partial answers

[Mike Spalding]

Allan,

You're lucky to have such an inquisitive apprentice. Maybe the answer is 
"Because it CAN", rather than "Because it DOES". It's been way too long 
since I struggled with the underlying math, but I have a feeling this 
could be explained by the second law of thermodynamics: Increase of 
entropy. Mechanical systems always move towards a state of decreased 
energy, which is often explained as an increase of disorder/chaos. The 
more modes of vibration in the string, the greater the "disorder". It 
certainly makes sense on an intuitive level that the vibrational energy 
of the string will dissipate most quickly when the maximum number of 
overtones are sounding. When we voice, we reduce or eliminate high 
overtones, and increase sustain. Maybe. Anybody out there want to offer 
a more rigorous analysis or rebuttal?

Mike

Allan Gilreath, RPT wrote:
>
> 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.”
>
> Any thoughts?
>
> Allan
>
> 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
>