Duowell
Duowell is a well-tuning of the Ellis Duodene, where a well-tuning is a regular tuning of a JI scale with an eye
to making it circulate. The Ellis Duodene is a Fokker block and Euler genus whose notes are 16/15, 9/8, 6/5, 5/4,
4/3, 45/32, 3/2, 8/5, 5/3, 9/5, 15/8, 2. I tempered this via the well-tuning which has as its fifth (7168/11)^(1/16)
and as its major third (11/7)^(1/2). This leads to a scale with four major thirds which are exact 14/11 thirds,
and eight which are (11/7)^(1/2) thirds, which means they are 4.93 cents sharp. The fifths consist of eight nearly
pure (7168/11)^(1/16) fifths, 0.86 cents flat and extremely close to the fifth of 457-equal, two fifths flat by
14 cents and extremely close to 262/457, and a sharp fifth extremely close to 272/457. The difference between the
tuning <457 724 1063| and the well-tuning with exact 14/11 thirds is well beyond the range of audibility, with
a fifth 0.000156 cents flatter and a major third 0.00125 cents sharper; hence this scale can be considered a scale
of 457-equal.
! duowell.scl
Ellis duodene well-tuned to fifth=(7168/11)^(1/16) third=(11/7)^(1/2)
12
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