Lumatone mapping for 42edo: Difference between revisions

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m →Lemba: Experimented with moving note 0 — rejected because of potential vertical wraparound problems, but found that range is almost six octaves
m →Whitewood + Qeema/Tritikleismic: Add another sscale and step ratios
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== Whitewood + Qeema/Tritikleismic ==
== 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 scale [[2L&nbsp;6s]]. [[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 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).
{{Lumatone EDO mapping|n=42|start=34|xstep=6|ystep=-1}}
{{Lumatone EDO mapping|n=42|start=34|xstep=6|ystep=-1}}


Revision as of 08:11, 25 February 2026

There are many conceivable ways to map 42edo onto the onto the Lumatone keyboard. However, as both of its fifths are about as far away from just as possible, neither the sharp or the flat versions of the Standard Lumatone mapping for Pythagorean work particularly well.

Diatonic

The flat fifth is the same as that of 7edo, which if used would result in six mutually-exclusive rings of fifths, so to cycle through all notes using the circle of fifths you need to use the sharp fifth instead, which gives ultrapyth.

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Pseudo-Isomorphic Pseudo-Diatonic

A pseudo-isomorphic pseudo-diatonic mapping for 42edo that duplicates note 0 (as note 18) enables diatonic playing while keeping octaves level — it is the 43edo diatonic layout, but with only 42 unique notes per octave. Bryan Deister has demonstrated this mapping in 42edo groove (2025).

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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 A Hunger Awakes - 42edo [short] (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).

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Lemba

The Lemba mapping is also of particular interest despite using a non-patent val. It achieves a range of almost six octaves, with only a slight downwards slope.

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