Negative bearing

[Delwin D Fandrich]

----- Original Message -----
From: "John Delacour" <JD@Pianomaker.co.uk>
To: <pianotech@ptg.org>
Sent: December 02, 2001 9:55 AM
Subject: Re: Negative bearing


> Greg, there is very little resemblance between the way a soundboard
> works and the way a loudspeaker works.  The cone of the speaker is
> light and stiff and ideally perfectly free to respond to the impulses
> from the solenoid.  It is in no way a medium for the transmission and
> amplification of a sound but a simply a plunger for compressing and
> rarefying air following the dictates of the solenoid.

Actually, the loudspeaker makes a rather good analogy for the piano
soundboard. Neither are amplifiers in any sense of the word: both are
transducers in that they convert energy from one form into sound energy.
Neither transmits sound, but are both relatively light and stiff
wave-carrying mediums.


>
> The soundboard of the "modern" piano, besides acting partly as a
> plunger, has to respond to over 200 separate complex signals from
> different places arriving at different points through various media.

Fewer different points than it might appear. True, there are generally in
excess of 200 individual strings, but these strings are attached to
(usually) two or three separate bridges. For vibrating energy in any one
string to move the soundboard panel it must first move the bridge(s). The
bridges span quite an area. Obviously there are differences--unlike the
loudspeaker with its more-or-less point driving source the soundboard is
driven over a broad area of its surface. But still, the analogy holds at
least reasonably well.


>
> It is restricted from responding to these signals as a plunger by a
> huge downward force on it up against which it is pressing with an
> equal force by dint of its crown and its inability to spread, so that
> the whole system is in equilibrium with the board in a state of
> compression, ideally at some point below the point at which the
> weakest of the summer growth gives up the fight and the board shears
> (compression marks).  For all this to be possible it is essential
> that the board be fixed for at least most of its perimeter to a
> massive and unyielding structure, which is the framing and specially
> the inner and outer rim.

Well, there is a lot here, most of which I (and others) have written about
in the past, both in the PT Journal and on this list. Briefly, soundboard
crown is not supported by the rim in spite of the claims made by M&H for
their Centripetal Tension Resonator. Wood is far too compliant and the crown
radius is far to large for it to function as a Roman arch. Soundboard crown
is built into the system because it is an excellent way to add stiffness to
the soundboard assembly without adding mass to the system. The aggregate
stiffness of the soundboard assembly combined with its mass combine to
determine the rate of energy transfer from the vibrating strings to the
soundboard assembly. In other words, the combined effect of soundboard
stiffness and mass, coupled with its internal friction and rate of energy
losses to the rim, plate, etc. determine sustain.


>
> Sound travels IN the board and not just out from the top and bottom
> of it.  A material needs to be used that will carry sound rapidly
> through the medium.  The winter growth of the fir or spruce
> soundboard carries the waves fast along the length of the boards and
> owing to the slower and less efficient movement of the waves across
> the grain, the board is crossed by bars which transmit fast and also
> compensate for the increased flexibility of the board across the
> grain.  The waves are reflected in all directions through the board
> from the rigidly held perimeter.  I see Ron Overs uses laminae of
> spruce to achieve uniform propagation of the sound.  Properly
> disposed ribs have done the job pretty well for a long while.

Sound does not travel in the soundboard assembly. Sound is created as the
soundboard panel vibrates in response to the energy input from the strings
and compresses and rarefies the air around it. Wave energy from the strings
moves the bridge which in turn moves the soundboard. The resultant wave
energy travels primarily along the soundboard surface until it reaches some
boundary. There it is either absorbed or reflected back into the soundboard
panel. The difference is, perhaps, a subtle one but it is important to
understanding the function of the soundboard. Most of the effective rigidity
of the soundboard system comes from the ribs. As you point out wood,
especially soft woods such as spruce, are not particularly stiff across
grain. Hence the ribs. Stiffness along the grain of the soundboard panel is
of less significance than we usually give it credit for. It does have a
considerable (positive) effect through the highest part of the treble and a
generally negative effect through the low bass. (Assuming a conventional
soundboard/rib configuration.) But, through the rest of the scale (given the
typical soundboard panel grain angles used in the 'modern' piano) it has
relatively little effect. Through the mid-section of the piano compass the
ribs are the primary wave carrying component.

A fairly good, though brutally technical, description of vibrating plates is
given in "The Physics of Musical Instruments" (Fletcher & Rossing, 1991,
Springer-Verlag, New York.). See Chapters 3 & 12.


>
> Quite a few uprights have
> the board freed up along the bottom.  None of these expedients is
> designed to reduce the overall firmness of the structure but to apply
> topical variations to the stiffness of the structure.  I'd guess that
> 90% of all such work is empirical and that 100 faculties working for
> ten years would probably produce no better science.

Quite the contrary. The purpose is to improve the mobility of the
structure--or to 'reduce the overall firmness of the structure.' I'm
assuming by 'overall firmness' you mean overall stiffness? If not, what? To
develop reasonable bass tone the soundboard must be able to move which it
cannot do if it is tied to the rim or soundboard liner just next to the bass
bridge. By freeing the bottom of the soundboard the soundboard/bridge system
is given much more freedom of motion.

The understanding of soundboard function has moved a bit beyond the purely
empirical--even beyond 90% empirical--though certainly not to the stage of
pure science either. Still, techniques such as modal analysis have enabled
the study of soundboard function at a level not even dreamed of even thirty
or forty years ago. It is my hope that before I pass from the scene that
this understanding will be still some closer to scientific and much less
reliant on the empirical.

Del