Lumatone mapping for 48edo: Difference between revisions

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== ~~Negri-related~~ 8th-octave temperament ==

== 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 ~~wraprounds~~.

[[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 23: / Line 23: @@
 {{Lumatone EDO mapping|n=48|start=7|xstep=9|ystep=-8}}
-== Negri-related 8th-octave temperament ==
+== 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 wraprounds.
+[[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)