Re: [abcusers] ABC, AHC, Do-Re-Mi

[Laurie Griffiths]

> = John walsh
> ... (Ts)Chebyshev polynomials ... use polynomials which are ortho-normal
> relative to the particular weight function chosen. 
Ah!  I hadn't realised that you DID know your maths.  Splendid!


> ... I think that the method should work for whole tunes, not
> just snippets, tho the matrices get larger as the tune lengthens, and the
> numbers get much larger, which might be the worst problem.

I suspect that unless you choose a good basis set of functions 
(I was just guessing about Chebyshev and Fourier) not only do
the matrices get larger but also the equations become stiff - so 
that very small changes in the tune cause large changes in the 
polynomial coefficients, which is exactly what you do NOT 
want if you are going to compare tunes on that basis!  My 
maths is not up to proving that they'll get stiff, but I think I
would put money on it.

Laurie

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