Harmonic Entropy represented as a convolution integral: an O(nlogn) time algorithm to compute HE

Harmonic entropy is probably the best psychoacoustic model that we
have today. However, it is extremely slow to compute, and no feasible
way to compute HE for anything beyond triads currently exists at the
moment. However, it can be proven that HE can be transformed into a
convolution integral, and hence can be computed in O(nlogn) time.

I have worked out a mathematical derivation of the convolution
integral from HE, showing that they're equivalent:

http://www.mikebattagliamusic.com/music/HEConvolutionTheorem.html

However, the algorithm is still a work in progress, and the current
hurdle to cross is that to express the integral in a discrete-time
implementation leads to some irritating artifacts in the end signal
unless the resolution is really fine (around 0.01 cents). This for the
moment counterbalances the good done by the convolution speedup, so I
have to work it out before I can roll out a fancy HE javascript applet
or anything like that.

This general result has a lot of other implications as well, however,
besides just making it feasible to compute HE a lot faster - see the
notes at the bottom on Euclid's orchard for some ideas on how to work
some of this in with Tenney interval space.

-Mike