partial answers

[Jim Moy]

On 6/29/07, Allan Gilreath, RPT <allan at allangilreath.com> wrote:
> "Why does the string divide into all of the
> different available fractional segments and not just even multiples of two?"

I seem to remember from my systems class in engineering school that a
theoretical impulse contains *all* frequencies, and that a system's
output will  filter, amplify, attenuate, etc. according to its
characteristics.

So in the case of a piano as a system, an impulse (hammer strike) is
applied to the string and most frequencies rapidly dampen out, except
those where nature of the string and the rest of the assembly (bridge,
soundboard) cause them to dampen less rapidly according to the
vibration physics we've all become acquainted with.

Or at least, that's how I've modeled it in my head :-)  (and it's been
a long time since I've been able to do anything like the math I did
back then...)

So maybe one response to Allan's apprentice would be to put on your
best Yoda face and say "The wrong question you ask. Should not a
string vibrate at all frequencies?"

Jim Moy
Fort Collins, Colorado
(Not a technician -- hopefully someday -- merely a lurker until now...)