com/shorts/rfkVLuoC2gM ''23edo''] (2023), although with MIDI note numbering offset relative to what is shown here. The rightward generator 4\23 corresponds to a somewhat sharp directly-approximated Pythagorean whole tone ~[[9/8]], as in [[didacus]] and [[isra]]; however, unlike these temperaments, it brings up a different set of intervals, all in the 2.9.15.21.33.13.17 subgroup (same as as used for the table of intervals on the 23edo page, and required to get ~9/8 and most of the following intervals to map correctly). Two of these generators make a near-just undecimal (pentacircle) major third ~[[14/11]]; three of them make a mildly sharp greater septimal tritone ~[[10/7]]; four of them make a somewhat flat lesser tridecimal neutral sixth ~[[13/8]]; and five of them make a mildly flat undecimal neutral seventh ~[[11/6]]. The range is a bit over five octaves, and the octaves slope upwards.

~~[[Category:~~Lumatone ~~mappings]] [[Category:23edo]]~~

@@ Line 1: / Line 1: @@
-There are many conceivable ways to map [[23edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]].
+{{Lumatone mapping intro}}
+== Antidiatonic ==
+The flat fifth is slightly closer, however, which produces the following layout. However, as 23edo is a [[mavila]] temperament, its best fifths are both quite dissonant and the chromatic semitone goes in the opposite direction to usual. In fact, all 4 of its first prime harmonics are tuned almost as badly as is possible with its step size.
 {{Lumatone EDO mapping|n=23|start=13|xstep=3|ystep=1}}
-However, as 23edo is a [[mavila]] temperament, it's best fifths are quite dissonant and the chromatic semitone goes in the opposite direction to usual. In fact, all 4 of its first prime harmonics are tuned almost as badly as is possible with its step size. The first harmonics that are decently tuned are 9, 13, 15, 17 & 21. The most efficient way to reach these is the [[sephiroth]] mapping, which forms a neat 16:17:21:26:32 chord with -3 generators.
+== Mavila (Superdiatonic) + Baldy (Amsochromic) ==
+Still using the [[23edo]] flat fifth ~[[3/2]] for [[mavila]] temperament, an alternative to the antidiatonic mapping is the superdiatonic mapping, having a [[7L&nbsp;2s]] scale (3:1 step ratio), with the generator 13\23 being reached by moving four keys right plus one key down-right. This reduces the range from just under five octaves to about 3½ octaves, although it keeps them nearly level &mdash; rising gently enough to support division into multiple manuals. It also supports a [[6L&nbsp;5s]] scale (3:1 step ratio) if the mildly sharp directly-approximated Pythagorean whole tone ~[[9/8]] is used as a generator instead, although this causes the octaves to slope down enough to prevent vertical division into two contiguous manuals; this generator (4\23) is reached by moving one key right plus one key down-right, which is easier than reaching the mavila generator. This mapping is demonstrated on the left Lumatone in {{W|David Wise}}'s [https://www.youtube.com/watch?v=joi8vyChSy4&list=WL&index=266 ''Aquatic Ambience''] (1993 via {{W|Donkey Kong Country}} (1994) – microtonal cover in 23edo by [[Stephen Weigel]] (right) and [[Vito Sicurella]] (left) on Lumatones (2026, from UnTwelve 2025); the color scheme is for the superdiatonic scale, but different between the left and right halves of the layout to represent division into two horizontal zones for different soft synthesizers. This layout is used on the left Lumatone; for the right Lumatone layout, see Oolong (Smitonic) below.
+{{Lumatone EDO mapping|n=23|start=0|xstep=3|ystep=-2}}
+== Oolong (Smitonic) ==
+An alternative for [[23edo]] to using either (highly inaccurate) fifth as a generator is stacking the much more accurate (only slightly flat) classic minor third ~[[6/5]], as in [[oolong]] temperament, having a [[4L&nbsp;3s]] scale (5:1 step ratio); the generator 6\23 is reached by moving one key right plus one key down-right. This results in a moderate downwards slope of the octaves, but the range is 5¾ octaves, still with a generous allocation of repeated notes to mitigate vertical wraparounds. This mapping is demonstrated on the right Lumatone in {{W|David Wise}}'s [https://www.youtube.com/watch?v=joi8vyChSy4&list=WL&index=266 ''Aquatic Ambience''] (1993 via {{W|Donkey Kong Country}} (1994) – microtonal cover in 23edo by [[Stephen Weigel]] (right) and [[Vito Sicurella]] (left) on Lumatones (2026, from UnTwelve 2025). This layout is used on the right Lumatone; for the left Lumatone layout, see Mavila (Superdiatonic) + Baldy (Amsochromic) above.
+{{Lumatone EDO mapping|n=23|start=0|xstep=5|ystep=-4}}
+== Sephiroth ==
+The first harmonics that are decently tuned are 9, 13, 15, 17, and 21. The most efficient way to reach these is the [[sephiroth]] mapping, which forms a neat 16:17:21:26:32 chord with −3 generators.
 {{Lumatone EDO mapping|n=23|start=6|xstep=7|ystep=-5}}
-Also quite effective is the [[Subgroup_temperaments#A-team|A-team]] mapping, which turns the harmonic sequence 16:18:21 and it's inversion into easy to play consonant cluster chords.
+== A-Team ==
-{{Lumatone EDO mapping|n=23|start=20|xstep=5|ystep=-1}}
+Also quite effective is the [[Subgroup_temperaments#A-team|A-Team]] mapping, which turns the harmonic sequence 16:18:21 and its inversion into easy to play consonant cluster chords that only require a single finger to hit all three notes.
+{{Lumatone EDO mapping|n=23|start=22|xstep=9|ystep=-4}}
+== Didacus/Isra-related Machinoid ==
+[[Bryan Deister]] has demonstrated a [[5L&nbsp;1s]] (4:3 step ratio) mapping for [[23edo]] in [https://www.youtube.com/shorts/rfkVLuoC2gM ''23edo''] (2023), although with MIDI note numbering offset relative to what is shown here. The rightward generator 4\23 corresponds to a somewhat sharp directly-approximated Pythagorean whole tone ~[[9/8]], as in [[didacus]] and [[isra]]; however, unlike these temperaments, it brings up a different set of intervals, all in the 2.9.15.21.33.13.17 subgroup (same as as used for the table of intervals on the 23edo page, and required to get ~9/8 and most of the following intervals to map correctly). Two of these generators make a near-just undecimal (pentacircle) major third ~[[14/11]]; three of them make a mildly sharp greater septimal tritone ~[[10/7]]; four of them make a somewhat flat lesser tridecimal neutral sixth ~[[13/8]]; and five of them make a mildly flat undecimal neutral seventh ~[[11/6]]. The range is a bit over five octaves, and the octaves slope upwards.
+{{Lumatone EDO mapping|n=23|start=15|xstep=4|ystep=-1}}
-[[Category:Lumatone mappings]] [[Category:23edo]]
+{{Navbox Lumatone}}