On Thu, 29 Jun 2000, John Walsh wrote:
>
...
> 3) Measure the (signed) distance of each successive note
> above/below middle C. Form a vector of these, (v(1),v(2),...,v(n)).
> Think of this as a function for the moment: v(t), t=1,2,...,n. In order
> to make the result independent of the key, subtract the (weighted) mean
> value from each v(i), and call the resulting vector V.
As Mark notes in another mail, this would not make it independent of
key/pitch. The distance has to be measured in semitones from the tonic,
not from C.
> (4) Choose an integer k <= n, and find the best
> weighted-least-squares approximation of V by a kth order polynomial in t.
>
> (5) Compare two tunes by measuring the distance between their
> polynomials.
Isn't it easier to use the squared distances between matching pairs of V?
You don't need the polynomials to measure the distance. However, there is
more to simililarity than this. I like Phil Taylor's protein metaphore,
since tunes evolves somewhat like proteins.
There will be
deletions: a segment of notes is removed.
insertions: a segment of notes is inserted
duplication: a segment of notes is repeated
In genetics we also have inversions, but I reckon they are extremely rare
in music. The protein software is capable of recognize similarity, even if
events of these kinds have occured. Given a database might even be
possible to find a "source tune" from which a segment has been taken for
inserting it in a "target tune".
Sigge
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