RE: [tuning] Calculating Harmonic Entropy

John de Laubenfels wrote,

>I've just gotten a C++ program up and running; it calculates the
>following values:

> For 551.32, entropy is 4.234279
> For 617.49, entropy is 4.179904
> For 782.49, entropy is 4.080664
> For 231.17, entropy is 4.383823
> For 1071.70, entropy is 3.940651
> For 435.08, entropy is 4.270048
> For 933.13, entropy is 4.015730
> For 266.87, entropy is 4.341114
> For 1049.36, entropy is 3.922407
> For 813.69, entropy is 4.028784
> For 1017.60, entropy is 3.912540
> For 315.64, entropy is 4.257082
> For 582.51, entropy is 4.119130
> For 968.83, entropy is 3.875105
> For 386.31, entropy is 4.141619
> For 884.36, entropy is 3.742208
> For 498.04, entropy is 3.905651
> For 701.96, entropy is 3.405798
> For 1200.00, entropy is 1.840298
> For 0.00, entropy is 2.023188

These are pretty close to my values, except for the most consonant ratios,
which are farther off (I get 2.2122 for 0.00 cents).

>. Sum all the "raw probabilities"; they should add up to 1, but of
> course they won't!

They should sum to sqrt(2*pi*s).

I think I figured out why my results differ from John deLaubenfels' -- I'm
actually integrating over the bell curve from mediant to mediant (by
subtracting the two corresponding values of the Error Function), while John
is approximating the integral with the area of a rectangle.