Lumatone mapping for 13edo: Difference between revisions

[[Bryan Deister]] has demonstrated a [[3L 2s]] (3:2 step ratio) [[Aurora]]/[[Father]] mapping for [[13edo]], in [https://www.youtube.com/shorts/YiIr9l0M67w ''Holding Back My Endless Sigh - 13edo''] (2026). The generator 8\13 (three keys right and one key down-right from the root note) can be taken as a very sharp fifth (~[[3/2]], for Father temperament) or a moderately sharp septimal superfifth (~[[32/21]], for Aurora temperament). Even more simply, this mapping also functions for a [[4L 5s]] (2:1 step ratio) scale for a variant of [[Orwell]] temperament, with the one key right generator being 3\13, which functions as (among other things) a rather sharp septimal minor third ~[[7/6]] (requires the 13d val) or a flat tridecimal minor third ~[[13/11]], of which two make a slightly sharp undecimal major fourth ~[[11/8]]; three of them make a sharp classic minor sixth ~[[8/5]]; four of them make a very flat classic major seventh ~[[15/8]]; and after octave-reduction, seven of them make the super-sharp fifth ~[[3/2]] (better constituted as a near-just vicesimotertial inframinor sixth ~[[23/15]] or a slightly sharp septendecimal superfifth ~[[26/17]]); and eight of them make a very sharp septimal minor seventh ~[[7/4]] (if using the 13d val) or a near-just classic minor seventh ~[[9/5]] (requires constitution of the 9 as 3♯ × 3♭). The range is over seven octaves, with notes repeated multiple times, but unfortunately the downwards slope of the octaves, although mild, would make mapping to multiple manuals tricky.