Lumatone mapping for 65edo: Difference between revisions

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== Squirrel ==

It is possible to map [[65edo]] with [[squirrel]] temperament, using as a generator the near-just undecimal submajor second ~[[11/10]], reminiscent of [[tetracot]] but producing a a [[1L 6s]] scale (11:9 step ratio) instead of [[6L 1s]]. Three of these generators make the near-just perfect fourth ~[[4/3]]; six of them make the near-just Pythagorean.minor seventh ~[[16/9]]; nine of them (with octave reduction) make the slightly flat otonal (undevesimal) minor third ~[[19/16]]; and twenty-one of them (with more octave reduction) make the near-just classic major seventh ~[[15/8]]. Unfortunately, this mapping does not cover all of the notes in the range of over 4½ octaves; even so, [[Bryan Deister]] has used this mapping in [[https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026).

It is possible to map [[65edo]] with [[squirrel]] temperament, using as a generator the near-just undecimal submajor second ~[[11/10]], reminiscent of [[tetracot]] but producing a a [[1L 6s]] scale (11:9 step ratio) instead of [[6L 1s]]. Three of these generators make the near-just perfect fourth ~[[4/3]]; six of them make the near-just Pythagorean.minor seventh ~[[16/9]]; nine of them (with octave reduction) make the slightly flat otonal (undevesimal) minor third ~[[19/16]]; and twenty-one of them (with more octave reduction) make the near-just classic major seventh ~[[15/8]]. Unfortunately, this mapping does not cover all of the notes in the range of over 4½ octaves; even so, [Bryan Deister]] has used this mapping in [[https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026).

This can be expanded to a [[7L 1s]] scale that does cover the full gamut in the middle octaves, but has a range of slightly less than 4 octaves and a stronger upward slant.

This can be expanded to a [[7L 1s]] scale (9:2 step ratio) that does cover the full gamut in the middle octaves, but has a range of slightly less than 4 octaves and a stronger upward slant.

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 == Squirrel ==
-It is possible to map [[65edo]] with [[squirrel]] temperament, using as a generator the near-just undecimal submajor second ~[[11/10]], reminiscent of [[tetracot]] but producing a a [[1L&nbsp;6s]] scale (11:9 step ratio) instead of [[6L&nbsp;1s]]. Three of these generators make the near-just perfect fourth ~[[4/3]]; six of them make the near-just Pythagorean.minor seventh ~[[16/9]]; nine of them (with octave reduction) make the slightly flat otonal (undevesimal) minor third ~[[19/16]]; and twenty-one of them (with more octave reduction) make the near-just classic major seventh ~[[15/8]]. Unfortunately, this mapping does not cover all of the notes in the range of over 4½ octaves; even so, [[Bryan Deister]] has used this mapping in [[https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026).
+It is possible to map [[65edo]] with [[squirrel]] temperament, using as a generator the near-just undecimal submajor second ~[[11/10]], reminiscent of [[tetracot]] but producing a a [[1L&nbsp;6s]] scale (11:9 step ratio) instead of [[6L&nbsp;1s]]. Three of these generators make the near-just perfect fourth ~[[4/3]]; six of them make the near-just Pythagorean.minor seventh ~[[16/9]]; nine of them (with octave reduction) make the slightly flat otonal (undevesimal) minor third ~[[19/16]]; and twenty-one of them (with more octave reduction) make the near-just classic major seventh ~[[15/8]]. Unfortunately, this mapping does not cover all of the notes in the range of over 4½ octaves; even so, [Bryan Deister]] has used this mapping in [[https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026).
 {{Lumatone EDO mapping|n=65|start=26|xstep=9|ystep=2}}
-This can be expanded to a [[7L 1s]] scale that does cover the full gamut in the middle octaves, but has a range of slightly less than 4 octaves and a stronger upward slant.
+This can be expanded to a [[7L 1s]] scale (9:2 step ratio) that does cover the full gamut in the middle octaves, but has a range of slightly less than 4 octaves and a stronger upward slant.
 {{Lumatone EDO mapping|n=65|start=13|xstep=9|ystep=-7}}