Negative crown

[Ron Nossaman]

At 10:03 AM 12/29/98 -0800, you wrote:
>Ron,
>I have a question for you.  You said that when the crowned soundboard is
>loaded by the strings, the impedance goes up.  I would agree with that.  The
>question is from the string perspective.  The piano has strings with
>frequencies ranging from ~50 Hz to ~4kHz and the I imagine the soundboard
>has 30-50 natural modeshapes in that range.  So my question is: with such a
>broad range of soundboard and string frequencies, what is the soundboard
>impedance "matching"?
>
>I don't really have an answer to this either...
>
>
>doug richards
>San Jose, CA
>


Doug,

Well, 'matching' is probably too definite a word here, but the soundboard
impedance should change along the scale to accommodate the impedance of the
string plane at a given point. The individual strings have their own
impedance value, which changes drastically from low bass to high treble, but
it's not linear with frequency, although frequency is a factor. That would
make it way too easy and everyone could be making well designed soundboards.
(I didn't mean it Del, I slipped) In theory, it's a matter of tailoring the
soundboard stiffness/mass to receive string energy at the proper rate,
relative to the rate at which the string supplies it. Assume a given point
in a given string scale. A soundboard assembly with a too low impedance in
that area will have more volume and, in the extreme, a tendency to
'splatter' on the attack, and short sustain. A board with too high an
impedance will be quieter, thinner sounding, and have a much longer sustain.
Both of these conditions can, and often do, exist in the same soundboard in
different areas of the scale. The trick is to arrange the proper balance of
mass and stiffness in any particular portion of the soundboard assembly to
reasonably accommodate the impedance levels of the string plane in the same
area to get the overall sound we're after, while still having the overall
strength to support the string bearing load over a long period of time. Are
we having fun yet? The assembly needs to be quite stiff in the treble, and
much more flexible in the bass. In practice, there are about a billion
variables to factor in, and it still comes down to best guess on some of the
factors involved. Del pointed out that, unlike an individual doing a one-off
redesign in the shop, a manufacturer can have the luxury of making small
incremental changes to fine tune the assembly. Even then, what seems to be a
short term gain could end up being a long term detriment as the design ages
in the piano. Throw in the nearly infinite variations of density and
stiffness in the materials used, the possible configurations of size, case
shape, rib scale, crowning method, grain angle, bridge construction and
position, string bearing and load distribution, and the fact that no two
practitioners of the soundboard design, installation, maintenance, and
repair art seem to agree on what they all are looking at, and we are most
definitely having fun.       

Is that what you asked?

Regards, 
 Ron