Re: Sethares's equation

Hi Paul, 

sorry for the late reply.

>> May I ask you what monotonic transform of the dissonance
>> function did you use in the case of Sethares's equation?

>I didn't even try Sethares's equation, because of the scaling
>problem, and the large number of parameters (such the
>amplitudes of all the tones' partials). However, it *should*
>work fine, especially if "octave-equivalencized" as below,
>even without any transform applied, since the MDS result
>will automatically satisfy the triangle inequality even if the
>original data doesn't.

I tried to use Sethares's equation with a prototype version of my
Microtuner software, but the results are not good at the moment.
I think the MDS algorithm I am using (SMACOF) does not work
fine when the triangle inequality is not satisfied, as far as the
n-dimensional non-euclidean distance matrix is concerned.

>> I still have to consider the
>> harmonic entropy method, though.

>Clearly, this approach gives terrific results at least for 12-equal,
>for diatonic scales, and for decatonic scales.

I would like to test the Plomp-Levelt approach for first, mainly
because of its psychoacoustical foundation.

Kind Regards,
Victor Cerullo

>I would like to test the Plomp-Levelt approach for first, mainly
>because of its psychoacoustical foundation.

The harmonic entropy approach has as strong or stronger a
pyschoacoustic foundation as the Plomp-Levelt approach. Please
visit the harmonic_entropy list for more info.

-Carl