--- In harmonic_entropy@yahoogroups.com, "Bohlen, Heinz"
<heinz.bohlen@c...> wrote:
> This is a message for Paul.
> Your answer to the "newbie question" made me look at your entropy
>graphs
> once more, and from that resulted two comments.
>
> 1. It would be helpful if the graphs didn't just end at 2:1, but
>would
> include 3:1. Not only because this would aid an assessment of the
>BP scale
> with regard to harmonic entropy, but also because it might
>generally shed
> some light on the perception of intervals that exceed the octave
>span.

Most of the graphs (including the one on the homepage of this group)
go to 4:1, some go even further.

> 2. The differentiation between intervals as presented in the graphs
>appears
> a bit low, and the entropy for intervals generally accepted as
>strikingly
> consonant a bit high, at least from my admittedly subjective view
>point.

Sure. You may prefer the version of harmonic entropy which includes
unreduced ratios, though then the weighting of the ratios is more
arbitrary since the concept of "width" is no longer applicable. It
seems that in the usual case, the simplest ratios get an entropy
proportional to log(n*d) above the entropy of 1:1, while if you
include unreduced ratios, it's proportional to n*d above the entropy
of 1:1.

> To
> explain what I mean: using Shannon's entropy expression, the
>probability
> resulting from the Mann series for the fifth (HE ~ 2.5) turns out
>to be ~ 18
> % only, and for the major sixth (HE ~ 3) ~ 12 % only,

How are you obtaining these probabilities? You have to assume an
actual heard interval in addition to a putative ratio . . . Maybe
you're misinterpreting Shannon's expression? It's a sum of (-p*log(p))
over probabilites which themselves sum to 1, but it cannot relate to
a single probability.