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Lumatone mapping for 13edo

Revision as of 10:16, 4 March 2026 by Lucius Chiaraviglio (talk | contribs) (→Father + Aurora + Variant Orwell: Insert Bryan Deister's Sephiroth + Variant Orwell + Meansquared mapping after this)
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There are several possible ways to map 13edo onto the onto the Lumatone keyboard. However, none of them even remotely approximate the Standard Lumatone mapping for Pythagorean.

Archaeotonic (exo-Tetracot)

The following mapping for 13edo can be used for every MOS scale in 13edo with L = 2\13 and s = 1\13, such as 5L 3s and 6L 1s.

 
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Fibotonic (compressed)

Since 13edo is a small edo, you can compress this down to a 2L 1s scale that extends range past human hearing (or more practically, enables division into multiple zones for different instruments) and puts all kinds of intervals within easy reach in different directions while still having a moderate number of repeated notes.

 
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Father + Aurora + Variant Orwell

Bryan Deister has demonstrated a 3L 2s (3:2 step ratio) aurora/father mapping for 13edo, in Holding Back My Endless Sigh - 13edo (2026). The generator 8\13 (three keys right and one key down-right from the root note) can be taken as a very sharp fifth (~3/2, for father temperament) or a moderately sharp septimal superfifth (~32/21, for aurora temperament). Even more simply, this mapping also functions for a 4L 5s (2:1 step ratio) scale for a variant of Orwell temperament, with the one key right generator being 3\13, which functions as (among other things) a rather sharp septimal minor third ~7/6 (requires the 13d val) or a flat tridecimal minor third ~13/11, of which two make a slightly sharp undecimal major fourth ~11/8; three of them make a sharp classic minor sixth ~8/5; four of them make a very flat classic major seventh ~15/8; and after octave-reduction, seven of them make the super-sharp fifth ~3/2 (better constituted as a near-just vicesimotertial inframinor sixth ~23/15, or a slightly sharp septendecimal superfifth ~26/17, or a moderately sharp septimal superfifth ~32/21 as in aurora above); and eight of them make a very sharp septimal minor seventh ~7/4 (if using the 13d val) or a near-just classic minor seventh ~9/5 (requires constitution of the 9 as 3♯ × 3♭). The range is over seven octaves, with notes repeated multiple times, but unfortunately the downwards slope of the octaves, although mild, would make mapping to multiple manuals tricky.

 
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Sephiroth + Variant Orwell + Meansquared

It is possible to follow in the footsteps of magic/muggles temperament for 13edo, but using a much flatter classic major third ~5/4 (as 4\13) as the generator, as sephiroth, producing a 3L 1s scale (4:1 step ratio) going right and up, as used by Bryan Deister in a microtonal totentanz in 13edo (2023). This also supports scales 1L 3s (4:3 step ratio, going down-right, as in variant orwell, although it would be awkward to play the more familiar 4L 5s scale) and 5L 2s (4/1-equivalent) (4:3 step ratio, going overall straight right through the octave zig-zag, as in meansquared). Octaves alternate between near/mid/far and mid-near/mid-far, with double octaves being perfectly level (thus enabling dual manuals); the range is 10¼ octaves.

 
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