re: Ferguson-Forcade algorithm

[John Chalmers wrote...]
>What exactly was Carl's question or the musical application?

[Paul Erlich wrote...]
>John, the question Carl brings up is not a simple problem, nor is it
>a question of speed of convergence. According to Pierre's quote from
>the now-censored Wolfram site, Brun's and all other algorithms known
>before 1991 failed in certain cases to act as a generalization of the
>continued fraction algorithm for two-term ratios, with all relevant
>properties thereof. While the point is moot for the problem of simply
>approximating a certain proportion with a given restriction on the
>integers involved, since a brute-force computer search is fast enough
>these days, for the much larger problem of partitioning the 2-d plane
>according to a generalized mediant function.

>Note the emphasis on the _iterative_ nature of the procedure -- that
>property seems essential to its applicability to the generalized-
>mediant problem. Or maybe we're barking up the wrong tree . . .

Why don't we focus on the link between the Euclidean algorithm and
the mediant process. We won't know what properties we need to generalize
before we understand the 1-D case.

I'll be traveling to California tomorrow, to return on Sunday. I hope
to see a digest in my inbox!

-Carl