Lumatone mapping for 74edo: Difference between revisions

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{{Lumatone mapping intro}} However, due to its size, this mapping does not cover all the notes, although this does not matter in many keys because lower limit harmonics are relatively close together, which opens the possibility that even modulation to remote keys might be accommodated in some cases by the use of Lumatone presets mapping different diatonic subsets of 74edo.

== Diatonic ==

Despite the missing notes, [[Bryan Deister]] has used the diatonic mapping in [https://www.youtube.com/shorts/dB9_3TC3yPo ''Resonance - Home (microtonal cover in 74edo)''] (2026).

=== Flipped/Rotated version ===

One option for dealing with the large gamut of [[74edo]] on a standard-sized Lumatone is to flip and rotate the diatonic mapping, as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/shorts/vi-KljzPkGs ''74edo improv''] (2026). The scale is still [[5L 2s]] with a 12:7 step ratio, but now the whole tones proceed down-right while the diatonic semitones proceed right. Each octave is still missing some notes, but due to the octave slope, they are different missing notes in each octave (other than the octaves chopped off by the upper left and lower right corners); the range is three mostly-complete octaves plus a bass octave of full compass but severely truncated gamut, plus a partial treble octave.

== Semimeantone ==

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== Cantonismic-Werckismic rank-3 temperament ==

[[Bryan Deister]] has demonstrated the [[7L 6s]] mapping of [[74edo]] in [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025). The rightward generator (8\74) functions as ~[[14/13]]; three of them make a classic major third ~[[5/4]] (the [[cantonisma]] 10985/10976 is tempered out); five of them make an essentially-just undecimal subfifth ~[[16/11]]; and eight of them make a highly accurate undecimal supraminor seventh ~[[20/11]]. The upward generator (5\74) functions as ~[[21/20]] and ~[[22/21]] (the Werckisma ([[441/440]] is tempered out); two of these make ~[[11/10]]; five of these make ~[[24/19]] (which is distinguished from ~5/4); and eight of these make ~[[16/11]]. The range is ~~about~~ just over 3 octaves with no missing notes, and the octaves slope down and wrap around vertically.

[[Bryan Deister]] has demonstrated the [[7L 6s]] (8:3 step ratio) mapping of [[74edo]] in [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025). The rightward generator (8\74) functions as a near-just tridecimal supraminor second ~[[14/13]]; three of them make a classic major third ~[[5/4]] (the [[cantonisma]] 10985/10976 is tempered out); five of them make an essentially-just undecimal subfifth ~[[16/11]]; and eight of them make a highly accurate undecimal supraminor seventh ~[[20/11]]. The upward generator (5\74) functions as ~[[21/20]] and ~[[22/21]] (the Werckisma ([[441/440]] is tempered out); two of these make ~[[11/10]]; five of these make ~[[24/19]] (which is distinguished from ~5/4); and eight of these make ~[[16/11]]. The range is just over 3 octaves with no missing notes, and the octaves slope down and wrap around vertically.

==== Flipped version with divided octave ====

If the above mapping is flipped (so that what was the upwards generator is now the down-right generator), the scale becomes [[8L 2s]] (8:5 step ratio, now dividing the octave in half), as demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/shorts/TKZ05H4jYGc ''<nowiki>Waltz in 74edo [short clip]</nowiki>''] (2026). The octaves are closer to level (now sloping mildly upwards), and the range is actually slightly extended to 3¼ octaves, while still having a few repeated notes to mitigate vertical wraparounds.

@@ Line 1: / Line 1: @@
 {{Lumatone mapping intro}} However, due to its size, this mapping does not cover all the notes, although this does not matter in many keys because lower limit harmonics are relatively close together, which opens the possibility that even modulation to remote keys might be accommodated in some cases by the use of Lumatone presets mapping different diatonic subsets of 74edo.
 == Diatonic ==
+Despite the missing notes, [[Bryan Deister]] has used the diatonic mapping in [https://www.youtube.com/shorts/dB9_3TC3yPo ''Resonance - Home (microtonal cover in 74edo)''] (2026).
 {{Lumatone EDO mapping|n=74|start=70|xstep=12|ystep=-5}}
+=== Flipped/Rotated version ===
+One option for dealing with the large gamut of [[74edo]] on a standard-sized Lumatone is to flip and rotate the diatonic mapping, as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/shorts/vi-KljzPkGs ''74edo improv''] (2026). The scale is still [[5L&nbsp;2s]] with a 12:7 step ratio, but now the whole tones proceed down-right while the diatonic semitones proceed right. Each octave is still missing some notes, but due to the octave slope, they are different missing notes in each octave (other than the octaves chopped off by the upper left and lower right corners); the range is three mostly-complete octaves plus a bass octave of full compass but severely truncated gamut, plus a partial treble octave.
+{{Lumatone EDO mapping|n=74|start=0|xstep=7|ystep=5}}
 == Semimeantone ==
@@ Line 12: / Line 17: @@
 == Cantonismic-Werckismic rank-3 temperament ==
-[[Bryan Deister]] has demonstrated the [[7L&nbsp;6s]] mapping of [[74edo]] in [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025). The rightward generator (8\74) functions as ~[[14/13]]; three of them make a classic major third ~[[5/4]] (the [[cantonisma]] 10985/10976 is tempered out); five of them make an essentially-just undecimal subfifth ~[[16/11]]; and eight of them make a highly accurate undecimal supraminor seventh ~[[20/11]]. The upward generator (5\74) functions as ~[[21/20]] and ~[[22/21]] (the Werckisma ([[441/440]] is tempered out); two of these make ~[[11/10]]; five of these make ~[[24/19]] (which is distinguished from ~5/4); and eight of these make ~[[16/11]]. The range is about just over 3 octaves with no missing notes, and the octaves slope down and wrap around vertically.
+[[Bryan Deister]] has demonstrated the [[7L&nbsp;6s]] (8:3 step ratio) mapping of [[74edo]] in [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025). The rightward generator (8\74) functions as a near-just tridecimal supraminor second ~[[14/13]]; three of them make a classic major third ~[[5/4]] (the [[cantonisma]] 10985/10976 is tempered out); five of them make an essentially-just undecimal subfifth ~[[16/11]]; and eight of them make a highly accurate undecimal supraminor seventh ~[[20/11]]. The upward generator (5\74) functions as ~[[21/20]] and ~[[22/21]] (the Werckisma ([[441/440]] is tempered out); two of these make ~[[11/10]]; five of these make ~[[24/19]] (which is distinguished from ~5/4); and eight of these make ~[[16/11]]. The range is just over 3 octaves with no missing notes, and the octaves slope down and wrap around vertically.
 {{Lumatone EDO mapping|n=74|start=4|xstep=8|ystep=-5}}
+==== Flipped version with divided octave ====
+If the above mapping is flipped (so that what was the upwards generator is now the down-right generator), the scale becomes [[8L&nbsp;2s]] (8:5 step ratio, now dividing the octave in half), as demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/shorts/TKZ05H4jYGc ''<nowiki>Waltz in 74edo [short clip]</nowiki>''] (2026). The octaves are closer to level (now sloping mildly upwards), and the range is actually slightly extended to 3¼ octaves, while still having a few repeated notes to mitigate vertical wraparounds.
+{{Lumatone EDO mapping|n=74|start=70|xstep=8|ystep=-3}}
 {{Navbox Lumatone}}