Grand piano design - parallel vs angled strike line?

[Ron Nossaman]

>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.  

Hi Scott,
Absolutely correct. This comes up occasionally, usually in connection with
"I have a Finestkind piano with no bearing or crown whatsoever that has the
most WONDERFUL tone!" Unfortunately, there isn't any dependable way (that I
have available) to tell just how close to the edge of functionality one of
these boards really is until the sound falls apart as the room humidity
gets down around or below 30% one fine winter day.


>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.

Correct again, but the stiffness and mass of the assembly under any given
point on the bridge (given an adequate rim attachment) will be determined
by the bridge materials, construction and dimensions, rib materials and
dimensions, panel composition and thickness, crowning method, and panel
area controlled by adjacent ribs. The stringing scale figures in there too,
since you'd design the soundboard assembly to accommodate it. A soundboard
doesn't have just a single measurable impedance level. It changes
tremendously from one end of the bridge to the other, and while load
bearing deflection at any single point isn't by itself an exact indicator
of the ultimate vibrational characteristics of any other single point of
the assembly, it is one valuable and relatively dependable indicator when
the rest of the variables are factored in as best we can.    



> 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).

The Steinway soundboard is a considerably different sort of system than
what Del and I talk about, so it isn't exactly that simple. 



>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

That's been my experience. Centered is good for diaphragm response
efficiency, but the reflected wave cancellation effect doesn't seem to be a
problem in practice if the bridge is a bit off center.

Regards, 
Ron N