partial answers

[David Boyce]

My thought, Allan, is that you have a very good apprentice!  He will go 
far.....

Best regards,

David.

>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?