Lumatone mapping for 33edo: Difference between revisions

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== Diatonic ==

== 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.

== Semiquartal ==

The [[4L 1s]] Semiquartal mapping gives you an even wider range, is a fraction of a cent off the 9-odd limit minmax tuning for [[beep]] temperament using the ccd val and is also a significant non patent tuning for [[godzilla]].

== Sephiroth ==

To maximise your range while covering all the notes and keeping octaves near horizontal, use the [[3L 1s]] layout.

~~To maximise your range while keeping octaves~~ near ~~horizontal~~, ~~use~~ the [[~~semiquartal~~]] ~~layout~~.

== 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.

=== Forward chroma ===

Demonstrated in [https://www.youtube.com/shorts/mkaaAJEyGFU ''33edo riff''] (2025).

=== Reverse chroma ===

Demonstrated in [https://www.youtube.com/watch?v=GypR6x_Ih1I ''33edo jam''] (2025).

@@ Line 1: / Line 1: @@
 {{Lumatone mapping intro}}
+== Diatonic ==
 {{Lumatone EDO mapping|n=33|start=27|xstep=5|ystep=-1}}
+== 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.
 {{Lumatone EDO mapping|n=33|start=0|xstep=6|ystep=-1}}
+== Semiquartal ==
+The [[4L&nbsp;1s]] Semiquartal mapping gives you an even wider range, is a fraction of a cent off the 9-odd limit minmax tuning for [[beep]] temperament using the ccd val and is also a significant non patent tuning for [[godzilla]].
+{{Lumatone EDO mapping|n=33|start=24|xstep=7|ystep=-2}}
+== Sephiroth ==
+To maximise your range while covering all the notes and keeping octaves near horizontal, use the [[3L&nbsp;1s]] layout.
+{{Lumatone EDO mapping|n=33|start=5|xstep=10|ystep=-7}}
-To maximise your range while keeping octaves near horizontal, use the [[semiquartal]] layout.
+== Augmented (Triforce) + Bohpier Lumatone mappings ==
-{{Lumatone EDO mapping|n=33|start=24|xstep=7|ystep=-2}}
+[[Bryan Deister]] has demonstrated two mappings for [[33edo]] that function for the temperaments [[Augmented]] ([[Augmented family#Triforce|Triforce]], 33d val, [[3L&nbsp;3s]] scale with 7:4 step ratio) and [[Bohpier]] (33cd val, [[8L&nbsp;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.
+=== Forward chroma ===
+Demonstrated in [https://www.youtube.com/shorts/mkaaAJEyGFU ''33edo riff''] (2025).
+{{Lumatone EDO mapping|n=33|start=0|xstep=7|ystep=-3}}
+=== Reverse chroma ===
+Demonstrated in [https://www.youtube.com/watch?v=GypR6x_Ih1I ''33edo jam''] (2025).
+{{Lumatone EDO mapping|n=33|start=15|xstep=4|ystep=3}}
 {{Navbox Lumatone}}