Phil Taylor writes:
>>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:-)
>
Well....I usually try to avoid being technical, but this time it
was clear from the questions that I couldn't describe the method without
going into the gory details...but...say, who was it who brought in the
mathematics of gene-splicing in the first place...? :-) (Besides, when
my wife asked me---and she knows I'll do almost anything to avoid
actually writing up the stuff I'm working on---"Are you doing
mathematics or music this time?" it gave me the chance to show her a
page filled with matrix algebra and say, "See, honey, it's music!")
>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
>[...]
>Or consider a song tune where the singer has transposed part of the
>tune by an octave to suit the range of her voice.
>
I get the impression that I'm being raised in this game when I
shou0ld just be checking to the next bettor. My original idea was that
one should just sample the first few measures of a tune, but when someone
mentioned taking longer samples, I thought that it would be possible to do
so. And still do. (There may be numerical problems with the polynomials,
as Laurie suggested, but I think that the tent functions I mentioned in my
last post don't pose numerical difficulties.)
However, I don't know if it is desirable to take long samples. The
longer the sample, the more likely it'll be to decide that two similar
tunes are different. The algorithm I described, although it may not
appear so, tries to simplify the tunes being compared enough so that there
is a chance of getting a match. (I originally described it as a computer
version of the "up-down-up-down" method of classifying tunes according to
whether their successive intervals go up or down.) Taking long samples
overcomes the simplification.
The objections you raise have to be dealt with in any tune
searching/analyzing scheme which goes much beyond the first couple of
measures. I'd say that the issue of repeats should be handled in the
pre-processing. One would probably want to get rid of them if
possible--that's the lowest common denominator---but then if someone
cleverly uses repeats just to avoid writing a bar or two in the middle of
things, the scheme would probably be hosed. But of course this would throw
a statistical interval-counting scheme off the scent too.
Similarly, if there's some unexpected key-change, piccolo passage,
or other arranger's trick in the midst of things, it's probably also
hosed. Depends on how long the interpolated passage is. And other things.
There are some interesting questions related to this, e.g. "How
different are different tunes?" and "How much do you have to screw up a
given tune before it becomes unrecognizable?" but I'd like to have some
facts at hand before getting into that morass. (And one might get some
facts by turning some of the algorithms already implemented loose
on some tune collections.)
The question is whether or not the algorithm works in the ideal
simple and uncomplicated case. Frankly, I don't know. I've haven't tested
it, so I can't make any claims. (But if the apparently unpromising scheme
of simply measuring the (unordered) note frequencies works, almost
anything else should too...:-)
Well, I should test it...if I get some energy...or have to do some
other work I *really* want to put off...
Cheers,
John Walsh
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