Lumatone mapping for 49edo: Difference between revisions

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Keep in mind that 49edo is a [[superpyth]] temperament, so 5/4 is mapped to the interval of an augmented second (e.g. a 5/4 above C is D♯).

== ~~Other mappings~~ ==

== Didacus ==

If you want to access single step movements in a more intuitive way and slightly extend your range, the rotated [[6L 1s]] mapping ~~is probably~~ the ~~best compromise~~, although ~~it puts octaves all over~~ the ~~place~~.

If you want to access single step movements in a more intuitive way and slightly extend your range, [[Hemimean_clan#Didacus|Didacus]] mappings may be the best compromise. Didacus uses a flat Pythagorean whole tone ~[[9/8]] as its generator, which is the rightward generator in these mappings; it uses the direct approximation of the 9th harmonic instead of building it by stacking the 3rd harmonic. Unfortunately, these mappings put octaves all over the place.

=== Flipped 6L 1s (add rotated Sevond + Whitewood) ===

One possibility is a flipped [[6L 1s]] mapping (8:1 step ratio, with the short step being up instead of down-right), with a range of five octaves, although with a severe upwards slope that incurs a wraparound. This version also functions as a rotated [[Whitewood]] or [[Keemic_temperaments#Sevond|Sevond]] mapping, both dividing the octave into seven parts, and the latter using the flat fourth ~[[4/3]] (20\49, but 1/7-octave-reduced to 1\49) as its generator, which is reached by going left one key and up-left three keys.

=== 3L 5s (add Catalan + Clyde) ===

Another possibility is a [[3L 5s]] (8:5 step ratio) mapping for [[49edo]], as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/shorts/zb1Z6o-Uvuw ''weathergirl - FLAVOR FOLEY (microtonal cover in 49edo)''] (2025). This mapping lends itself to three rank-2 temperaments, one of which is Didacus as explained above. Another temperament is [[Kleismic_family#Catalan|Catalan]], for which the right + down-right generator 13\49 is a near-just (slightly sharp) classic minor third ~[[6/5]]; this uses the 3rd harmonic, which is quite sharp, but has most of its error canceled by the sharp 5th harmonic. Yet another temperament is [[Kleismic_family#Clyde|Clyde]], for which the right = 2 down-right generator 18\49 is a mildly sharp septimal major third ~[[9/7]]; this also uses the (sharp) 3rd harmonic to make an even sharper patent 9th harmonic, which has most of its error canceled by the sharp 7th harmonic. The range is just over five octaves with no missed notes and a few repeated notes in each octave, but the octaves slope down severely, incurring a vertical wraparound.

@@ Line 7: / Line 7: @@
 Keep in mind that 49edo is a [[superpyth]] temperament, so 5/4 is mapped to the interval of an augmented second (e.g. a 5/4 above C is D♯).
-== Other mappings ==
+== Didacus ==
-If you want to access single step movements in a more intuitive way and slightly extend your range, the rotated [[6L&nbsp;1s]] mapping is probably the best compromise, although it puts octaves all over the place.
+If you want to access single step movements in a more intuitive way and slightly extend your range, [[Hemimean_clan#Didacus|Didacus]] mappings may be the best compromise. Didacus uses a flat Pythagorean whole tone ~[[9/8]] as its generator, which is the rightward generator in these mappings; it uses the direct approximation of the 9th harmonic instead of building it by stacking the 3rd harmonic. Unfortunately, these mappings put octaves all over the place.
+=== Flipped 6L&nbsp;1s (add rotated Sevond + Whitewood) ===
+One possibility is a flipped [[6L&nbsp;1s]] mapping (8:1 step ratio, with the short step being up instead of down-right), with a range of five octaves, although with a severe upwards slope that incurs a wraparound. This version also functions as a rotated [[Whitewood]] or [[Keemic_temperaments#Sevond|Sevond]] mapping, both dividing the octave into seven parts, and the latter using the flat fourth ~[[4/3]] (20\49, but 1/7-octave-reduced to 1\49) as its generator, which is reached by going left one key and up-left three keys.
 {{Lumatone EDO mapping|n=49|start=25|xstep=8|ystep=-1}}
+=== 3L&nbsp;5s (add Catalan + Clyde) ===
+Another possibility is a [[3L&nbsp;5s]] (8:5 step ratio) mapping for [[49edo]], as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/shorts/zb1Z6o-Uvuw ''weathergirl - FLAVOR FOLEY (microtonal cover in 49edo)''] (2025). This mapping lends itself to three rank-2 temperaments, one of which is Didacus as explained above. Another temperament is [[Kleismic_family#Catalan|Catalan]], for which the right + down-right generator 13\49 is a near-just (slightly sharp) classic minor third ~[[6/5]]; this uses the 3rd harmonic, which is quite sharp, but has most of its error canceled by the sharp 5th harmonic. Yet another temperament is [[Kleismic_family#Clyde|Clyde]], for which the right = 2 down-right generator 18\49 is a mildly sharp septimal major third ~[[9/7]]; this also uses the (sharp) 3rd harmonic to make an even sharper patent 9th harmonic, which has most of its error canceled by the sharp 7th harmonic. The range is just over five octaves with no missed notes and a few repeated notes in each octave, but the octaves slope down severely, incurring a vertical wraparound.
+{{Lumatone EDO mapping|n=49|start=44|xstep=8|ystep=-3}}
 {{Navbox Lumatone}}