RE: [tuning] Insight

>The tree in front of you has
>"1/0", the one two your left

To your right?

>has "0/1" the one up and to the right of you
>has "1/1", the one to the right of that one has "1/2"

That's a very good analogy, Keenan. It's the same picture of the rational
numbers that Hardy and Wright use in one of their three proofs of the basic
identity for adjacent ratios in a Farey series, n(j)*d(i)-n(i)*d(j)=1.

>Get this, the distance a
>tree is from you exactly corresponds to its musical consonance.

Well, if you really mean dissonance, and you define dissonance of a ratio
n/d as sqrt(n^2+d^2), then OK, this is a measure somewhat similar to others
like Tenney's. I've looked at the series of ratios generated by choosing an
upper bound on this measure, and unfortunately these series don't display
some of the nice spacing properties of Farey and "Tenney" series.

>How well you
>can see through the trees is harmonic entropy.

Hmm . . . I suppose if the trees had finite width, then you might get
something like harmonic entropy, though far less continuous. However,
understanding what you would see in a three-dimensional forest would
certainly be a great first step toward a triadic harmonic entropy model.