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Encyclopedia of Microtonal Music Theory

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poptimal

[Joe Monzo]

p-optimal, specifies error criteria for calculating musical temperament tunings, as described in more detail below.

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[Gene Ward Smith, Yahoo tuning, message 42429 (Tue Feb 18, 2003 9:23 pm)]

p-optimal. For some p, 2 <= p <= infinity, we have that the generator is optimal for unweighted pth powers of the absolute values of the errors.

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[Paul Erlich, Yahoo tuning, message 42459, (Fri Feb 21, 2003 1:51 pm)]
poptimal meantone generators

After generating the graph, i decided to attempt to localize the minimum, and it appears that it occurs at p=2.8149, where the optimal generator is ~696.1146 cents. Any generator between that and the 1/4-comma meantone generator ~696.5784 cents is therefore poptimal for meantone ... that is, if you weight all the 5-limit consonance equally . . .

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