Lumatone mapping for 20edo: Difference between revisions

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

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

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.

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/Squares), thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.

@@ Line 19: / Line 19: @@
 {{Lumatone EDO mapping|n=20|start=3|xstep=7|ystep=-1}}
-== Tetracot (+ Diminished + Blackwood + Skwares) ==
+== Tetracot (+ Diminished + Blackwood + Skwares/Squares) ==
-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.
+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/Squares), 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}}