Lumatone mapping for 100edo: Difference between revisions

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{{Lumatone EDO mapping|n=100|start=12|xstep=8|ystep=-7}}
{{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 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.
{{Lumatone EDO mapping|n=100|start=74|xstep=7|ystep=3}}
{{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 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.
{{Lumatone EDO mapping|n=100|start=12|xstep=6|ystep=-5}}


{{Navbox Lumatone}}
{{Navbox Lumatone}}

Latest revision as of 14:27, 23 September 2026

There are many conceivable ways to map 100edo onto the onto the Lumatone keyboard. However, it has 2 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them.

Diatonic

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.

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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

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12L 4s

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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.

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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 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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