A.Pander’s Musical Journal

EarSlap (aka Batuhan Bozkurt) released a GA lib for SuperCollider recently. I hadn’t thought about AiI techniques in a long time but associating it in the sound domain opens up many possibilities I hadn’t thought of before.

The tricky bit is the fitness function for the GA, which Bozkurt hints at using a simple of Mean Squared Error (MSE):

The fitness function is tricky, it uses an UGen I’ve coded in C for the purpose. It compares the MSE distance between complex spectrums of the source and synthesized sound and the MSE distance becomes the similarity rating therefore the output of the fitness function (lower is better). I’ll let you know when the paper describing the internals is published.
Here is a paper by Ricardo A. Garcia where he grows sound synthesis graphs (instead of parameters to fix synthesizer graphs), I use the same similarity rating formula, but discard the phase:

http://galileo.cincom.unical.it/Music/workshop/articoli/garcia.pdf

This reminded me of a question about Mel Frequency Cepstral Coefficients the other day on the SC mailing list:

To look into exactly what MFCCs are, you might want to start with
regular cepstrum. Leaving out all the details, the idea behind
cepstrum is that it’s the spectrum of a spectrum – an FT of an FT -
and it (sort of) deconvolves two convolved sounds. A sung vowel is a
convolution of source and filter – glottal impulses filtered by the
singer’s head. If you look at a cepstrum of a sung vowel, you get a
condensed representation of the general spectral envelope at the
beginning of the cepstrum, and a peak that corresponds to pitch a
little higher up (depending on frequency). In the best circumstances,
you can look at a second cepstrum of the same singer singing a
different note, and the early part of the cepstrum will look the same,
but the position of the pitch peak will be different. That’s because
the singer’s timbre is the same – only the pitch has changed. So
that’s why early cepstral coefficients are used as a feature to
describe timbre. The analyses I’ve done on voice have been the
cleanest and easiest for me to interpret. With other instruments the
“deconvolution” of spectral envelope and pitch isn’t as nice.

MFCCs are a lot different than regular cepstral coefficients. The
results of an initial FFT are multiplied against a filterbank composed
of filters that are evenly spaced on the Mel scale. The Mel scale is
an old (and now controversial) scale for pitch based on perceptual
experiments, but it does relate strongly to the Bark scale which has
been thoroughly established in relation to our hearing mechanism. If
you look at the plot of Mels against Hz on wikipedia, you can see that
Mels, like Barks, favor the low end of the spectrum. By running a
regular spectrum through a Mel-weighted filterbank, the spectral
detail of the low end is preserved much more than in the high end.
That’s because the width of the low filters is relatively small, and
the higher filters are very wide. So all that high end detail gets
averaged out. The number of filters in the bank depends on the
spacing between the filters. My Pd objects let you specify any
spacing. With 150-Mel spacing, you get 25 filters. With 100-Mel
spacing, you get 38. So regardless of your original FFT window size,
you get back far fewer points with typical Mel spacings.

To finish off the MFCC calculation: the Mel-weighted reduced
resolution version of the spectrum is subjected to a discrete cosine
transform instead of a second FT (as in cepstrum). The first MFCC
ends up being a crude indication of overall loudness, and the
remaining coefficients can be used to describe timbre pretty
accurately. Unless you’ve got specific CPU limitations, in my
experience it has been best to use all the MFCCs. They sort of
naturally weight themselves in a way anyway – as the earlier
coefficients are usually much larger than the later ones. As for
accuracy, I found a very significant improvement classifying
percussion sounds when I systematically compared cepstrum to MFCCs. I
also use BFCCs – cepstral coefficients weighted according to the Bark
scale.

MFCCs might be a good in a fitness function perhaps taking the MSE of the MFC Coefficients?