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Lumatone mapping for 11edo

Revision as of 03:20, 8 May 2026 by Lucius Chiaraviglio (talk | contribs) (Add Bryan Deister's Hyperkleismic Lumatone mapping for 11edo)
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There are many conceivable ways to map 11edo 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.

The following mapping for 11edo can be used for every MOS scale in 11edo with L = 2\11 and s = 1\11, such as 4L 3s and 5L 1s.

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Hyperkleismic Lumatone mappings

Bryan Deister has used a 3L 1s (3:2 step ratio) mapping for an unequal derivative of 11edo that stacks sharp (by varying degrees) classic minor thirds to generate the scale (as in hyperkleismic temperament), in [short clip] 11 Tone March (2023). In principle, this would also work for vanilla 11edo. (Due to the very large errors that 11edo has for most of its primes, getting the classic major thirds to map correctly as ~6/5 requires use of the 2.9.15 subgroup or an extended version thereof, to constitute the minor thirds initially as 18/15.) The range is eight octaves, which slope very slightly upwards and have a generous number of repeated notes, thereby leaving open the possibility of splitting this layout into multiple manuals with only mild lopsidedness.

 
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