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<DIV>Hi all,</DIV>
<DIV> </DIV>
<DIV>All this discussion of hammers, strings, and SB is quite =
interesting.
I thought I would offer my impressions of the respective contributions =
of these
components, as I understand them. </DIV>
<DIV> </DIV>
<DIV>Hammer: The hammer delivers a broadband impulse to the =
string.
If you were to take a hammer and "whack" it against an unstrung =
soundboard, the
sound you would hear would be the "impulse" delivered into the =
system.</DIV>
<DIV> </DIV>
<DIV>String: The string is an oscillator -- or a filter. It
oscillates to the spectral components of the impulse corresponding to =
the
fundamental and all of the string's partials. Energy from the =
other
frequencies is quickly dissipated. Assuming it is responding in a =
linear
fashion, it will create no spectral energy of its own. If it is =
overdriven
(i.e. nonlinear), distortion products will be created. This will =
take the
form of energy from lower frequencies being distributed to higher =
harmonics
(partials). Perceptually, this will be a "brightening" of the =
sound.
The most important function of the string is that it *stores* energy =
from its
fundamental and partials, for measured dissipation through the =
soundboard.
Without this storage, there would be no sustain, and the piano would =
sound more
like a weird sort of drum.</DIV>
<DIV> </DIV>
<DIV>Soundboard: The soudboard bleeds off acoustic energy from the =
string
to the air. If the board were made of concrete, the string would =
vibrate
forever (assuming 0 inelasticity and 0 friction). If the =
soundboard didn't
exist, the string would also vibrate forever. When the board moves =
in
response to vibration, it is at a cost to continued vibration. =
(Consider
that the soundboard's movement is always driven by force from the =
string, so it
is a braking influence. It's a bit like running in sand, which can =
get
rather fatiguing rather quickly.) The board creates no spectral =
content of
its own, assuming it behaves in a linear fasion. Rather, it bleeds =
off the
energy of the string. It may vibrate more easily at one frequency =
than
another, and so it may bleed off energy at different rates for the =
different
partials, giving them different sustain. That is, the brightness,
darkness, and/or tonal properties of the note could change throughout =
the
sustain, as a function of the soundboard's response properties.</DIV>
<DIV> </DIV>
<DIV>Given all this, the largest impact on the spectral content of the =
sound is
obviously going to be in the hammer itself, since that is the source of =
all
spectral energy that goes into the system. Assuming linearity, of =
course,
the string and the soundboard merely store and dissipate the energy from =
the
impulse created by the hammer. Here are a few thoughts on the
impulse. (BTW, I apologize for trying to describe functions
verbally. It seemed preferable to drawing a bunch of =
graphs):</DIV>
<DIV> </DIV>
<DIV>The impulse can be represented by graphing force over time. =
When the
hammer hits the string, force increases to a point, and then it =
decreases.
For simplicity, I'll discuss what happens when it increases. The
decreasing phase is the same in reverse. (Well, really not, since =
there's
hysteresis, hammer deceleration, and string acceleration, =
but...)...</DIV>
<DIV> </DIV>
<DIV>The perfect broadband impulse would be a "step" =
function: Force
is zero, until some point in time, at which force and is =
suddenly
changed to some fixed value. This impulse would have have a flat =
spectrum,
from frequencies of zero to infinity. It would of course cause
displacement of whatever it is applied to, and with this displacement, =
there
would be energy delivered into the system, with uniform energy =
distribution (per
Hz) from zero to infinity. This step function is approximated by =
the "pop"
that one might hear when plugging a microphone or guitar into an =
amp (to
the ability of the speakers to reproduce it). A broadband impulse =
might be
delivered to a string, approximately, by striking the string with a =
glass
marble. Obviously the sound will be very bright. Assuming =
the
piano's response is flat (which it won't be), there will be equal =
spectral
energy at the fundamental and each partial.</DIV>
<DIV> </DIV>
<DIV>The perfect narrowband impulse wouldn't be an "impulse" at =
all. It
would be a continual sinusoidal variation in force at the fundamental =
frequency
of the string, fording the string into sympathetic motion. =
Assuming
perfect linearity, there would be no partials.</DIV>
<DIV> </DIV>
<DIV>Then there are gradations inbetween. The slower the ramping =
of force,
the darker the tone will be. Considering this, I would think these =
properties of the hammer would be important, and I would be very =
interested in
the impressions of those who have experience with voicing issues (which =
I do
not):</DIV>
<DIV> </DIV>
<DIV>The "spring constant" of the hammer felt. How much force =
results from
how much compression of the felt. The higher the spring constant, =
the
harder the hammer, the faster the ramping of force, the brighter the
sound.</DIV>
<DIV> </DIV>
<DIV>The shape of the hammer: As the tip of the hammer is =
compressed
against a flat surface, more and more felt mates with the surface, and =
so the
force is distributed across a larger area. This results in a =
change in
spring constant of the hammer during compression. For a given =
hammer
position, mass, felt composition, etc., a larger radius of crown (or a =
flatter
crown) should result in a brighter sound, as the mating area and applied =
force
would ramp more rapidly during the collision.</DIV>
<DIV> </DIV>
<DIV>Mass of the hammer: As Bernhard alluded, a heavier hammer =
will move
more slowly than a lighter hammer, given the same energy delivered at =
the
key. The collision will therefore be slower, the felt compression =
will be
slower, and so the ramping of force will be slower. A heavier =
hammer
should result, therefore, in a darker sound.</DIV>
<DIV> </DIV>
<DIV>Variation in felt consistency with depth into the hammer: If =
the
deeper felt is more tense, and the surface felt is well "sugar-coated," =
the
initial felt compression will not yield nearly so much ramping of force =
as the
deeper compression that follows. This arrangement will =
probably
produce fewer overtones than a tense surface with spongier felt =
underlying
it. The narrowest-band, darkest sounding collision would =
probably
occur with a slow ramp of force, gently accelerating, and then gently =
falling
off as the string builds velocity and the hammer loses velocity.</DIV>
<DIV> </DIV>
<DIV>Of course the latter factor would also impact the "linearity" of =
the
hammer. With a harder blow, felt deformation will go =
deeper into
the hammer and wider over the crown. The more quickly the =
felt
tension increases with increasing hammer depth, the more the sound would =
brighten with a hard blow. (Is this the "distortion" to which =
people
refer? If so, I submit that it's not distortion at all; rather, =
it's
merely a difference in the impulse spectrum.) </DIV>
<DIV> </DIV>
<DIV>Of course all this is quite complicated, and I suppose that's why =
it comes
down to more of an art than a science. Perhaps it's a bit like =
cooking, in
that a taste test will demand a bit more oregano or a pinch more =
salt.
Unlike cooking, there are undoubtedly tradeoffs in voicing.</DIV>
<DIV> </DIV>
<DIV>Anyway, as I said, I've merely scratched my head about this =
stuff. If
any of it resonates with the experienced voicing techs amongst you, I'd =
really
enjoy hearing your thoughts.</DIV>
<DIV> </DIV>
<DIV>Peace,</DIV>
<DIV>Sarah</DIV>
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