Lumatone mapping for 41edo: Difference between revisions

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== Diatonic ==

The [[Standard Lumatone mapping for Pythagorean]], as the name implies, works for using 41edo as an extended [[Pythagorean tuning]]. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/m8X-IqH8tok ''Waltz in 41edo''] (2025).

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).

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== Tetracot ==

The [[tetracot]] mapping also puts consonant intervals within easy reach, making major, minor, and neutral triads particularly intuitive to play~~. Though the [[7L 6s]] mos is somewhat lopsided, due to its rather hard 5:1 step ratio~~.

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

=== 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>.

This can be compressed down to a [[1L 5s]] mapping that extends range, but makes fingerings for common chords slightly more awkward

=== 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.

== Rodan ==

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.

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

== Baldy ==

[[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>]), 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) Lumatone mappings ==

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.

== Superkleismic Lumatone mappings ==

[[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.

== See also ==

@@ Line 2: / Line 2: @@
 == Diatonic ==
-The [[Standard Lumatone mapping for Pythagorean]], as the name implies, works for using 41edo as an extended [[Pythagorean tuning]]. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/m8X-IqH8tok ''Waltz in 41edo''] (2025).
+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}}
@@ Line 11: / Line 11: @@
 == Tetracot ==
-The [[tetracot]] mapping also puts consonant intervals within easy reach, making major, minor, and neutral triads particularly intuitive to play. Though the [[7L&nbsp;6s]] mos is somewhat lopsided, due to its rather hard 5:1 step ratio.
+The [[tetracot]] mapping also puts consonant intervals within easy reach, making major, minor, and neutral triads particularly intuitive to play.
+=== 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}}
-This can be compressed down to a [[1L&nbsp;5s]] mapping that extends range, but makes fingerings for common chords slightly more awkward
+=== 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}}
 == Rodan ==
 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.
 {{Lumatone EDO mapping|n=41|start=17|xstep=8|ystep=-1}}
 However, this puts octaves all over the place. The expanded rodan and [[baldy]] mappings still have a wider range than the standard one and are more ergonomic for play.
 {{Lumatone EDO mapping|n=41|start=18|xstep=8|ystep=-7}}
 == Baldy ==
+[[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>]), 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) Lumatone mappings ==
 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}}
-{{Lumatone EDO mapping|n=41|start=35|xstep=4|ystep=-1}}
+== Superkleismic Lumatone mappings ==
+[[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}}
 == See also ==