> Here's the way I was thinking of doing the "polynomial
>approximation" method I mentioned. Bear in mind that it all has to
>do with vectors, not functions of a continuous variable, so that the word
>"polynomials" might be slightly out of place, but I'll continue to use
>it since I think it makes things easier to understand.
Ah, to think I chose to study biology at school because I couldn't
do maths:-)
I do understand at least the outline of what you are doing here;
my problem is that I don't think your measure of distance between
two tunes will accord at all well with human perception.
Consider the problem of repeats; for a tune with a repeated first
part, one transcriber will simply enter the part and stick a repeat
sign at the end, ignoring the fact that the number of beats in the
last bar does not match the anacrusis. A second, more careful
transcriber will put in first and second endings so it plays properly.
A third transcriber leaves the repeat sign out (the first part of
a tune of this genre _always_ repeats, and we musicians don't need
to be told that). A fourth transcriber is making an exact transcription
of an actual performance, and writes the repeat out in full in order
to notate some subtle variations of ornamentation. No method which
depends on recognising the overall shape of the tune can see these
four versions as being essentially the same.
Or consider a song tune where the singer has transposed part of the
tune by an octave to suit the range of her voice.
The problem is that fairly trivial musical changes can make a big
difference to the shape of the tune, and vice versa.
In the long run, however, only experiment will show us which of the
reasonable approaches will produce the most useful result.
Phil Taylor
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