Lumatone mapping for 100edo: Difference between revisions

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== ~~Other Mappings~~ ==

== Submerged-related rank-2 temperament ==

To ~~maximise~~ your range while covering the full gamut, use the [[3L 10s]] scale generated by a submajor third of 31/100.

To maximize your range while covering the full gamut, use the [[3L 10s]] (10:7 step ratio) scale generated by a submajor third (in between ~[[5/4]] and ~[[16/13]]) of 31/100, which functions as a slightly sharp tridecimal submajor third ~[[26/21]] and a near-just (only slightly flat) tricesimoprimal submajor third ~[[31/25]]. The temperament is related to [[submerged]] in that 11 generators stack to make the flat ~[[4/3]] (41\100, corresponding to the sharp fifth ~[[5/3]] of 100edo), but it misses most of the other intervals of submerged temperament. The range is just under 2½ octaves, which slope mildly upwards.

== Unnamed rank-3 temperament ==

[[Bryan Deister]] has demonstrated a mapping for [[100edo]] that supports both a [[16L 4s]] scale (6:1 step ratio) and a flipped [[15L 2s]] scale (6:5 step ratio), in [https://www.youtube.com/shorts/gPbsSs4MFbQ ''100edo improv''] (2026). The rightward generator 6\100 functions as a near-just (only slightly flat) lesser vicesimotertial semitone ~[[24/23]] and a near-just (only slightly sharp) classic chromatic semitone ~[[25/24]]. Since 6 is not coprime with 100, an additional generator is required; since down-right 1\100 is used more often in the linked demonstration video, it can be considered the second generator; it functions as a sharp valinorsma ~[[176/175]] or a near-just (only slightly sharp major kirnbergerisma ~[[161/160]]. (Technically it could be used as a sole generator, but due to its small size, this would be very unwieldy. Also, technically the first generator 6\100 could be used as the sole generator for a rank-2 temperament with the octave divided into four parts, but this would be unwieldy for anything other than the aforementioned 16L 4s scale. The alternative upwards generator 5\100 is not co-prime with 100edo either, and would not work as the sole generator even with division of the octave into four parts.) The range (a bit over 1½ octaves) is even less than that of the [[12L 4s]] extra-expanded diatonic mapping, and the octaves slope upwards even more, but in exchange, this mapping enables easy fine adjustment of pitch and has a decent number of repeated notes to mitigate vertical wraparounds, while still having only a few notes of range chopped off in the corners.

@@ Line 11: / Line 11: @@
 {{Lumatone EDO mapping|n=100|start=12|xstep=8|ystep=-7}}
-== Other Mappings ==
+== Submerged-related rank-2 temperament ==
-To maximise your range while covering the full gamut, use the [[3L&nbsp;10s]] scale generated by a submajor third of 31/100.
+To maximize your range while covering the full gamut, use the [[3L&nbsp;10s]] (10:7 step ratio) scale generated by a submajor third (in between ~[[5/4]] and ~[[16/13]]) of 31/100, which functions as a slightly sharp tridecimal submajor third ~[[26/21]] and a near-just (only slightly flat) tricesimoprimal submajor third ~[[31/25]]. The temperament is related to [[submerged]] in that 11 generators stack to make the flat ~[[4/3]] (41\100, corresponding to the sharp fifth ~[[5/3]] of 100edo), but it misses most of the other intervals of submerged temperament. The range is just under 2½ octaves, which slope mildly upwards.
 {{Lumatone EDO mapping|n=100|start=74|xstep=7|ystep=3}}
+== Unnamed rank-3 temperament ==
+[[Bryan Deister]] has demonstrated a mapping for [[100edo]] that supports both a [[16L&nbsp;4s]] scale (6:1 step ratio) and a flipped [[15L&nbsp;2s]] scale (6:5 step ratio), in [https://www.youtube.com/shorts/gPbsSs4MFbQ ''100edo improv''] (2026). The rightward generator 6\100 functions as a near-just (only slightly flat) lesser vicesimotertial semitone ~[[24/23]] and a near-just (only slightly sharp) classic chromatic semitone ~[[25/24]]. Since 6 is not coprime with 100, an additional generator is required; since down-right 1\100 is used more often in the linked demonstration video, it can be considered the second generator; it functions as a sharp valinorsma ~[[176/175]] or a near-just (only slightly sharp major kirnbergerisma ~[[161/160]]. (Technically it could be used as a sole generator, but due to its small size, this would be very unwieldy. Also, technically the first generator 6\100 could be used as the sole generator for a rank-2 temperament with the octave divided into four parts, but this would be unwieldy for anything other than the aforementioned 16L&nbsp;4s scale. The alternative upwards generator 5\100 is not co-prime with 100edo either, and would not work as the sole generator even with division of the octave into four parts.) The range (a bit over 1½ octaves) is even less than that of the [[12L&nbsp;4s]] extra-expanded diatonic mapping, and the octaves slope upwards even more, but in exchange, this mapping enables easy fine adjustment of pitch and has a decent number of repeated notes to mitigate vertical wraparounds, while still having only a few notes of range chopped off in the corners.
+{{Lumatone EDO mapping|n=100|start=12|xstep=6|ystep=-5}}
+{{Navbox Lumatone}}