Continued fractions tutorial website

After receiving Paul Ehrlich's reply, I searched on "Continued
Fractions" in altavista and found this useful tutorial:

http://archives.math.utk.edu:80/~atuyl/confrac/intro.html

Harold I've got a couple of linx regarding this on my Geek page :

Introduction to Continued Fractions by Ron Knott
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/cfINTRO.html
The page for dummies (worked for me ) to actually understand continued
fractions.

Continued Fractions Site
http://www.calvin.edu/academic/math/confrac/index.html
Hard core introductory stuff plus loads of links for extensive exploration.
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The page for "Pianos and Continued Fractions by Edward Dunne" that
introduced me to the subject is no longer around.

I did get in touch with him via email :
____________________________________________________________________________
Edward G. Dunne
Editor, Book Program
American Mathematical Society E-mail: egd@ams.org
____________________________________________________________________________

He explained that although his web pages were around for 2 years after he
left Oklahoma State University for the American Mathematical Society, they
finally got rid of the site. He has yet to prepare a fresh version of it for
the web. I sent him a note that it would be nice to have it aroudn again.

A print version by Mark McConnell and Edward Dunne was published in the
MAA's Mathematics Magazine, vol 72, april, 1999.

Edward sent me a reprint of the article. It's a classic. At the conclusion
he makes an argument for 41-tET. Here r some bits from the concluding part
of the paper :
---------------------------------------------------------------
The 41 tone scale has a fairly good representation of the standard
acoustically distinct notes. One would guess that if we regularly used such
a scale, our ears would be trained to hear the difference between adjacent
mini-steps (1/41-sts). This interval is 1200/41=29.3 cents, only a few cents
more than the Pythagorean comma. We would probably come to believe that the
19.9%-of-a-mini-step error in the 41-tone major third is audible and bad,
just as musicians today believe the 14.7%-of-a-half-step error in he 12-tone
major third is audible and bad.

http://www.math.okstate.edu/~mmcconn/ 41tone.html contains a BASIC program
that converts a computer keyboard into a 41-tone "organ".

The failure to emplay the more natural microtones of the 41-tone scale is
clear & compelling evidence for the need for mathematics across the
curriculum, especially the need for number theory in music.
---------------------------------------------------------------

- Drew

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