Lumatone mapping for 41edo: Difference between revisions

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{{Lumatone mapping intro}} [[Herman Miller]] has documented [http://www.youtube.com/watch?v=ZeUdl-54CrI five 41edo layouts], available for download at [[File: 41edo lumatone layouts.zip]].

== Diatonic ==

The [[Standard Lumatone mapping for Pythagorean]], as the name implies, works for using 41edo as an extended [[Pythagorean tuning]]. However, as 41edo is a [[schismic]] tuning rather than a [[meantone]] one, the approximated [[5/4]] is found at the diminished fourth (C–F♭) rather than the major third (C–E). [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/m8X-IqH8tok ''Waltz in 41edo''] (2025).

== Magic ==

The [[magic]] mapping is particularly efficient at putting good intervals close to each other and dissonant ones far away, as demonstrated in more detail in the writings on the [[kite guitar]].

~~The [[magic]] mapping is particularly efficient at putting good intervals close to each other and dissonant ones far away, as demonstrated in more detail in the writings on the [[kite guitar]].~~

== Tetracot ==

The [[tetracot]] mapping also puts consonant intervals within easy reach, making major, minor, and neutral triads particularly intuitive to play.

The [[~~tetracot~~]] mapping ~~also puts consonant intervals within easy reach~~, but the [[~~7L 6s~~]] ~~MOS~~ has a 5:1 ~~step ratio~~, ~~making it somewhat lopsided~~.

=== Standard ===

The standard [[6L 1s]] mapping is less lopsided and offers over 4½ octaves of range, but the octaves slope up. [[Bryan Deister]] has demonstrated this mapping (although offset in MIDI note position) in ''Winds Up The Best - 41edo'' (2026) ([https://www.youtube.com/shorts/Ss5OZ08qejw <nowiki>[short 1]</nowiki>], [https://www.youtube.com/shorts/Sk_bknNmgCU <nowiki>[short 2]</nowiki>]), from a point a few seconds into <nowiki>[short 1]</nowiki> up to slightly beyond the halfway point of <nowiki>[short 2]</nowiki>, before switching on-the-fly to the [[baldy]] mapping (see below), which is also used in the first few seconds of <nowiki>[short 1]</nowiki>.

=== Compressed ===

This can be compressed down to a [[1L 5s]] mapping that extends range, but makes fingerings for common chords slightly more awkward, although it does slightly reduce the upward slope of octaves.

== Slendric (Rodan) + Guiron ==

In 41edo, the near-just fifth ~[[3/2]] is 24\41, and dividing this into three parts yields a slightly sharp septimal major second ~[[8/7]], which is the generator for [[slendric]] and its extension [[rodan]] and for [[guiron]], which meets with slendric/rodan at 41edo. In both versions below, this generator (8\41) is reached very simply by moving one key right from the root note.

=== Compressed ===

If you want to maximise your range while having access to all notes in each octave, the compressed rodan mapping is about as good as you can get (at 6¼ octaves); however, it puts octaves all over the place.

=== Expanded ===

The expanded rodan mapping still has a wider range (somewhat over five octaves except for one missing note 38 in the top octave) compared to the diatonic mapping (just under five octaves) and is more ergonomic for play, as is the [[baldy]] mapping below this.

~~If you want to maximise your range while having access to all notes~~ in ~~each octave~~, the ~~compressed~~ [[~~rodan~~]] mapping ~~is about as good as you can get~~.

== Baldy ==

[[Bryan Deister]] has demonstrated the baldy mapping (although offset in MIDI note position) in ''Winds Up The Best - 41edo'' (2026) ([https://www.youtube.com/shorts/Ss5OZ08qejw <nowiki>[short 1]</nowiki>], [https://www.youtube.com/shorts/Sk_bknNmgCU <nowiki>[short 2]</nowiki>]), in the first few seconds of <nowiki>[short 1]</nowiki> and the last slightly less than half of <nowiki>[short 2]</nowiki>, with the rest being in the [[tetracot]] mapping (see above), again having switched mappings on the fly.

== Miracle (miraculous) ==

It is possible to map [[41edo]] as a [[miracle]] ([[miraculous]]) tuning, with a [[8L 3s]] scale (4:3 step ratio), using a secor (~[[15/14]] tempered together with ~[[16/15]]) which is in turn tempered together with ~[[14/13]] (as per the miraculous 13-limit extension). In this mapping, the range is only three octaves, but the octaves are perfectly level, each note is repeated at least twice, with a few being repeated three times, thus enabling the use of two manuals if the layout is offset appropriately. [[Bryan Deister]] has used this layout in [https://www.youtube.com/shorts/kLMuRP82bZw ''microtonal dance in 41edo ''] (2023), although without a color scheme that would show the layout.

~~However~~, this ~~puts octaves all over~~ the ~~place. The expanded rodan or~~ [[~~baldy~~]] ~~mappings still have a wider~~ range ~~than the standard one and are more ergonomic for play~~.

== Superkleismic ==

[[Bryan Deister]] has demonstrated a [[superkleismic]] [[4L 3s]] (8:3 step ratio) mapping for [[41edo]], in [https://www.youtube.com/shorts/Ur--SKiRsY0 ''41edo groove''] (2025). Bryan Deister explains that the coloring in this video highlights major triads, where going right and up yields a major third (~[[5/4]], somewhat flat) and going right three times yields the fifth (~[[3/2]], near-just). The range is somewhat over five octaves, which slope down moderately.

== Bohpier ==

Since [[41edo]] is very close to [[BPS]] (Bohlen–Pierce–Stearns) with its generator split into 5 equal parts and the addition of prime 2, it makes sense to map it for [[bohpier]] temperament, as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/shorts/ZSRxYfCM1FQ ''41edo improv''] (2026-09-01). The generator 5\41 (reached very simply by moving one key right from the root note) functions as a flat undecimal neutral second ~[[12/11]] and a sharp lesser tridecimal neutral second ~[[13/12]]. The range is somewhat over 4½ octaves, although the octaves slope down severely, incurring vertical wraparounds.

~~{{Lumatone EDO mapping|n~~=~~41|start~~=~~26|xstep~~=~~7|ystep~~=~~-1}}~~

== See also ==

* [[41edo Keyboards #Lumatone Options]]

@@ Line 1: / Line 1: @@
-{{Lumatone mapping intro}}
+{{Lumatone mapping intro}} [[Herman Miller]] has documented [http://www.youtube.com/watch?v=ZeUdl-54CrI five 41edo layouts], available for download at [[File: 41edo lumatone layouts.zip]].
+== Diatonic ==
+The [[Standard Lumatone mapping for Pythagorean]], as the name implies, works for using 41edo as an extended [[Pythagorean tuning]]. However, as 41edo is a [[schismic]] tuning rather than a [[meantone]] one, the approximated [[5/4]] is found at the diminished fourth (C–F♭) rather than the major third (C–E). [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/m8X-IqH8tok ''Waltz in 41edo''] (2025).
 {{Lumatone EDO mapping|n=41|start=2|xstep=7|ystep=-4}}
+== Magic ==
+The [[magic]] mapping is particularly efficient at putting good intervals close to each other and dissonant ones far away, as demonstrated in more detail in the writings on the [[kite guitar]].
-The [[magic]] mapping is particularly efficient at putting good intervals close to each other and dissonant ones far away, as demonstrated in more detail in the writings on the [[kite guitar]].
 {{Lumatone EDO mapping|n=41|start=21|xstep=2|ystep=9}}
+== Tetracot ==
+The [[tetracot]] mapping also puts consonant intervals within easy reach, making major, minor, and neutral triads particularly intuitive to play.
-The [[tetracot]] mapping also puts consonant intervals within easy reach, but the [[7L&nbsp;6s]] MOS has a 5:1 step ratio, making it somewhat lopsided.
+=== Standard ===
+The standard [[6L&nbsp;1s]] mapping is less lopsided and offers over 4½ octaves of range, but the octaves slope up. [[Bryan Deister]] has demonstrated this mapping (although offset in MIDI note position) in ''Winds Up The Best - 41edo'' (2026) ([https://www.youtube.com/shorts/Ss5OZ08qejw <nowiki>[short 1]</nowiki>], [https://www.youtube.com/shorts/Sk_bknNmgCU <nowiki>[short 2]</nowiki>]), from a point a few seconds into <nowiki>[short 1]</nowiki> up to slightly beyond the halfway point of <nowiki>[short 2]</nowiki>, before switching on-the-fly to the [[baldy]] mapping (see below), which is also used in the first few seconds of <nowiki>[short 1]</nowiki>.
 {{Lumatone EDO mapping|n=41|start=29|xstep=6|ystep=-1}}
+=== Compressed ===
+This can be compressed down to a [[1L&nbsp;5s]] mapping that extends range, but makes fingerings for common chords slightly more awkward, although it does slightly reduce the upward slope of octaves.
+{{Lumatone EDO mapping|n=41|start=23|xstep=6|ystep=5}}
+== Slendric (Rodan) + Guiron ==
+In 41edo, the near-just fifth ~[[3/2]] is 24\41, and dividing this into three parts yields a slightly sharp septimal major second ~[[8/7]], which is the generator for [[slendric]] and its extension [[rodan]] and for [[guiron]], which meets with slendric/rodan at 41edo. In both versions below, this generator (8\41) is reached very simply by moving one key right from the root note.
+=== Compressed ===
+If you want to maximise your range while having access to all notes in each octave, the compressed rodan mapping is about as good as you can get (at 6¼ octaves); however, it puts octaves all over the place.
+{{Lumatone EDO mapping|n=41|start=23|xstep=8|ystep=-1}}
+=== Expanded ===
+The expanded rodan mapping still has a wider range (somewhat over five octaves except for one missing note 38 in the top octave) compared to the diatonic mapping (just under five octaves) and is more ergonomic for play, as is the [[baldy]] mapping below this.
+{{Lumatone EDO mapping|n=41|start=10|xstep=8|ystep=-7}}
-If you want to maximise your range while having access to all notes in each octave, the compressed [[rodan]] mapping is about as good as you can get.
+== Baldy ==
-{{Lumatone EDO mapping|n=41|start=17|xstep=8|ystep=-1}}
+[[Bryan Deister]] has demonstrated the baldy mapping (although offset in MIDI note position) in ''Winds Up The Best - 41edo'' (2026) ([https://www.youtube.com/shorts/Ss5OZ08qejw <nowiki>[short 1]</nowiki>], [https://www.youtube.com/shorts/Sk_bknNmgCU <nowiki>[short 2]</nowiki>]), in the first few seconds of <nowiki>[short 1]</nowiki> and the last slightly less than half of <nowiki>[short 2]</nowiki>, with the rest being in the [[tetracot]] mapping (see above), again having switched mappings on the fly.
+{{Lumatone EDO mapping|n=41|start=26|xstep=7|ystep=-1}}
+== Miracle (miraculous) ==
+It is possible to map [[41edo]] as a [[miracle]] ([[miraculous]]) tuning, with a [[8L&nbsp;3s]] scale (4:3 step ratio), using a secor (~[[15/14]] tempered together with ~[[16/15]]) which is in turn tempered together with ~[[14/13]] (as per the miraculous 13-limit extension). In this mapping, the range is only three octaves, but the octaves are perfectly level, each note is repeated at least twice, with a few being repeated three times, thus enabling the use of two manuals if the layout is offset appropriately. [[Bryan Deister]] has used this layout in [https://www.youtube.com/shorts/kLMuRP82bZw ''microtonal dance in 41edo ''] (2023), although without a color scheme that would show the layout.
+{{Lumatone EDO mapping|n=41|start=35|xstep=4|ystep=-1}}
-However, this puts octaves all over the place. The expanded rodan or [[baldy]] mappings still have a wider range than the standard one and are more ergonomic for play.
+== Superkleismic ==
-{{Lumatone EDO mapping|n=41|start=18|xstep=8|ystep=-7}}
+[[Bryan Deister]] has demonstrated a [[superkleismic]] [[4L&nbsp;3s]] (8:3 step ratio) mapping for [[41edo]], in [https://www.youtube.com/shorts/Ur--SKiRsY0 ''41edo groove''] (2025). Bryan Deister explains that the coloring in this video highlights major triads, where going right and up yields a major third (~[[5/4]], somewhat flat) and going right three times yields the fifth (~[[3/2]], near-just). The range is somewhat over five octaves, which slope down moderately.
+{{Lumatone EDO mapping|n=41|start=2|xstep=8|ystep=-5}}
+== Bohpier ==
+Since [[41edo]] is very close to [[BPS]] (Bohlen–Pierce–Stearns) with its generator split into 5 equal parts and the addition of prime 2, it makes sense to map it for [[bohpier]] temperament, as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/shorts/ZSRxYfCM1FQ ''41edo improv''] (2026-09-01). The generator 5\41 (reached very simply by moving one key right from the root note) functions as a flat undecimal neutral second ~[[12/11]] and a sharp lesser tridecimal neutral second ~[[13/12]]. The range is somewhat over 4½ octaves, although the octaves slope down severely, incurring vertical wraparounds.
+{{Lumatone EDO mapping|n=41|start=4|xstep=5|ystep=4}}
-{{Lumatone EDO mapping|n=41|start=26|xstep=7|ystep=-1}}
+== See also ==
+* [[41edo Keyboards #Lumatone Options]]
 {{Navbox Lumatone}}