Lumatone mapping for 48edo: Difference between revisions

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{{Lumatone mapping intro}} 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.

== 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).

== 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.

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

=== Negri ===

=== Squares ===

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

=== Buzzard ===

~~And~~ the [[~~Buzzard~~]] mapping.

== 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.

@@ Line 1: / Line 1: @@
-{{Lumatone mapping intro}} 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.
+{{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}}
+== 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.
-There are three other mappings that reach the perfect fith in 4 generator steps that might also be useful. These are the [[Negri]] mapping
+=== Negri ===
 {{Lumatone EDO mapping|n=48|start=4|xstep=5|ystep=3}}
+=== Squares ===
-The [[Squares]] mapping
 {{Lumatone EDO mapping|n=48|start=29|xstep=3|ystep=8}}
+=== Buzzard ===
+{{Lumatone EDO mapping|n=48|start=7|xstep=9|ystep=-8}}
-And the [[Buzzard]] mapping.
+== 8th-octave temperament with rotated Negri ==
-{{Lumatone EDO mapping|n=48|start=7|xstep=9|ystep=-8}}
+[[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)