Lumatone mapping for 48edo: Difference between revisions

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~~There are many conceivable ways to map [[48edo]] onto the [[Lumatone]] keyboard. Unfortunately, as it has multiple rings of 5ths, the [[Standard~~ Lumatone mapping ~~for Pythagorean]] is not one of them. Since it is [[Highly_composite_equal_division|highly composite]], many other mappings will also fail to cover the entire gamut.~~ 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.

== 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.

[[Bryan Deister]] demonstrates this layout (albeit with range restricted to 1 MIDI channel) in [https://www.youtube.com/shorts/w1m9PMj0Ato ''48edo layout''] (2025).

There are three other mappings that reach the perfect ~~5th~~ in 4 generator steps that might also be useful. These are the [[Negri]] ~~mapping~~

== 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.

== Other mappings ==

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 ===

~~The [[~~Squares~~]] mapping~~

=== Squares ===

~~Or the [[~~Buzzard~~]] mapping.~~

=== Buzzard ===

[[~~Category~~:~~Lumatone mappings~~]] [[~~Category~~:~~48edo~~]]

== 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.

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-There are many conceivable ways to map [[48edo]] onto the [[Lumatone]] keyboard. Unfortunately, as it has multiple rings of 5ths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. Since it is [[Highly_composite_equal_division|highly composite]], many other mappings will also fail to cover the entire gamut. 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.
+{{Lumatone mapping intro}}
+== 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&nbsp;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}}
-There are three other mappings that reach the perfect 5th in 4 generator steps that might also be useful. These are the [[Negri]] mapping
+== 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 ==
+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 ===
 {{Lumatone EDO mapping|n=48|start=4|xstep=5|ystep=3}}
-The [[Squares]] mapping
+=== Squares ===
 {{Lumatone EDO mapping|n=48|start=29|xstep=3|ystep=8}}
-Or the [[Buzzard]] mapping.
+=== Buzzard ===
 {{Lumatone EDO mapping|n=48|start=7|xstep=9|ystep=-8}}
-[[Category:Lumatone mappings]] [[Category:48edo]]
+== 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 &mdash; the [[undecimal octatonic comma]] 214990848/214358881 is tempered out. Supported scales include [[6L&nbsp;6s]] (5:1 step ratio) and rotated [[3L&nbsp;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}}

Lumatone mapping for 48edo: Difference between revisions

Lucius Chiaraviglio (talk | contribs)