Lumatone mapping for 26edo

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Revision as of 05:16, 25 August 2026 by Lucius Chiaraviglio (talk | contribs) (Reorganize; fill out descriptions add Bryan Deister's Fifive mapping)
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There are many conceivable ways to map 26edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.

Diatonic

Being in the flattone part of meantone, and indeed at the flat end of flattone itself, 26edo requires some adjustment to convert common practice music to sound right, and what is technically a diatonic layout (although fairly extreme in its softness) may require different usage than in a more middle-of-the-road diatonic tuning. YoVariable demonstrates this mapping in Jingle Bells (26edo microtonal Lumatone cover + Mystery Song) (2025) and explains the harmonic characteristics of 26edo (with demonstrations of chord shapes on this layout) in A rough introduction to 26edo on the Lumatone. However, being at the flat end of flattone, 26edo does not have very accurate 5-limit approximations, so other options are probably preferable.

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Orgone + Superkleismic

If you want to maximize the playable range and put the best consonances close to each other, the orgone + superkleismic mapping is the clear winner. These temperaments meet at 26edo; they use a sharp classic minor third ~6/5 (as 7\26) as their generator, which can also be mapped with greater accuracy but much greater complexity as a slightly flat doublewide minor third ~35/29. Either way, the generator chain is accessed very simply by moving right one key at a time. Two keys right yields a slightly flat undecimal minor fifth ~16/11; three keys right yields a near-just septimal minor seventh ~7/4; nine keys right with two octave-reductions (which translates into two keys up and one key right) gives the sharp fourth ~4/3; and another key right from this gives the very sharp classic minor sixth ~8/5.

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Lemba

The lemba mapping works well in 26edo, as Bryan Deister has demonstrated in Waltz in 26edo (2025); he explains that right (which is a near-just septimal major second ~8/7) and up yields the sharp classic minor third ~6/5 and right three times yields the flat fifth ~3/2 (bypassing the semioctave-reduction). The range is just under six octaves, with a gentle downward slope.

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Hendec

For those who favor stacking major rather than minor thirds, 26edo offers a good option with hendec, which uses a slightly flat undecimal (pentacircle) major third ~14/11 as its generator, which at 9\26, is reached simply by moving one key right plus one key down-right. Two of these generators make the very sharp classic minor sixth ~8/5. Five of these generators after octave-reduction (which translates to one key right plus four keys down-right) yields the flat classic major sixth ~5/3. The octaves still slope downwards gently, with a range a bit less than that of lemba, but in exchange, the diatonic scale is also easily accessible in a way reminiscent of neutral thirds mappings.

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Fifive

With the fifth ~3/2 being divisible by 5 (going from 15\26 down to 3\26, which is a near-just lesser tridecimal neutral second ~13/12), 26edo supports fifive temperament, as shown in Bryan Deister's Caprice in 26edo [short clip] (2026). This uses 3\26 as the (rightward) generator, and splits the octave in half. Two of these make a sharp septimal minor third ~7/6 which also functions as a flat tridecimal minor third ~13/11, or a mildly flat diatismic minor third ~20/17; three of these make a very flat septimal major third ~9/7 or a slightly flat undecimal (pentacircle) major third ~14/11; four of these make a slightly sharp undecimal major fourth ~11/8; five of these make a very flat fifth ~3/2 if bypassing the semioctave-reduction, or a very flat al-Farabi quarter tone ~33/32 with the semioctave-reduction. The range is about 4¾ octaves, and the octaves slope upwards so gently that it is tempting to move the note 0 position and use the generous allotment of repeated notes to split this mapping into two manuals.

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