Lumatone mapping for 33edo: Difference between revisions

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Add Bryan Deister's Augmented (Triforce) + Bohpier mapping
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To maximise your range while keeping octaves near horizontal, use the [[4L 1s]] layout.
To maximise your range while keeping octaves near horizontal, use the [[4L 1s]] layout.
{{Lumatone EDO mapping|n=33|start=24|xstep=7|ystep=-2}}
{{Lumatone EDO mapping|n=33|start=24|xstep=7|ystep=-2}}
== Augmented (Triforce) + Bohpier ==
[[Bryan Deister]] has demonstrated a mapping for [[33edo]] that functions for the temperaments [[Augmented]] ([[Augmented family#Triforce|Triforce]], 33d val, [[3L 3s]] scale with 7:4 step ratio) and [[Bohpier]] (33cd val, [[8L 1s]] scale with 4:1 step ratio), in [https://www.youtube.com/watch?v=GypR6x_Ih1I ''33edo jam''] (2025). The rightward generator is a somewhat flat Alpharabian tendoneutral second ~[[12/11]] which can be stacked to get several consonant intervals; however, some of them map inconsistently. Two of these generators make a near-just neogothic minor third ~[[13/11]], mapped consistently. Three of these generators make a near-just septimal major third ~[[9/7]] by sound, but the mapping only works if 9/7 is constituted as (3♭ × 3♯) ÷ 7 or as 9 ÷ 7♭ (33d val). Four of these generators make a near-just lesser septimal tritone ~[[7/5]], mapped consistently ([[patent val]] or 33cd val). Six of these generators make a flat classic major sixth ~[[5/3]] by sound, but the mapping only works if 5/3 is constituted as 5♭ ÷ 3 (33c val). Seven of these generators make a near-just classic minor seventh ~[[9/5]] by sound, but the mapping only works if 9/5 is constituted as (3♭ × 3♯) ÷ 5 or as 9 ÷ 5♭ (33c val). The range is a bit over five octaves, which slope moderately downwards, resulting in a vertical wraparound.
{{Lumatone EDO mapping|n=33|start=15|xstep=4|ystep=3}}


{{Navbox Lumatone}}
{{Navbox Lumatone}}

Revision as of 07:41, 4 August 2025

There are many conceivable ways to map 33edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.

Diatonic

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Terrain

While 33edo is poor at approximating harmonics in general, it does manage several composite ratios within fractions of a cent. The terrain mapping is a particularly efficient way to make those easy to play together.

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Semiquartal

To maximise your range while keeping octaves near horizontal, use the 4L 1s layout.

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Augmented (Triforce) + Bohpier

Bryan Deister has demonstrated a mapping for 33edo that functions for the temperaments Augmented (Triforce, 33d val, 3L 3s scale with 7:4 step ratio) and Bohpier (33cd val, 8L 1s scale with 4:1 step ratio), in 33edo jam (2025). The rightward generator is a somewhat flat Alpharabian tendoneutral second ~12/11 which can be stacked to get several consonant intervals; however, some of them map inconsistently. Two of these generators make a near-just neogothic minor third ~13/11, mapped consistently. Three of these generators make a near-just septimal major third ~9/7 by sound, but the mapping only works if 9/7 is constituted as (3♭ × 3♯) ÷ 7 or as 9 ÷ 7♭ (33d val). Four of these generators make a near-just lesser septimal tritone ~7/5, mapped consistently (patent val or 33cd val). Six of these generators make a flat classic major sixth ~5/3 by sound, but the mapping only works if 5/3 is constituted as 5♭ ÷ 3 (33c val). Seven of these generators make a near-just classic minor seventh ~9/5 by sound, but the mapping only works if 9/5 is constituted as (3♭ × 3♯) ÷ 5 or as 9 ÷ 5♭ (33c val). The range is a bit over five octaves, which slope moderately downwards, resulting in a vertical wraparound.

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