"Inversions" in genetic would correspond to "variations" in music
e.g. turning the descending scale
[K:D]e2d c2B
into
efe dcB
or turning the long note A3 into the twiddley version A^GA
on recorder and then turning that into ABA for fiddle.
Something that is in music but (I think) not in genetics is that
some notes are more important than others. In all of the
above cases "the bones" of the tune are the same, they are
just fleshed out differently.
Laurie Griffiths
http://www.musements.co.uk/muse
where you will find music notation software for PCs.
----- Original Message -----
From: Sigfrid Lundberg, Lub NetLab <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Friday, June 30, 2000 12:24 PM
Subject: Re: [abcusers] ABC, AHC, Do-Re-Mi
> 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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