Lumatone mapping for 20edo: Difference between revisions

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== Tetracot (+ diminished + blackwood + skwares/squares) ==

[[Tetracot]] tempers together the Ptolmaic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a quarter of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmaic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The tetracot mapping does have an embedded [[4L 4s]] (3:2 step ratio) diminished scale available by alternating right and down-right motions; it has embedded blackwood rings by way of moving two keys at a time down-right; and it even has an embedded 2L 1s (7:6 step ratio) scale for skwares/squares), thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.

[[Tetracot]] tempers together the Ptolmaic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a quarter of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmaic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The tetracot mapping does have an embedded [[4L 4s]] (3:2 step ratio) diminished scale available by alternating right and down-right motions; it has embedded blackwood rings by way of moving two keys at a time down-right; and it even has an embedded 2L 1s (7:6 step ratio) scale for skwares/squares), thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/GxElRqwqz-o ''Nocturne in 20edo''] (2025).

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 == Tetracot (+ diminished + blackwood + skwares/squares) ==
-[[Tetracot]] tempers together the Ptolmaic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a quarter of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmaic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The tetracot mapping does have an embedded [[4L&nbsp;4s]] (3:2 step ratio) diminished scale available by alternating right and down-right motions; it has embedded blackwood rings by way of moving two keys at a time down-right; and it even has an embedded 2L&nbsp;1s (7:6 step ratio) scale for skwares/squares), thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.
+[[Tetracot]] tempers together the Ptolmaic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a quarter of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmaic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The tetracot mapping does have an embedded [[4L&nbsp;4s]] (3:2 step ratio) diminished scale available by alternating right and down-right motions; it has embedded blackwood rings by way of moving two keys at a time down-right; and it even has an embedded 2L&nbsp;1s (7:6 step ratio) scale for skwares/squares), thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/GxElRqwqz-o ''Nocturne in 20edo''] (2025).
 {{Lumatone EDO mapping|n=20|start=17|xstep=3|ystep=-1}}
 {{Navbox Lumatone}}