Harmonic Entropy and Discordance

What function of harmonic entropy models diadic discordance? Leave it the
way it is? Take the exponential? I found that with the Farey series,
exp(entropy/2) = sqrt(exp(entropy)) keeps the shape of the curve the same no
matter what N is, except for the overall slope increasing with N. See:

http://www.egroups.com/files/tuning/perlich/manuel2.jpg

The independence from N is a desirable quality. What causes it? I bet it has
something to do with the widths being inversely proportional to 1/sqrt(n*d),
and the entropy for simple ratios being proportional to log(n*d) ? ? ?