Lumatone mapping for 20edo: Difference between revisions

Combining blackwood with [[skwares]] is another possibility. In the version of skwares used for this, instead of substantially sharpening the undecimal major third ~[[14/11]] (or even a septimal major third ~[[9/7]]) to get a diatonic fourth ~[[4/3]] (by stacking and octave-reducing four generators), the undecimal major third (7\20 as one move right and one move down-right) is near-just, and the fourth is very flat at 480{{c}} (corresponding to the blackwood sharp fifth at 720{{c}}).

Tetracot tempers together the Ptolmaic 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 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.