Lumatone mapping for 37edo: Difference between revisions

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== Diatonic ==

The patent fifth ~[[3/2]] is so sharp that attempting to play a standard diatonic scale produces almost exactly a Barbados third ~[[13/10]], so sharp that even though the septimal major third ~[[9/7]] is mapped to the same interval, it is mapped inconsistently; furthermore, the Pythagorean whole tone ~[[9/8]] ~~itself~~ is itself mapped inconsistently, so if you want to play something sounding traditional diatonic, you have to start your scale moving up one key (instead of right one key) to get a classic-sounding whole tone (rather than the septimal version ~[[8/7]], which is just slightly flat), and then up another key (again instead of right) to get the near-just classic major third ~[[5/4]]; getting further classic intervals likewise requires some unusual movements, which would be awkward in combination. Thus, the diatonic mapping in 37edo is actually a xenharmonic mapping by default.

The patent fifth ~[[3/2]] is so sharp that attempting to play a standard diatonic scale produces almost exactly a Barbados third ~[[13/10]], so sharp that even though the septimal major third ~[[9/7]] is mapped to the same interval, it is mapped inconsistently; furthermore, the Pythagorean whole tone ~[[9/8]] is itself mapped inconsistently, so if you want to play something sounding traditional diatonic, you have to start your scale moving up one key (instead of right one key) to get a classic-sounding whole tone (rather than the septimal version ~[[8/7]], which is just slightly flat), and then up another key (again instead of right) to get the near-just classic major third ~[[5/4]]; getting further classic intervals likewise requires some unusual movements, which would be awkward in combination. Thus, the diatonic mapping in 37edo is actually a xenharmonic mapping by default.

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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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 == Diatonic ==
-The patent fifth ~[[3/2]] is so sharp that attempting to play a standard diatonic scale produces almost exactly a Barbados third ~[[13/10]], so sharp that even though the septimal major third ~[[9/7]] is mapped to the same interval, it is mapped inconsistently; furthermore, the Pythagorean whole tone ~[[9/8]] itself is itself mapped inconsistently, so if you want to play something sounding traditional diatonic, you have to start your scale moving up one key (instead of right one key) to get a classic-sounding whole tone (rather than the septimal version ~[[8/7]], which is just slightly flat), and then up another key (again instead of right) to get the near-just classic major third ~[[5/4]]; getting further classic intervals likewise requires some unusual movements, which would be awkward in combination. Thus, the diatonic mapping in 37edo is actually a xenharmonic mapping by default.
+The patent fifth ~[[3/2]] is so sharp that attempting to play a standard diatonic scale produces almost exactly a Barbados third ~[[13/10]], so sharp that even though the septimal major third ~[[9/7]] is mapped to the same interval, it is mapped inconsistently; furthermore, the Pythagorean whole tone ~[[9/8]] is itself mapped inconsistently, so if you want to play something sounding traditional diatonic, you have to start your scale moving up one key (instead of right one key) to get a classic-sounding whole tone (rather than the septimal version ~[[8/7]], which is just slightly flat), and then up another key (again instead of right) to get the near-just classic major third ~[[5/4]]; getting further classic intervals likewise requires some unusual movements, which would be awkward in combination. Thus, the diatonic mapping in 37edo is actually a xenharmonic mapping by default.
 {{Lumatone EDO mapping|n=37|start=10|xstep=7|ystep=-6}}
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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 ==