Fwd: [tuning-math] Re: Fried Alaska

>From: "wallyesterpaulrus" <wallyesterpaulrus@...>
>Delivered-To: mailing list tuning-math@yahoogroups.com
>Date: Tue, 17 Jun 2003 05:57:17 -0000
>Subject: [tuning-math] Re: Fried Alaska
>
//
>>> The Van Eck width of ratio Ri is log(R(i-1))-log(R(i+1)), where
>>> Ri is, say, the ith ratio in a Farey series of order n.
>
>or a "tenney series", or whatever.
>
>> Great! Now someone should be able to write down a formula for
>> harmonic entropy in terms of the function VE(r).
>
>for a logarithmic interval q, the unnormalized probability of hearing
>it as ratio r, P(q,r), is
>
>UP(q,r)=e^-((log(r)-q)^2/2s) [for bell-curve entropy]
>
>or
>
>UP(q,r)=e^-(|(log(r)-q)|/s) [for Vos-curve entropy]
>
>where s parameterizes one's hearing resolution.
>
>the probability is simply the normalized probability divided by the
>sum of the unnormalized probabilities:
>
>P(q,r)=UP(q,r)/SUM(UP(q,r))
>
>where the sum takes r over all possible values within the farey,
>tenney, whatever series in question.
>
>then the harmonic entropy of interval q, HE(q), is
>
>SUM[P(q,r)*log(P(q,r))]
> r
>
>ok?