Lumatone mapping for 74edo: Difference between revisions

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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.

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 == 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}}
 {{Navbox Lumatone}}