verifying weighting rule

As I think Carl was warning at one point, if we are using a weighting rule
to mimic the "width" or "area" in a harmonic entropy calculation, we should
be sure that the probabilities thus calculated (before scaling to sum to 1)
should sum to something that is independent of where you are on the curve. I
looked at this sum for the 1/sqrt(n*d) rule I've been using for dyadic
harmonic entropy, with n*d<10000 and s=1%. At the unison, the sum is 104% of
its mean value; at 30 cents, it's 98% of its mean value; and thereafter it
fluctates between 99% and 101%. By contrast, if we use a -log(n*d) rule, the
fluctuations range from 61% to 114%; a 1/(n*d) rule leads to a range from
43% to 1150%(!) (and a believable discordance curve already -- _without_
calculating entropy -- perhaps we should think about this), and a
1/cuberoot(n*d) rule fluctuates between 65% and 107%.

As far as I am concerned, this verifies the 1/sqrt(n*d) weighting rule for
dyads. Now to verify, or find an alterative to, the 1/cuberoot(l*m*n) rule
for triads, armed with the set of triads with l*m*n<1million that Graham
sent me (thanks Graham!) This could take a lot of CPU cycles!