Lumatone mapping for 99edo: Difference between revisions

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== Würschmidt~~/Hemiwürschmidt/Würschmidt/Hemiwur~~ ==

== Würschmidt and extensions thereof ==

The Würschmidt generator, which is the classic major third ~[[5/4]] (near-just), is 32\99 in [[99edo]], so it is divisible by 2 or 4 but not by 3 (seen with [[65edo]]. Division by 2 to get 16\99 yields [[Hemimean_clan#Hemiwürschmidt|Hemiwürschmidt/Würschmidt/Hemiwur]] with a slightly flat septimal) middle whole tone ~[[28/25]] for the divided generator, with a scale [[6L 1s]] (16:3 step ratio). This mapping only splits the [[Würschmidt]] in half to get greater range (over four octaves) than when splitting it in quarters, but at the cost of missing many notes in each octave. Despite the missing notes, [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/p9OUaFuTUek ''99edo waltz''] (2025).

The Würschmidt generator, which is the classic major third ~[[5/4]] (near-just), is 32\99 in [[99edo]], so it is divisible by 2 or 4 but not by 3 (seen with [[65edo]].

=== Hemiwürschmidt/Würschmidt/Hemiwur ===

Division by 2 to get 16\99 yields [[Hemimean_clan#Hemiwürschmidt|Hemiwürschmidt/Würschmidt/Hemiwur]] with a slightly flat septimal) middle whole tone ~[[28/25]] for the divided generator, with a scale [[6L 1s]] (16:3 step ratio). This mapping only splits the [[Würschmidt]] in half to get greater range (over four octaves) than when splitting it in quarters, but at the cost of missing many notes in each octave. Despite the missing notes, [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/p9OUaFuTUek ''99edo waltz''] (2025).

=== Würschmidt unnamed extension with generator divided by 4 ===

Division of the generator by 2 again (for 4 overall) yields a further extension that uses this mapping's rightward generator 8\99 as a slightly sharp ptolemaic chromatic semitone (major limma) ~[[135/128]], with a scale [[12L 3s]] (8:1 step ratio), implying that the octave is also divided into three equal parts. As befits Würschmidt, eight classic major thirds (32\65) make a near-just 6th harmonic ~[[6/1]]. The range is just over two octaves, and the octaves slant up mildly, now with no missing notes and some repeated notes to ease vertical wraparound. Compared to the [[Amity]] ([[Amity family#Amicable|Amicable]]) mapping with split period, this mapping is more lopsided with the hard scale step ratio, but on the other hand gets some consonant ratios with only a few generator steps. [[Bryan Deister]] has experimented with this mapping, but no demonstration video is available yet (as of 2025-07-24).

== Amity (Amicable) (currently untested, and shown for comparison) ==

@@ Line 12: / Line 12: @@
 {{Lumatone EDO mapping|n=99|start=12|xstep=8|ystep=-7}}
-== Würschmidt/Hemiwürschmidt/Würschmidt/Hemiwur ==
+== Würschmidt and extensions thereof ==
-The Würschmidt generator, which is the classic major third ~[[5/4]] (near-just), is 32\99 in [[99edo]], so it is divisible by 2 or 4 but not by 3 (seen with [[65edo]]. Division by 2 to get 16\99 yields [[Hemimean_clan#Hemiwürschmidt|Hemiwürschmidt/Würschmidt/Hemiwur]] with a slightly flat septimal) middle whole tone ~[[28/25]] for the divided generator, with a scale [[6L&nbsp;1s]] (16:3 step ratio). This mapping only splits the [[Würschmidt]] in half to get greater range (over four octaves) than when splitting it in quarters, but at the cost of missing many notes in each octave. Despite the missing notes, [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/p9OUaFuTUek ''99edo waltz''] (2025).
+The Würschmidt generator, which is the classic major third ~[[5/4]] (near-just), is 32\99 in [[99edo]], so it is divisible by 2 or 4 but not by 3 (seen with [[65edo]].
+=== Hemiwürschmidt/Würschmidt/Hemiwur ===
+Division by 2 to get 16\99 yields [[Hemimean_clan#Hemiwürschmidt|Hemiwürschmidt/Würschmidt/Hemiwur]] with a slightly flat septimal) middle whole tone ~[[28/25]] for the divided generator, with a scale [[6L&nbsp;1s]] (16:3 step ratio). This mapping only splits the [[Würschmidt]] in half to get greater range (over four octaves) than when splitting it in quarters, but at the cost of missing many notes in each octave. Despite the missing notes, [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/p9OUaFuTUek ''99edo waltz''] (2025).
 {{Lumatone EDO mapping|n=99|start=40|xstep=16|ystep=-13}}
+=== Würschmidt unnamed extension with generator divided by 4 ===
 Division of the generator by 2 again (for 4 overall) yields a further extension that uses this mapping's rightward generator 8\99 as a slightly sharp ptolemaic chromatic semitone (major limma) ~[[135/128]], with a scale [[12L&nbsp;3s]] (8:1 step ratio), implying that the octave is also divided into three equal parts. As befits Würschmidt, eight classic major thirds (32\65) make a near-just 6th harmonic ~[[6/1]]. The range is just over two octaves, and the octaves slant up mildly, now with no missing notes and some repeated notes to ease vertical wraparound. Compared to the [[Amity]] ([[Amity family#Amicable|Amicable]]) mapping with split period, this mapping is more lopsided with the hard scale step ratio, but on the other hand gets some consonant ratios with only a few generator steps. [[Bryan Deister]] has experimented with this mapping, but no demonstration video is available yet (as of 2025-07-24).
+{{Lumatone EDO mapping|n=99|start=12|xstep=8|ystep=-7}}
 == Amity (Amicable) (currently untested, and shown for comparison) ==