partial answers

[J Patrick Draine]

A quick Google on Pythagorus yields, among others, a page such as
<http://www.aboutscotland.com/harmony/prop.html>. In a nut shell,
Pythagorus was interested in mathematics and music, and his was a
process of emperical discovery, and description of systems that "make
sense" of his discoveries. The link to Alberti shows how these
mathematical-musical principles led to architectural theories of
proportion.
A good reason to brush up on classical & Renaissance history science
and philosophy!
I don't know what modern day heavy duty physics has to say about it.
Sigh, so much forgotten from school daze, and so little follow up on
these topics in the form of "leisure reading."
Patrick Draine

On 6/29/07, Allan Gilreath, RPT <allan at allangilreath.com> wrote:
>
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>
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> Good morning folks,
>
>
>
> I had a question from my apprentice that someone on the list may be able to
> help me with. We all know that vibrating strings divide up into segments
> with lengths approximately equal to fractional portions, i.e. ½, 1/3, ¼,
> 1/5, 1/6, etc. (we're not even taking inharmonicity into account at this
> level.) His question is, "Why does the string divide into all of the
> different available fractional segments and not just even multiples of two?"
> I was hoping for a much better answer than just, "Because it does" but
> Benade, Helmholtz and Rayleigh, the best I can tell, all assume this to be a
> fact and I don't really find the "why."
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> Any thoughts?
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> Allan
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> Allan L. Gilreath, RPT
>
> Registered Piano Technician
>
> Allan Gilreath & Associates, Inc.
>
> The Piano Experts
>
> PO Box 1133 - Calhoun, GA 30703
>
> 2612 Hwy 41 S - Calhoun, GA 30701
>
> allan at allangilreath.com - www.allangilreath.com
>
> phone 706 602-7667 - fax 706 602-0979
>
>