Continued Fractions ?

Hi,

I've been refering to Edward Dunne's excellent web page
on Pianos &
Continued fractions.
The section on Continued fractions is fascinating,but I don't quite get
it.I also wound up on this page ,an intro. to the subject,but still
don't,.
Could anyone explain how one gets from Euclid's Algorithm (for GCD),to
the Continued Fraction Algorithm ?
BTW,I also found a collection of pages on constants/continued fractions
on MathSoft's site :

Oh,and about microtonality in popular/rock music,I believe Steve Vai had
a piece on an album a
couple of years ago.I think it was 22-TET ?

Thanks in advance.

Cheers,
Drew