Lumatone mapping for 33edo: Difference between revisions

== Augmented (Triforce) + Bohpier Lumatone mappings ==

[[Bryan Deister]] has demonstrated two mappings for [[33edo]] that function 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). The down-right (forward chroma version) or rightward (reverse chroma version) 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 six octaves in the forward chroma version or five octaves in the reverse chroma version; in both cases, the octaves slope moderately downwards resulting in a vertical wraparound.