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Copop hanson

🔗Gene Ward Smith <gwsmith@svpal.org>

7/4/2004 1:28:07 PM

7, 9 and 11 limit hanson/catakleismic have a copop generator of
123/466. 5-limit hanson has a range a bit above, with poptimals of
246, 299, 352. The minimal 5-limit poptimal is 3^(1/6), and the
maximum poptimal for 7 and 9 is 56^(1/22); in between these two are
53, 125, 178... 197 is copoptimal for 7 and 9, 269 for 7 and 11, and
466 for 9 and 11. 3^(1/6) is both the maximum kleismic popimal and the
minimal hanson poptimal, so 53 is good for both.

123/466 gives a minor third generator 1.0969 cents sharp, fifth 1.5358
cents flat, major third 2.6227 cents flat, 7/4 0.5856 cents flat, and
11/8 2.82001 cents flat. You do slightly better than the 72-et version
of hanson with 466, and therefore hanson in the 7 or 11 limit beats
miracle slightly in tuning accuracy, but of course it is much more
complex.