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Rational wolves for some temperaments

🔗Gene Ward Smith <gwsmith@svpal.org>

5/1/2004 1:48:20 PM

Here are some rationalized wolves for three temperaments (meantone,
hanson/kleismic, magic) which have consonances as a generator. I give
the generator leading to a (13-odd-limit or less) rational wolf, the
wolf itself, and a basis obtained by adding to the existing (7-limit
in the case of meantone and magic, 5-limit for hanson) basis the
condition that the approriate number of generator steps gives us the
wolf. Note that one of the Meantone[17] tunings is a version of the
Meantone[19] tuning. The two magic wolves lead to two different
11-limit versions of magic, identical in 41-equal, which I give
wedgies and mappings for.

meantone[12]
generator (416/5)^(1/11)
wolf 20/13
TM basis 81/80 126/125 105/104

meantone[17]
generator (5632/9)^(1/16)
wolf 18/11
TM basis 81/80 126/125 99/98

meantone[17]
generator (8192/13)^(1/16)
wolf 13/8
TM basis 81/80 125/125 640/637

meantone[19]
generator (18432/13)^(1/18)
wolf 13/9
TM basis 81/80 126/125 640/637

hanson[15]
generator 13^(1/14)
wolf 16/13
TM basis 325/324 625/624

hanson[19]
generator (352/13)^(1/18)
wolf 13/11
TM basis 352/351 15625/15552

magic[16]
generator (352/13)^(1/15)
wolf 13/11
TM basis 225/224 245/243 275/273

magic[19]
generator (576/11)^(1/18)
wolf 11/9
TM basis 100/99 225/224 245/243
<<5 1 12 -8 -10 5 -30 25 -22 -64||
[<1 0 2 -1 6|, <0 5 1 12 -8|

magic[22]
generator (707/7)^(1/21)
wolf 14/11
TM basis 225/224 245/243 441/440
<<5 1 12 33 -10 5 35 25 73 51||
[<1 0 2 -1 -7|, <0 5 1 12 33|]