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Convex hull yet again

🔗Gene Ward Smith <gwsmith@svpal.org>

2/4/2004 3:08:11 AM

For some reason it didn't come out right; this seems to be correct. It
gives us a compact poygonal region, we can use the top border as a
badness cutoff and the bottom one (in case anyone thinks goodness
should be punished) as a goodness cutoff. The goodness line runs from
Beep to Ennealimmal, and an alternative approach is simply to take a
line with the same slope and use it as a badness cutoff. No specific
error and complexity cutoffs would be used. I think I'll see if that
works. This would probably end up making Beep and Ennealimmal come out
at the top of the list, if people can stand that idea, but we shall
see. The bad line runs up from Ennealimmal (in error) to Parakleismic,
tnen to Valentine, Pelogic, the {21/20, 28/27} temperament and then
around to Beep. This suggests drawing a line between what you think
are the best two temperaments in the log(error) log(complexity) plane
and using a line with that slope as a badness cutoff might work.

Beep
[2, 3, 1, 0, -4, -6] [1.55382450640435, 2.65155778136775]

Ennealimmal
[18, 27, 18, 1, -22, -34] [3.68458824092559, -3.31382430859740]

Parakleismic
[13, 14, 35, -8, 19, 42] [3.67847399261317, -1.33966326804887]

Valentine
[9, 5, -3, -13, -30, -21] [3.10891281481728, .485909326707073e-1]

Pelogic
[1, -3, -4, -7, -9, -1] [2.00498200415831, 2.27563066979103]

{21/20, 28/27}
[1, 4, 3, 4, 2, -4] [1.71780572949088, 2.65701243004446]