Grand piano design - parallel vs angled strike line?

Robert Scott Kuhn rskuhn@ev1.net
Tue, 12 Dec 2000 21:23:17 -0600


Just a quick comment on thinking about soundboard stiffness from an
infrequent posting occasional lurker.

I recently did some computer modeling of soundboards with sinusoidal inputs
and one thing this did is help me understand what "stiffness" means in terms
of the board and the impedance it presents to the vibrating string.  It was
something I had not thought of before I "ran some numbers".

It should be noted that stiffness of the board in terms of static stiffness
supporting the string bearing is very different than stiffness presented by
the board to a vibrating string.  Take a note in the "killer octave for
example.  When the string starts to vibrate the board at these frequencies,
the wavelength in the board is on the order of a few inches.  The string
does not "care" or "see" how long or how big the board is underneath it.  At
these frequencies, it is only the stiffness and mass of the board in a small
area around the string that counts in terms of what impedance the board
presents to the string.

Think of it as dropping a pebble in a pond.  The waves move out from the
initial point depending on the density and viscosity of the water in the
area you dropped the pebble in.  If the wavelength is 3 inches, the waves
don't care if there is a "stiffer" fluid 2 feet away.  Yes, there are
reflections from shore (the edge of the board) that come back, but when they
get back to the area that the pebble was dropped they will take on a form
based on the conditions at that point.

Of course, beefing up the ribs in this area to better support bearing in the
region (which is as Ron and Del frequently point out -- a real problem in
most pianos) will affect the stiffness in the area at the board frequencies
as well and you will get the result you seek.  In some cases, however,
equating the static stiffness of the board with stiffness under vibration
can lead down the wrong path or at least can cause you to focus on the wrong
thing.  One example would be to watch that the feathering of the ribs does
not come so close to the bridge as in many Steinways (and others).

In terms of Ron O's concern that centering the bridge between the belly rail
and rim would lead to waves hitting the edges and bouncing back to meet at
the bridge and cancel each other out.  All I can say is that if you look at
all the reflected action of a board in motion, you cease to worry about such
things.  What counts is to just have a stiff and massive edge to the board
that cleanly terminates and reflects the boards vibration as Del and Ron so
frequently point out.


Scott Kuhn
PTG Associate
Houston, Texas



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