Lumatone mapping for 74edo: Difference between revisions

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[[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.

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 [[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}}