I'm not sure what you mean by more mathematical...
More mathematical than describing music in first-order logic. I admit that such a thing would be impractical, as you point out. But it could offer an interesting excercise--perhaps in futility, but interesting nonetheless.
It takes a signal input and outputs the song's genre and aesthetic quality on a scale of 1-10.
Actually, even though I think many æsthetical judgements can be formalized, not all can, and even, who gets to decide the æsthetical rules? They tend to be very contextual and ever-changing; well, unless the Academy or the Church emits strict rules, but we're not in that era anymore =) There is a multitude of possible æsthetical models and in the end it all depends on which crowd you are trying to please -- even within _one_ so-called genre...!
I'm afraid my humor may have been lost somewhere in its translation to the bitstream. I am the first to agree that aesthetics are not only difficult to formalize and judge, but also that aesthetics are very often not the primary interest of art. Doing all that in realtime through PD is not only technically impossible, but undesired.
However, I found out more about the method of compression to find similarities in music that I mentioned in my first email. The practice originated in analyzing DNA. A Markov chain analysis essentially is looking for similarities in the probability functions between states in (in this case) a piece of music. Instead, you can compress the music using any old compression scheme (there has been quite a bit of research into which ones work best for what). Then you compare the compressed music to another piece of compressed music. Since the compression is looking for similarities, just like Markov Chain modeling does, the difference in the two filesizes is directly porportional to the amount of difference in the two songs. The advantage (I guess) is that there is much less specialization required in writing the analysis functions. In twenty words or less.
But, as gml@xs4all.nl points out:
Actually that looks more like a audio/video track database description/querying method. The question was more about how to get analysis information from an audio stream.
we've gotten off topic. On my part this digression sprouted from wondering what to do with all the waveform analysis data once you have it.
gml@xs4all.nl:
Besides the analytical tools with orthonormal function-spaces (fourier etc.) I am also looking into classification based on the geometric/topological properties of the wave. Things like the fractal dimension of the waveform over either a short window, like fft's, or on longer segments. They use this kind of stuff to analyse heart-rythms f.i.
I would be interested in any links you might have, as I'm unfamiliar with this kind of analysis.
Cheers, Ian