Soundboard crown

[Sarah Fox]

Hi Del et al.,

Fascinating discussion!

In addition to stiffness arguments, I wonder about the impact of a crown on
the vibrational mode of the board.  If a domed panel is deflected at one
point nearer to one edge, the opposite end of the board would deflect in the
opposite direction, with a nodal point in the middle -- more or less.
Correct???  Now consider the same board, flattened:  A deflection nearer to
one edge would result in a deflection in the same direction over the
remainder of the board, to greater or lesser degrees.  Thus, at a frequency
of zero, the board would "vibrate"/flex in a bimodal pattern (correct term?)
with a crown and in a unimodal pattern with no crown.   I'm not saying that
the board would be incapable of other vibrational modes at other
frequencies, which of course it would.  I'm merely suggesting that the
vibrational properties of the board would certainly *change* from this
factor alone.  Perhaps a crowned soundboard would be predisposed to enter
into higher vibrational modes, responding better to higher frequencies???
(Just guessing.)

The spector of manmade materials has also been raised, another subject I
find fascinating.  I particularly enjoyed hearing an audio file of a piano
with a steel soundboard in the five/six/seven (can't remember) lecture
series.  The piano had a beautiful, full, rich bass, well defined tenor, and
a bizarre, pingy, ringy, un-piano-like treble.  I was left wondering whether
the soundboard was too efficient at higher frequencies, not
absorbing/damping vibrational energy as badly as wood -- or whether the
soundboard had other sorts of mechanical differences.  What exactly were the
*functional* differences between this board and a wooden one?

Has anyone ever played around with carbon fiber?  That might behave a bit
more like wood, yet without the problems associated with varying MC.

Peace,
Sarah

PS My initial, noninvasive, cursory experiments with mass loading of the
killer octave region seem to alter the spectral properties of the sound --
*somewhat* longer sustain, but kinda pingy.  Interesting.  I think the
"pingy" nature of the sound comes from a frequency dependence of energy
transfer from the string to the bridge, hence different decay rates for
different partials.  I'm also finding, I believe, that a very large part of
the responsiveness in this region is attributable to the properties of the
*entire* soundboard, not just the top end.  After a short initial period,
vibrations from the string are dissipated, exciting harmonic frequencies in
other strings throughout the piano -- perhaps especially in the backscale?
If I try to damp vibrations in the high treble strings with my finger, I can
only do it within a short timeframe after the attack (progressively shorter
for higher notes).  Thereafter, there is still sustain, but it cannot be
damped, because the vibrations have been excited throughout the piano, while
the vibrations of the note's three strings have all but dissipated.  I think
this "whole board response" keeps the mass loading of the upper end from
having any more of an effect on the overall sustain of a high treble note.


> As a purely theoretical question, I would say definitely maybe. There are,
> of course, a number of qualifiers, variabilities and dependencies....
>
> Soundboards, of whatever nature and material, need a certain combination
of
> mass, stiffness and internal resistance to function in the way in which we
> have become accustomed. (For the purposes of this discussion let's ignore
> the effects of humidity and wood MC on any part of the soundboard system.)
> If we deviate overly much from the parameters that have evolved over the
> centuries we will no longer have an instrument definable as a piano.
> History defines the tone standard we are striving for. Or at least it did
> until the flood of piano-like objects with their granite hammers and their
> massive marketing campaigns arrived on the scene.
>
> In 1700 wood was the only logical material from which to make soundboards.
> And it remained the only logical material until fairly recently. While the
> piano soundboard started out as basically an overloaded harpsichord
> soundboard, it had evolved considerably by the late 1800s. The motivation
> for this evolution was the increasing demand for power and the resultant
> string loads placed on them. In response it became thicker and, by virtue
> of increasingly stiff and massive rib systems, stiffer. Using construction
> techniques that seemed reasonable to piano makers of the day, one viable
> way to achieve an adequately stiff soundboard system without overloading
it
> with excess mass was to form a positive wood spring and then compress it
> with another spring--the string set that was stretched across the bridge
> with some amount of tension and deflection. In so doing the stiffness of
> the soundboard system was increased considerably with no increase in mass.
>
> With all this in mind, if we are to deviate from the established pattern
we
> must come up with a soundboard construction having a mass that falls
within
> certain limits combined with an amount of stiffness that will control the
> rate of energy transfer from the vibrating string(s) to the soundboard
> panel. One can argue that what the soundboard needs is stiffness, not
> crown. If the requisite amount of stiffness can be obtained sans crown a
> workable soundboard can readily be built without it. Certainly this was
> accomplished by Rippen with their laminated soundboards. These boards had
> no crown as built, though they did end up with "negative" crown through
> string loading.
>
> Nearly any degree of stiffness (within reason) can be obtained with a
> standard wood panel/rib combination by simply making the ribs as tall as
> need be to achieve the desired amount of stiffness--without any crown
being
> included at all. The mass of these ribs can easily be controlled by simply
> making them narrower. And this is basically what we do when we make a
> rib-crowned soundboard system. The ribs, instead of being anti-crown
> devices, now become structural beams with their stiffness being controlled
> by their cross-section height and width coupled with some projected amount
> of deflected crown. By removing crown from the equation we could still
come
> up with the same amount of stiffness by adding a bit more height to the
> ribs.
>
> Having come this far, we must now bring up the question of whether or not
> string deflection in the form of string bearing working against the
> soundboard is really necessary. The traditional string set/soundboard
> system works on a principle of two opposing non-linear springs--the
> soundboard system pressing up against the string set which is pressing
down
> against the bridge/soundboard system. Now, is our crownless soundboard
> going to have any string bearing? If so, is the soundboard going to start
> out with some slight crown and become flat through the application of that
> string bearing? Or is it going to start out flat and be forced into some
> kind of reverse crown by the string bearing (ala Rippen)? Or is it going
to
> start out flat and remain flat having the strings attached without any
> deflection, hence no string bearing against the bridge?
>
> Keeping in mind that I've not done much of any real research specifically
> designed to resolve these questions, I do have a couple of thoughts. A
> system in which a string without deflection is working against a flat
> soundboard is not going to respond like a system in which a string with
> deflection is working against a sprung soundboard system. Considering just
> the soundboard, in the first configuration--both the string and the
> soundboard system working through their zero axis--the soundboard's
> stiffness will be least at its rest position, increasing somewhat as it is
> forcibly deflected from rest by the motion of the vibrating strings
working
> through the bridge(s). In the second, the stiffness of the soundboard
> system increases as it is forced down and decreases as it returns and
moves
> up beyond its rest position. The opposite effect is seen in the string
set.
>
> As to exactly how much difference this makes in the final sound envelope,
I
> don't know, I've not attempted to define and measure it. I suspect,
though,
> that if two pianos were built having carefully controlled soundboards, one
> being designed to have a given amount of mass and stiffness with no crown
> and no string bearing and the other being designed with just enough crown
> so that it would become completely flat with some amount of string bearing
> (and at that point having exactly the same mass and stiffness as the
> first), the latter piano will have a better balance between power and
> sustain. I suspect that the first piano would have a somewhat more
> percussive sound and, consequently, a shorter sustain time.
>
> It would be an interesting experiment, but lacking that we are not left
> without clues. We can come close to this in real life by examining a
> selection of otherwise nicely rebuilt pianos having old soundboards that
> have ended up little or no discernable crown after stringing. I've
> encountered examples of both: freshly rebuilt pianos with zero crown and
no
> measurable string deflection and freshly rebuilt pianos with zero
> crown--i.e., some distorted but with the bridge line at the same elevation
> as the outside edges--but with some string bearing. Yes, they both work,
> but it becomes a judgment call as to how well they work. In general the
> respective pianos have exhibited the tonal characteristics described
above.
>
> Del
>
>
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