User:Lucius Chiaraviglio/Keyboard Layout Lab: Difference between revisions

[[Bryan Deister]] has demonstrated the [[9L 4s]] mapping of [[74edo]] in [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025). The rightward generator (6\74) functions as ~[[17/16]] and ~[[18/17]] (the semitonisma [[289/288]] is tempered out); two of them make a meantone whole tone (which functions as ~[[10/9]], ~[[9/8]], and ~[[19/17]] — the ganassisma [[153/152]] and the malcolmisma [[171/170]] are both tempered out); three of them make the neogothic minor third ~[[13/11]]; four of them make the classic major third ~[[5/4]]; and six of them make the lesser septimal tritone ~[[7/5]]. The down-right 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 stacking of two or four instances of ~[[3/2]] (43\74) and octave-reducing also yields the same results as two or four instances (respectively) of the rightward generator, making this a meantone mapping as expected for the [[patent val]] of 74edo; yet the usefulness of the down-right generator for reaching higher-limit intervals is undeniable, making this a mapping for a [[Meantone]]-related rank-3 temperament in the [[19-limit]] that is different from [[Didymus]]. The range is about 2⅔ octaves with no missing notes (indeed, with a few duplicate notes which partially alleviate vertical wraparounds), and the octaves slope downward very gently.