how to measure entropy of music?

Richard Dobson wrote:

> Music has been described as "audible mathematics" (obvious
> Pythagorean notion here); but (writing as a confirmed non-
> mathematician) I wonder how keen mathematicians really are
> on surprises, contradictions, non-sequiturs, etc! African
> musicians say "every wrong note is a new style" (cited by
> Christopher Small in his book "Music of the Common tongue");
> but a wrong formula is just plain wrong, leaving very little
> scope within mathematics for rhetoricism.

While that last remark is certainly true, the actual doing of 
mathematics starts out with inductive reasoning and tinkering like 
any other trail on the quest for knowledge. I would liken the musical 
notion of wrongness you mention to seeming incongruence at that stage 
rather than to formal incorrectness. Of course, it is paramount to 
follow up on mathematical intuition with rigorous deduction -- if you 
end up with a contradiction there's a mistake somewhere, no arguing. 
But if you cannot manage that you might just be on to something new! 
So yes, surprise has much value in mathematics. The difference is 
that music has no absolute reference frame for truth; it is neither 
capable nor in need of going beyond induction. At least that's my 
view, as ideological as the opposite assertion.


Martin

-- 
Quidquid latine dictum sit, altum viditur.

On 2004-12-04 00:54:56 +0100, Richard Dobson 
<richarddobson@blueyonder.co.uk> said:

> African musicians say "every wrong note is a new style" (cited by 
> Christopher Small in his book "Music of the Common tongue"); but a 
> wrong formula is just plain wrong, leaving very little scope within 
> mathematics for rhetoricism.

Absolutely.

If someone made a mistake, my mathmatics professor always used to say 
"You're almost right!" Seeing that the student looked happy, he added: 
"Don't look too happy - I could have said that you're totally wrong, 
because to a mathematician that's the same - but I wanted to be polite".

:-)
-- 
Stephan M. Bernsee
http://www.dspdimension.com

"Eric Jacobsen" <eric.jacobsen@ieee.org> wrote in message
news:41b0bb23.928505843@news.west.cox.net...
> On Sat, 04 Dec 2004 01:07:34 +0800, Steve Underwood <steveu@dis.org>
> wrote:
>
> >John Bailey wrote:
> >
> >> The basics are at:
> >> http://www.music-cog.ohio-state.edu/Music829D/Notes/Infotheory.html
> >>
> >> Thanks to the stimulation of your question, with a search based on the
> >> key words: hmm, entropy, and music I have learned the question is of
> >> significance today for serveral reasons:
> >> 1) Recognizing when TV commercials are playing.
> >> 2) Separating out background music behind speech in speech
> >> recognition.
> >
> >I wonder if they could figure a why to identify background music and
> >separate it from the sound reaching my ears :-)
>
> Good point!  If the predictor works then you can make a pretty good
> canceller!
>

Not sure how you can come to that conclusion. If you have one microphone and
a perfect algorithm you could determine what is music and what is
speech.However, to cancel the music you would need to subtract it from the
sum of music + speech and without a second sensor this would not be
possible - unless you assume the statistics of the music do not change
rapidly so that the music during the speech was approx the same as during
non-speech - an assumption which may be true for some music maybe?
On the other hand if we used multiple microphones then maybe we would have
something worthwhile.


Tom