Lumatone mapping for 91edo: Difference between revisions

Line 14:

=== Isomorphic ===

[[Bryan Deister]] has demonstrated an isomorphic [[9L 2s]] mapping for [[91edo]] in [https://www.youtube.com/shorts/z6PeEocYMV8 ''improv 91edo''] (2025). The range is just one note beyond 3 full octaves, with octaves sloping up mildly (which results in a wraparound of note 0). The rightward generator 9\91 is the septimal diatonic semitone ~[[15\14]]. The upward generator 4\91 is a quartertone that functions as ~[[32/31]], ~[[33/32]], ~[[34/33]], and ~[[36/35]]; two of them make the minor diatonic semitone ~[[17/16]]; six of them make a near-just minor third ~[[6/5]]. The use of this generator makes this a mapping for [[Quartkeenlig]]; however, since stacking the upward generator quickly leads to wraparounds, and attempting to get the perfect fifth in 91edo with this generator yields 52\91, which is the [[7edo]] (91bb) fifth. Therefore, this mapping really needs to be treated as a rank-3 temperament mapping; for instance, to get the patent fifth 53\92 (a mildly flat ~[[3/2]], almost exactly [[1/7-comma meantone]]), it is easiest to stack five rightward generators and two upward generators.

[[Bryan Deister]] has demonstrated an isomorphic [[9L 2s]] mapping for [[91edo]] in [https://www.youtube.com/shorts/z6PeEocYMV8 ''improv 91edo''] (2025). The range is just one note beyond 3 full octaves, with octaves sloping up mildly (which results in a wraparound of note 0). The rightward generator 9\91 is the septimal diatonic semitone ~[[15/14]]. The upward generator 4\91 is a quartertone that functions as ~[[32/31]], ~[[33/32]], ~[[34/33]], and ~[[36/35]]; two of them make the minor diatonic semitone ~[[17/16]]; six of them make a near-just minor third ~[[6/5]]. The use of this generator makes this a mapping for [[Quartkeenlig]]; however, since stacking the upward generator quickly leads to wraparounds, and attempting to get the perfect fifth in 91edo with this generator yields 52\91, which is the [[7edo]] (91bb) fifth. Therefore, this mapping really needs to be treated as a rank-3 temperament mapping; for instance, to get the patent fifth 53\92 (a mildly flat ~[[3/2]], almost exactly [[1/7-comma meantone]]), it is easiest to stack five rightward generators and two upward generators.

@@ Line 14: / Line 14: @@
 === Isomorphic ===
-[[Bryan Deister]] has demonstrated an isomorphic [[9L&nbsp;2s]] mapping for [[91edo]] in [https://www.youtube.com/shorts/z6PeEocYMV8 ''improv 91edo''] (2025). The range is just one note beyond 3 full octaves, with octaves sloping up mildly (which results in a wraparound of note 0). The rightward generator 9\91 is the septimal diatonic semitone ~[[15\14]]. The upward generator 4\91 is a quartertone that functions as ~[[32/31]], ~[[33/32]], ~[[34/33]], and ~[[36/35]]; two of them make the minor diatonic semitone ~[[17/16]]; six of them make a near-just minor third ~[[6/5]]. The use of this generator makes this a mapping for [[Quartkeenlig]]; however, since stacking the upward generator quickly leads to wraparounds, and attempting to get the perfect fifth in 91edo with this generator yields 52\91, which is the [[7edo]] (91bb) fifth. Therefore, this mapping really needs to be treated as a rank-3 temperament mapping; for instance, to get the patent fifth 53\92 (a mildly flat ~[[3/2]], almost exactly [[1/7-comma meantone]]), it is easiest to stack five rightward generators and two upward generators.
+[[Bryan Deister]] has demonstrated an isomorphic [[9L&nbsp;2s]] mapping for [[91edo]] in [https://www.youtube.com/shorts/z6PeEocYMV8 ''improv 91edo''] (2025). The range is just one note beyond 3 full octaves, with octaves sloping up mildly (which results in a wraparound of note 0). The rightward generator 9\91 is the septimal diatonic semitone ~[[15/14]]. The upward generator 4\91 is a quartertone that functions as ~[[32/31]], ~[[33/32]], ~[[34/33]], and ~[[36/35]]; two of them make the minor diatonic semitone ~[[17/16]]; six of them make a near-just minor third ~[[6/5]]. The use of this generator makes this a mapping for [[Quartkeenlig]]; however, since stacking the upward generator quickly leads to wraparounds, and attempting to get the perfect fifth in 91edo with this generator yields 52\91, which is the [[7edo]] (91bb) fifth. Therefore, this mapping really needs to be treated as a rank-3 temperament mapping; for instance, to get the patent fifth 53\92 (a mildly flat ~[[3/2]], almost exactly [[1/7-comma meantone]]), it is easiest to stack five rightward generators and two upward generators.
 {{Lumatone EDO mapping|n=91|start=0|xstep=9|ystep=-4}}
 {{Navbox Lumatone}}