Lumatone mapping for 20edo: Difference between revisions

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== Tetracot (+ Diminished + Blackwood) ==

== Tetracot (+ Diminished + Blackwood + Skwares) ==

Tetracot tempers together the Ptolmeic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a fourth of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmeic 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; ~~and~~ it has embedded Blackwood rings by way of moving two keys at a time down-right, thus making these temperaments also accessible if one needs to switch temperaments frequently.

Tetracot tempers together the Ptolmeic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a fourth of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmeic 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, thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.

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 {{Lumatone EDO mapping|n=20|start=3|xstep=7|ystep=-1}}
-== Tetracot (+ Diminished + Blackwood) ==
+== Tetracot (+ Diminished + Blackwood + Skwares) ==
-Tetracot tempers together the Ptolmeic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a fourth of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmeic 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; and it has embedded Blackwood rings by way of moving two keys at a time down-right, thus making these temperaments also accessible if one needs to switch temperaments frequently.
+Tetracot tempers together the Ptolmeic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a fourth of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmeic 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, thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.
 {{Lumatone EDO mapping|n=20|start=17|xstep=3|ystep=-1}}
 {{Navbox Lumatone}}