Lumatone mapping for 56edo: Difference between revisions

Line 8:

The [[2L 8s]] mapping for [[Pajara]] mapping has a smaller range and some repeated notes, but makes 5-limit chords easier to play.

== Bidia (+ Diminished + Charismic + Semitonismic) ==

[[Bryan Deister]] has demonstrated a [[4L 4s]] (9:5 step ratio) mapping for [[56edo]], in [https://www.youtube.com/watch?v=xkfao6yGKGE ''Curious Light - DOORS (microtonal cover in 56edo)''] (2025). Right + down-right divides the octave into slices of 14\56; as an interval in its own right, this is the same as the minor third of [[12edo]], which functions as ~[[19/16]] and ~[[25/21]] (both being near-just). Down-right alone is 5\56, which is the [[Normal forms#Minimal_form|minimal form]] generator for [[Bidia]]; it functions as the classic diatonic semitone ~[[16/15]], the large septendecimal semitone ~[[17/16]], and the small septendecimal semitone ~[[18/17]], meaning that the charisma [[256/255]] and the semitonisma [[289/288]] are both tempered out; two of them make a rather sharp whole tone ~[[9/8]]; three of them (passing the quarter-octave) make a mildly sharp classic minor third ~[[6/5]], although the afore-mentioned quarter-octave (12edo-style) minor third is easier to reach; in contrast, the near-just classic major third ~[[5/4]] is very easy to reach with just two moves rightwards, and a down-right move from this reaches the moderately flat fourth ~[[4/3]]; two more down-right moves reaches the rather sharp fifth ~[[3/2]]. The efficiency is almost as good as that of the diatonic mapping, with no missed notes and one repeated note per octave; the overall range is somewhat under five octaves, with no notes chopped off by the left and right edges before reaching the end of overall range. The cost of this is that octaves slant downwards.

@@ Line 8: / Line 8: @@
 The [[2L&nbsp;8s]] mapping for [[Pajara]] mapping has a smaller range and some repeated notes, but makes 5-limit chords easier to play.
 {{Lumatone EDO mapping|n=56|start=23|xstep=5|ystep=3}}
+== Bidia (+ Diminished + Charismic + Semitonismic) ==
+[[Bryan Deister]] has demonstrated a [[4L&nbsp;4s]] (9:5 step ratio) mapping for [[56edo]], in [https://www.youtube.com/watch?v=xkfao6yGKGE ''Curious Light - DOORS (microtonal cover in 56edo)''] (2025). Right + down-right divides the octave into slices of 14\56; as an interval in its own right, this is the same as the minor third of [[12edo]], which functions as ~[[19/16]] and ~[[25/21]] (both being near-just). Down-right alone is 5\56, which is the [[Normal forms#Minimal_form|minimal form]] generator for [[Bidia]]; it functions as the classic diatonic semitone ~[[16/15]], the large septendecimal semitone ~[[17/16]], and the small septendecimal semitone ~[[18/17]], meaning that the charisma [[256/255]] and the semitonisma [[289/288]] are both tempered out; two of them make a rather sharp whole tone ~[[9/8]]; three of them (passing the quarter-octave) make a mildly sharp classic minor third ~[[6/5]], although the afore-mentioned quarter-octave (12edo-style) minor third is easier to reach; in contrast, the near-just classic major third ~[[5/4]] is very easy to reach with just two moves rightwards, and a down-right move from this reaches the moderately flat fourth ~[[4/3]]; two more down-right moves reaches the rather sharp fifth ~[[3/2]]. The efficiency is almost as good as that of the diatonic mapping, with no missed notes and one repeated note per octave; the overall range is somewhat under five octaves, with no notes chopped off by the left and right edges before reaching the end of overall range. The cost of this is that octaves slant downwards.
+{{Lumatone EDO mapping|n=56|start=0|xstep=9|ystep=-4}}
 {{Navbox Lumatone}}