Hi there,

I am a new subscriber to the list so excuse me for my silly
preliminary questions.

1) I must be missing something, but I did not find any clear
indication of a how harmonic entropy is computed. What I see is a lot
of nice figures and diagrams but I am still looking for clues to how
they are obtained... I understand that it is directly related to
Shannon's entropy definition Xlog(X), where X is a probability density
function, but could not derive an algorithm by myself. If available,
could anyone give a pointer to a place where the computations are
explained more precisely? The best introductory site I could find
is on the <a href="http://tonalsoft.com/enc/harmentr.htm"> harmony
entropy page at Joe Monzo's Site</a> but this page is lacking the
maths I am looking for.

2) Actually I am interested in finding a way to measure the
consonance/dissonance of complex chords: not only for dyads, triads,
or tetrads, but for an arbitrary multi-component cluster. I understand
that in this case the decomposition into individual dyads does not
lead to a correct measure of harmonic entropy, as stated in the
page <a href="http://tonalsoft.com/td/erlich/entropy.htm"> on Harmonic
Entropy</a>. How did you obtain the HE for triads and tetrads ?

3) Last question, how closely is harmonic entropy related to Barlow's
harmonicity? Harmonicity seems less mathematically founded than
harmonic entropy, but it has a straightforward generalization to
complex chords by substituting LCM/GCD to the original p/q ratio.

Thanks.