Lumatone mapping for 100edo: Difference between revisions

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== Diatonic ==

However, you can use the 100b val (using 59\100) to generate a hard diatonic (18:5 step size ratio. This will fail to cover the whole gamut due to the size of the edo.

However, you can use the 100b val (using 59\100) to generate a hard diatonic (18:5 step size ratio) that is a good tuning for [[quasisupra]]. This will fail to cover the whole gamut due to the size of the edo.

(~~Note~~: ~~When I~~ ([[~~User:MisterShafXen~~]]) ~~tried adding~~ the mapping ~~starting with~~ 7 ~~and steps xsteps~~=~~18 ysteps~~=-13, it ~~didn't~~ work.)

Since 50edo is already divisible by two, [[injera]] and its extensions also fail to cover all the notes in 100edo unless you divide the octave into four. The [[4L 8s]] mapping covers most of the notes with the occasional skip, while the [[12L 4s]] one does cover all the notes, but with very limited range and lopsided step size.

=== 4L 8s ===

=== 12L 4s ===

== Submerged-related rank-2 temperament ==

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.

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 == Diatonic ==
-However, you can use the 100b val (using 59\100) to generate a hard diatonic (18:5 step size ratio. This will fail to cover the whole gamut due to the size of the edo.
+However, you can use the 100b val (using 59\100) to generate a hard diatonic (18:5 step size ratio) that is a good tuning for [[quasisupra]]. This will fail to cover the whole gamut due to the size of the edo.
+{{Lumatone EDO mapping|n=100|start=16|xstep=18|ystep=-13}}
-(Note: When I ([[User:MisterShafXen]]) tried adding the mapping starting with 7 and steps xsteps=18 ysteps=-13, it didn't work.)
+Since 50edo is already divisible by two, [[injera]] and its extensions also fail to cover all the notes in 100edo unless you divide the octave into four. The [[4L&nbsp;8s]] mapping covers most of the notes with the occasional skip, while the [[12L&nbsp;4s]] one does cover all the notes, but with very limited range and lopsided step size.
+=== 4L 8s ===
+{{Lumatone EDO mapping|n=100|start=80|xstep=8|ystep=1}}
+=== 12L 4s ===
+{{Lumatone EDO mapping|n=100|start=12|xstep=8|ystep=-7}}
+== Submerged-related rank-2 temperament ==
+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}}