Lumatone mapping for 42edo: Difference between revisions

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== Whitewood + Qeema/Tritikleismic ==

Since [[42edo]] is a multiple of [[7edo]], and not far beyond the last diatonic-incapable tuning [[35edo]], [[whitewood]] is still a legitimate mapping for it; since the 5th harmonic is also close to maximally far from just, this suggests [[qeema]]/[[tritikleismic]] temperament, using the 42bc [[val]] (42bcd if using the 7-limit), for which the generator is a near-just classic minor third ~[[6/5]] (with the very large errors in the 3rd and 5th harmonics canceling each other almost perfectly)~~; this generator~~ corresponds to one key right ~~(which itself~~ is the very flatly approximated ~~major second~~ ~[[9/8]]) ~~plus~~ one key down-right. ~~Use of this~~ generator plus some extra down-right key movements as needed gives rise to the scales [[2L 6s]] (6:5 step ratio) and [[2L 4s]] (11:5 step ratio). [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/B90JT_SxSSE ''<nowiki>A Hunger Awakes - 42edo [short]</nowiki>''] (2026), although with different placement of MIDI note 0. The range is about 4¾ octaves, which slant up with the rows (as normal for whitewood mappings).

Since [[42edo]] is a multiple of [[7edo]], and not far beyond the last diatonic-incapable tuning [[35edo]], [[whitewood]] is still a legitimate mapping for it; since the 5th harmonic is also close to maximally far from just, this suggests [[qeema]]/[[tritikleismic]] temperament, using the 42bc [[val]] (42bcd if using the 7-limit), for which the generator 11\42 is a near-just classic minor third ~[[6/5]] (with the very large errors in the 3rd and 5th harmonics canceling each other almost perfectly), and corresponds to one key right plus one key down-right, although the two mappings below differ in how the generator is constituted.

==== 2L 6s + 2L 4s version ====

On one version of the mapping, one key right 6\42 corresponds to the very flatly approximated ptolemaic whole tone ~[[10/9]]), and one key down-right 5\42 is a neutral second close to ~[[25/23]] by direct approximation (which, however, does not map to this interval by [[patent val]] [[mapping]]). Combining these to form the generator plus some extra down-right key movements as needed gives rise to the scales [[2L 6s]] (6:5 step ratio) and [[2L 4s]] (11:5 step ratio). [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/B90JT_SxSSE ''<nowiki>A Hunger Awakes - 42edo [short]</nowiki>''] (2026), although with different placement of MIDI note 0. The range is about 4¾ octaves, which slant up with the rows (as normal for whitewood mappings).

==== 2L 7s + 2L 5s version ====

In an alternate version of the above mapping, one key right 7\42 corresponds to the werckismic tone ~[[55/49]] (since the similar ~[[9/8]] maps inconsistently to another interval), and one key down-right 4\42 corresponds to a sharp large septendecimal semitone ~[[17/16]]. Combining these to form the generator generator plus some extra down-right key movements as needed gives rise to the scales [[2L 7s]] (7:4 step ratio) and [[2L 5s]] (11:4 step ratio). [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/D_YgzRJFg8I ''<nowiki>Waltz in 42edo [short]</nowiki>''] (2026). The range is a bit over five octaves, which slant up with the rows (as normal for whitewood mappings).

== Lemba ==

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 == Whitewood + Qeema/Tritikleismic ==
-Since [[42edo]] is a multiple of [[7edo]], and not far beyond the last diatonic-incapable tuning [[35edo]], [[whitewood]] is still a legitimate mapping for it; since the 5th harmonic is also close to maximally far from just, this suggests [[qeema]]/[[tritikleismic]] temperament, using the 42bc [[val]] (42bcd if using the 7-limit), for which the generator is a near-just classic minor third ~[[6/5]] (with the very large errors in the 3rd and 5th harmonics canceling each other almost perfectly); this generator corresponds to one key right (which itself is the very flatly approximated major second ~[[9/8]]) plus one key down-right. Use of this generator plus some extra down-right key movements as needed gives rise to the scales [[2L&nbsp;6s]] (6:5 step ratio) and [[2L&nbsp;4s]] (11:5 step ratio). [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/B90JT_SxSSE ''<nowiki>A Hunger Awakes - 42edo [short]</nowiki>''] (2026), although with different placement of MIDI note 0. The range is about 4¾ octaves, which slant up with the rows (as normal for whitewood mappings).
+Since [[42edo]] is a multiple of [[7edo]], and not far beyond the last diatonic-incapable tuning [[35edo]], [[whitewood]] is still a legitimate mapping for it; since the 5th harmonic is also close to maximally far from just, this suggests [[qeema]]/[[tritikleismic]] temperament, using the 42bc [[val]] (42bcd if using the 7-limit), for which the generator 11\42 is a near-just classic minor third ~[[6/5]] (with the very large errors in the 3rd and 5th harmonics canceling each other almost perfectly), and corresponds to one key right plus one key down-right, although the two mappings below differ in how the generator is constituted.
+==== 2L&nbsp;6s + 2L&nbsp;4s version ====
+On one version of the mapping, one key right 6\42 corresponds to the very flatly approximated ptolemaic whole tone ~[[10/9]]), and one key down-right 5\42 is a neutral second close to ~[[25/23]] by direct approximation (which, however, does not map to this interval by [[patent val]] [[mapping]]). Combining these to form the generator plus some extra down-right key movements as needed gives rise to the scales [[2L&nbsp;6s]] (6:5 step ratio) and [[2L&nbsp;4s]] (11:5 step ratio). [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/B90JT_SxSSE ''<nowiki>A Hunger Awakes - 42edo [short]</nowiki>''] (2026), although with different placement of MIDI note 0. The range is about 4¾ octaves, which slant up with the rows (as normal for whitewood mappings).
 {{Lumatone EDO mapping|n=42|start=34|xstep=6|ystep=-1}}
+==== 2L&nbsp;7s + 2L&nbsp;5s version ====
+In an alternate version of the above mapping, one key right 7\42 corresponds to the werckismic tone ~[[55/49]] (since the similar ~[[9/8]] maps inconsistently to another interval), and one key down-right 4\42 corresponds to a sharp large septendecimal semitone ~[[17/16]]. Combining these to form the generator generator plus some extra down-right key movements as needed gives rise to the scales [[2L&nbsp;7s]] (7:4 step ratio) and [[2L&nbsp;5s]] (11:4 step ratio). [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/D_YgzRJFg8I ''<nowiki>Waltz in 42edo [short]</nowiki>''] (2026). The range is a bit over five octaves, which slant up with the rows (as normal for whitewood mappings).
+{{Lumatone EDO mapping|n=42|start=0|xstep=7|ystep=-3}}
 == Lemba ==