Lumatone mapping for 37edo: Difference between revisions

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Since the perfect fifth is so sharp, you lose little accuracy by using the flat fifth as a generator instead, which can be interpreted as near equalised [[mavila]], or more accurately but complexly as [[undecimation]].

== Aureus Pseudo-Meantone + Mediantone + Roulette + Hemiwürschmidt + Hemiwur ==

[[Bryan Deister]] has demonstrated a [[6L 1s]] (6:1 step ratio) mapping for [[37edo]] in [https://www.youtube.com/shorts/Jt6_r6r3lGY ''37edo improv''] (2026). This mapping functions as an aureus pseudo-meantone mapping; this functions for temperaments [[mediantone]], [[roulette]], [[hemiwürschmidt]], and [[hemiwur]]; it has a generator 6\37 that functions as both a slightly sharp quasi-meantone ~[[19/17]] and a slightly flat septimal middle whole tone ~[[28/25]]. (In contrast to actual [[meantone]] temperament, 37edo represents ~19/17 (or 28/25), ~[[10/9]], and ~[[9/8]] as distinct intervals — the syntonic comma [[81/80]] is not tempered out, but inflated to 2\37, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) The range is a bit under 4½ octaves, and the octaves slope upwards moderately.

== Diatonicized Chromaticism via Rotated Antidiatonic ==

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 Since the perfect fifth is so sharp, you lose little accuracy by using the flat fifth as a generator instead, which can be interpreted as near equalised [[mavila]], or more accurately but complexly as [[undecimation]].
 {{Lumatone EDO mapping|n=37|start=23|xstep=5|ystep=1}}
+== Aureus Pseudo-Meantone + Mediantone + Roulette + Hemiwürschmidt + Hemiwur ==
+[[Bryan Deister]] has demonstrated a [[6L&nbsp;1s]] (6:1 step ratio) mapping for [[37edo]] in [https://www.youtube.com/shorts/Jt6_r6r3lGY ''37edo improv''] (2026). This mapping functions as an aureus pseudo-meantone mapping; this functions for temperaments [[mediantone]], [[roulette]], [[hemiwürschmidt]], and [[hemiwur]]; it has a generator 6\37 that functions as both a slightly sharp quasi-meantone ~[[19/17]] and a slightly flat septimal middle whole tone ~[[28/25]]. (In contrast to actual [[meantone]] temperament, 37edo represents ~19/17 (or 28/25), ~[[10/9]], and ~[[9/8]] as distinct intervals &mdash; the syntonic comma [[81/80]] is not tempered out, but inflated to 2\37, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) The range is a bit under 4½ octaves, and the octaves slope upwards moderately.
+{{Lumatone EDO mapping|n=37|start=12|xstep=6|ystep=-5}}
 == Diatonicized Chromaticism via Rotated Antidiatonic ==