soundboardinstal again

[Delwin D Fandrich]

----- Original Message -----
From: <ranjacob@umich.edu>
To: "Pianotech" <pianotech@ptg.org>
Sent: July 30, 2003 10:11 AM
Subject: RE: soundboardinstal again


> Right, bridges serve to distribute load among the ribs, and don't
> support crown, and I was asking whether or not a counter-bridge or
"sister
> bridge" had ever been intended, at least partly, to support crown. Or if,
> without adding way too much stiffness and mass, a set of counterbridges
(or
> better, quasi-ribs parallel to the grain of the panel) *could* be
designed
> to support crown, so that, *assuming* there was anything to be gained
from
> it, ribs could be designed without having to have all of the crown
support
> as one of their functions.

Yes, a bridge system could be designed such that it would "support crown."
As to whether that is desirable or not is another question. With this
subject coming up so regularly it has given me some reason to think about
it some. I'm not at all sure this would be a good thing. A bridge that
would be so stiff and structural as to be effective as a crown-supporting
member would (regardless of the mass involved) also be an overly effective
acoustical bridge. That is, it would spread the energy from a particular
string set (at a particular frequency) over too broad an area. There is a
reason why the flugal, or wing-shape, design has won out over the years.


>
> I think that due to Del's reply and yours, I see better why this might
not
> work, or, at least, might be wholly unnecessary. (Understand, by the way,
> that I am after grand piano tone, not, what might result if we tried to
> "simplify" matters by pretending that we are trying to reproduce string
> oscillations as found at the bridge cap, in the same way that an audio
> engineer tries to reproduce air oscillations arriving at a microphone.)

Gosh, and here all the time I thought that was just what we were trying to
do.


>
> One way of visualizing the problem lies in considering the consequences
of
> the fact that the gaining of downbearing necessarily changes, from a
right
> angle, the angle of the string to the downward vector of board assembly
> movement. (The assembly does have very high resistance to any change in
the
> exact angle at which its own deflection, as a complex of end-supported
> beams, operates in response to the "live load" bearing down on it. ((Now,
> *there's* a simplification...)) :) .)  Rather than being merely "just a
> very small change of angle", this lessening of the right angle
> fundamentally alters the right angle that is shown in a drawing, on
> acoustic theory of the string, of the string as having one vertically
fixed
> termination (the capo or agraffe) and one termination that is fixed
> horizontally, but whose vertical "quasi"-fixing is to a mass that is free
> to move vertically -- e.g., a mass free to move vertically because, in
> fact, in that dimension, it is a spring.  That is, the change from that
> right angle to a smaller angle in the grand piano will cause the string
to
> have more tension than its resting tension at the top of its complete
cycle
> of vertical oscillation, and less tension than its resting tension at the
> bottom of the complete cycle. These differences cancel each other out,
> yielding a tone that is steady in pitch, just as the process of the
> formation of the string's standing wave after the upward blow of the
hammer
> is, in part, a process of cancelling out certain of the effects of the
> blow's having been upward rather than downward.
>
> It is, therefore, this lessening from the right angle to the
> assembly's vector as a spring that makes the string itself
> an *opposing* string, in the sense that, at the required times
> in the course of the fundamental's cycle (and, correspondingly, of the
> cycles of the harmonics), the string is a not "simply" a
> spring that hardens when moving upward from the rest position
> of zero amplitude, but a spring that has the required degrees of
> stiffness at that rest position and at all higher amplitudes.
> The provision and adjustment of the adjustment of downbearing, therefore,
> is a means to control the rate of vertical transmission "beyond", and, so
> to speak, horizontal reflection backward from,
> the coupling of the string to the bridge.

This is a good way to go nuts! It's time for a little simplicity. Varying
string bearing against the bridge controls (varies) the amount of string
loading against the soundboard system, hence the spring rate of the system,
hence mechanical impedance of the system, hence the rate at which energy is
transfered from the strings to the soundboard system.

If you're really determined to add in some complexity this would be a good
time to consider the effect of the string backscale on the
bridge/soundboard system.


>
> If I haven't made a new mistake here, my next question is:
> are *lateral* transverse vibrations of the string (or, large lateral
> vectors of vibrations that are significantly "slanted" from the vertical)
> thought to be transmitted in any way that the theory
> of the board assembly, and of the interaction of its components,
> has been able to explain, or (usefully) speculate about?

This would depend on your defination of "usefully." In terms of piano
design I can't see how pondering this line of speculation could be usefully
applied. From a purely scientific perspective it may well be usefully
considered and studied. This all goes back to something I have observed
several times in the past--there is much scientific exploration into the
physics of musical instruments that has been largely useless in the
development of those instruments. That doesn't mean it shouldn't be done,
it just all needs to be kept in perspective.

Del