Connecting function to ideas (Was Re: [abcusers] ABC, AHC, Do-Re-Mi)

[Sigfrid Lundberg, Lub NetLab]

On Fri, 7 Jul 2000, Laurie Griffiths wrote:

> I thought I should say how welcome this discussion is.

It is a *very* stimulating discussion

> Here we are, all throwing rocks at each others' ideas in the best
> traditions of university argument without anyone getting upset and with
> everyone (especially the rock throwers) learning new stuff and acquiring
> respect for the generators of the ideas.  L. 

I think that one single idea will not solve all the problems that these
ideas are adressing. Below I'll try to list a number of problems, then we
can perhaps tie the various ideas to those problems and thereby get a
further understanding. The problems are listed in no particular order:

A. Comparisons of entire tunes
------------------------------

1. Deduplication in sizable collections of tunes. People are transcribing
the same tunes, and in a large collection there might be duplicates.

2. Drawing family trees of tunes. A bit harder than deduplication, since
we need to a measure of similarity. I suppose that only imagination is
limiting what could be performed with such software.

3. A special case of 2. Submit an entire tune into a search engine and get
a list of similar tunes.

...

B. Comparison of fragments with entire tunes
--------------------------------------------

1. Tune searching is the typical use

2. Scanning a tune collection for certain motifs, cadenzas etc

...

C. Comparison between fragments
-------------------------------

Seems to me that the uses here includes both A and B above. The problem
is: What is a fragment?

================================================================

It seems to me as if the "spectral" methods could be applied mainly in
case A and to some extent in B. In the B case we have a kind of
statistical problem. Assume that we have a collection of 32 bar tunes.
Then we submit 4 bars as a search. We calculate a spectrum for those 4
bars and want find 32 bar tunes that matches. Giving that the method could
solve the this "sampling error" problem, I think that the spectral methods
possibly could be used for tune searching.

I suppose that the spectral method would fail completely on problem B2,
which I think would be soluble using the interval sequence methods (ie
"protein sequence" metaphore", or perhaps the polynomial methods). 



Sigge

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