Lumatone mapping for 48edo: Difference between revisions
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m →Negri-related 8th-octave temperament: → 8th octave temperament with rotated Negri; fix punctuation and a typo |
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== Tetracot == | == Tetracot == | ||
If you want an evenly distributed heptatonic scale that gives easy access to the perfect 5th, you instead need to use the [[Tetracot]] mapping, which is probably the most efficient and intuitive way of organising its intervals. Though, the [[7L 6s]] MOS has a 6:1 step ratio, making it very lopsided. | If you want an evenly distributed heptatonic scale that gives easy access to the perfect 5th, you instead need to use the [[Tetracot]] mapping, which is probably the most efficient and intuitive way of organising its intervals. Though, the [[7L 6s]] MOS has a 6:1 step ratio, making it very lopsided. | ||
[[Bryan Deister]] demonstrates this layout (albeit with range restricted to 1 MIDI channel) in [https://www.youtube.com/shorts/w1m9PMj0Ato ''48edo layout''] (2025). | |||
{{Lumatone EDO mapping|n=48|start=33|xstep=7|ystep=-1}} | {{Lumatone EDO mapping|n=48|start=33|xstep=7|ystep=-1}} | ||
== Doublewide == | |||
If you don't mind skipping the occasional step, the [[doublewide]] mapping expands your range and is particularly efficient at spanning the 11-limit. | |||
{{Lumatone EDO mapping|n=48|start=5|xstep=11|ystep=-9}} | |||
== Other mappings == | == Other mappings == | ||
There are three other mappings that reach the perfect | There are three other mappings that reach the perfect fourth or fifth in 4 generator steps that might also be useful. These are the [[Negri]], [[Squares]], and [[Buzzard]] mappings. | ||
=== Negri === | === Negri === | ||
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=== Buzzard === | === Buzzard === | ||
{{Lumatone EDO mapping|n=48|start=7|xstep=9|ystep=-8}} | {{Lumatone EDO mapping|n=48|start=7|xstep=9|ystep=-8}} | ||
== 8th-octave temperament with rotated Negri == | |||
[[Bryan Deister]] has demonstrated an [[8th-octave_temperaments|8th-octave temperament]] mapping for [[48edo]], in [https://www.youtube.com/watch?v=UgngKVswJfI ''48edo improv''] (2026). This temperament equates the near-just Alpharabian tendoneutral second ~[[12/11]] (one key right, as 6\48) to 1/8 of an octave — the [[undecimal octatonic comma]] 214990848/214358881 is tempered out. Supported scales include [[6L 6s]] (5:1 step ratio) and rotated [[3L 3s]] (11:5 step ratio). Following the reverse chroma 5\48 downwards, which maps as a very sharp classic diatonic semitone ~[[16/15]], and bypassing the 8th-octave period, one gets the sharp approximation of the septimal major second ~[[8/7]] (requires using the 48d val) at two of these, the flat but consistent approximation of the classic major third ~[[5/4]] at three of these, and the near-just fourth ~[[4/3]] at four of these, thereby making this also a rotated [[negri]] mapping. Octaves slope up with the rows; the range is 4½ octaves, with a few repeated notes to mitigate vertical wraparounds. | |||
{{Lumatone EDO mapping|n=48|start=42|xstep=6|ystep=5}} | |||
{{Navbox Lumatone}} | {{Navbox Lumatone}} | ||