RE: [tuning] Dan, Dave, experience, entropy

Even with standard deviation of one syntonic comma, 11:9 comes out as more
consonant than 11:8 and 9:7, but not longer more consonant than 8:5:

/harmonic_entropy/files/perlich/stearns3.jpg

Dan,

Still using a standard deviation of one syntonic comma, but seeding the
harmonic entropy calculation with about 8 times as many ratios, 11:9 still
comes out as more concordant than 11:8 and 9:7:

/harmonic_entropy/files/perlich/stearns4.jpg

So we have seen that for a couple of "average" standard deviations and
rather different "limits" for seeding the calculation, 11:9 always comes out
as more concordant for its product that _any other ratio_ with product 100
or less; more concordant, even, than ratios with product 40, 60, or 63,
depending on which particular calculation we're looking at.

I'm not claiming harmonic entropy is perfect, and I've always claimed that
it's only one component of what we call "discordance", but it sure looks
like your observations about 11:9 conform quite nicely with what the
assumptions behind harmonic entropy would imply when worked out.

-Paul