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Dale<br>
There is just such a relationship and it is no a mystery,
although, as far as I can tell it is neither comprehended nor taken
into account in the flexural view of soundboard function. This factor
is precisely what I suggested be taken into account in a post put up
three years ago during the debate on the behavior of soundboards,
entitled Rocking Bridges, Dec 30, 2001, in commentary on the Modulus
of Resilience, which was ignored, or misunderstood as an impedance
matter which is not the case. In my opinion, one should view the
soundboard, as I have repeatedly urged, not through the prism of
deflection mechanics or cyclic static pressures but, rather, as an
energy absorbtive, concentrating and transmitting medium, the energy
absorbed being the output of the string, which is a pressure excitation
at the terminations. <br>
In my opinion, (and, I am going to drop this phrase through the
remainer of this post although it all should be taken with this
qualification) the soundboard should be seen as a device which has
several functions. These functions themselves are not necessarily
complementary and, in fact, are perhaps somewhat contradictary. How
they are adjusted, vis a vis, one another is the particular solution
found by any given design approach. At one and the same time, the
board, bridge and ribs together, must be stiff enough to ensure loop
stability on the strings which motion of the terminations past certain
limits would preclude; at the same time, it must absorb this energy,
which is just sound, another problem in and of itself;, it must then
concentrate the sound in ways that build up the amplitude and, finally,
transfer momentum out of the system as acoustic radiation. <br>
I will not repeat here the many arguments I have made for the
nature of motion at the bridge and the energy loading that occurs
there, they are, likely, well known. <br>
What follows will be a synoptic treatment of this entire question
which will be published in substantially greater detail later this
year, elsewhere. <br>
There are critical distinctions that arise, as I said in the post
referred to above, from the nature of loading. These were dismissed as
mere impedance issues. Not so. <br>
The absorption by the soundboard of this energy is a function of
its energy resistance. Quoting from the post referred to above, which
I will then elaborate upon:<br>
"The approach taken by your school of thought is generally, as
far as I can tell, expressed in terms of mass and stiffness, flexion,
and the ratio of stress to strain, that is the modulus of
elasticity.(here I can't render appropriate notation due to the
limitations of the keyboard I am using); These are the terms of
deflection mechanics, among others. When applied to the transfer
relations between string and bridge they are inadequate. A better
measure of the relations is the one used in energy loading and that is
the modulus of resilience which is half the quotient of the square of
the stress to the modulus of elasticity. Although the modulus of
resilience is in fact a measure of how much energy is absorbed per unit
volume of the material when the material is stressed to the
proportional limit, its implications for the design and manufacture or
remanufacture of soundboards are profound as it can be used as a
predictor for the absorbion of energy or energy resistance of a member
and therefore models the transfer relations between string and bridge,
among others. <br>
Critical implications of the modulus of resilience and energy
loading arise in comparison to those of static loading. Static
loading, whether flexion or axial depends upon the maximum stress
developed, energy loading is substantially different, (quoting from
Seely) " the resistance... of the bar((bridge, rh) to an energy
load......depends not only the maximum unit-stress, s, but also, (1) on
the distribution of stress through the body, since the energy absorbed
by a given unit volume is ((the modulus of resilience is quoted, rh)),
and hence depends upon the degree to which that VOLUME (caps mine, rh)
is stressed, and (2),<br>
and on the number of units of volume of material in the bar ((bridge,
rh)). What this means to those that have not grasped it is that the
transfer relations between string and bridge/soundboard are a function
of the VOLUME and the DISTRIBUTION of stress in the bridge itself, and
not simply the stiffness and mass. The undercutting of the bridge,
thinning of soundboards, tapering of ribs, inner rib angles, etc. are
in fact methods of volume and stress control the purpose of which is to
equalize the stress distribution in the material and thereby optimize
its energy absorptive capacity or control its energy resistance. As
far as I can see, this should be a matter dear to the heart of anyone
attempting to design, remanufacture, or otherwise modify a piano
soundboard.<br>
To further quote from Seely, "...show that the material in a beam
having a constant cross-section is inefficient in absorbing energy.
For example,........a rectangular beam, when loaded at mid-span with a
concentrated load, can absorb only one-ninth as much energy as the
same beam could absorb if all the material in the beam were stressed
to the same degree." The requirement for stress-equalization, hence
control of energy resistance, can be expressed as taper of ribbing,
undercutting of bridges, notching of struts, etc.<br>
It is absolutely critical to understand that energy absorption
under dynamic loading, as indicated above, is functionally different
from that of static loading, one being dependant upon the maximum
stress developed, the other the nature of the stress distribution, a
more complex formulation requiring cognizance of the volume and stress
together. This is, at the least, one important relationship between
mass/stiffness/soundboard area which fundamentally influences the tonal
qualities of an instrument, to use Ron O.'s words. <br>
It is often maintained, erroneously in my view, that the loudness
or softness of a given note is some function of an "impedance" problem,
and that, generally, this is true for the entire system. A much better
view would be to see the entire piano structure as part of a completely
whole, organic system, coupled in a dynamic manner, loaded with
acoustic energy, and subjected to a forced vibration. The energy of
these vibrations may find sinks where it is lost through excessive
damping, or, it may superpose in ways which build it up in the
soundboard which, itself, is the greatest sink of all. One can
evaluate the soundfield in a piano soundboard, the rim, or the plate
through various means. A simple way is to use the mechanic's
stethoscope I suggested several years ago and explore the distribution
of sound. The sound produced by the string is distributed to a
greater or lesser degree, throughout the entire piano structure, which
itself is also coupled to the floor, air, and, generally, the world.
Piano design has attempted to control the distribution and
superposition of these forced vibrations, particularly by attempting
to control energy absorption, or its inverse, energy resistance, in the
soundboard, bridge, ribs and rim, using just the principles described
above, whether conscious or not. <br>
The sound does indeed traveld, as structure-borne-sound, through
the entirety of the system, that is all components of the piano but,
particularly through the soundboard, rim and plate. Good design will
attempt to direct sound back into the soundboard where it may assist in
building up the sound pressure level. The acoustic dowel is a design
feature that attempts to facilitate this process. This is, regardless
of any outlandish sales claims arising from this process, the dreaded
"Circle of Sound", and, as such, is a real process. That such things
will happen is a commonplace notion, just taken for granted, a
complete given, and is the norm in sonic analysis. It is astonishing
that technicians, who really should know better, confuse this process,
one indubitably real, with their antagonism for what may be exaggerated
claims by certain factories. <br>
The modulus of resilience is a measure, as I have indicated
before, of the amount of energy a structure may absorb up to the
proportional limit and is, in a way, inadequate for the
structure-borne- sound found in a piano, as we are not looking to take
the energy level to such a point. Its usefulness, however, lies in the
perspective it affords. That is, what are the capabilties of a medium
which influence its ability to absorb and transmit energy, in this
case, acoustic energy and how does one maximize this. <br>
The soundboard can be made more effective at acquiring energy from
the string, and, further, reacquiring it numerous times from the rim
and plate by control of energy resistance and stress distribution, and,
in particular, the equality of stress distribution. Consider an
unribbed soundboard: it has a kind of moisture induced stress to some
degree or the other. Dry it to some point and rib it, either by rib
crowning or compression crowning, a new level of stress, glue it in,
now a different distribution and then press it down by string bearing a
further change in stress. I think it plainly evident piano design has
evolved methods to impart certain stresses into the system for several
reasons, for example, equalization for purposes of acoustic absorption,
but also mechanical reasons such as the need to maintain tuning
stability, and string termination. <br>
Crown, downbearing pressure, board thinning, ribbing, rib-tapering
and inner rim angling achieve a number of these objectives
simultaneously. That is, they can all be made to work together to give
the best chance for equality of stress distribution. If terminations
are to be secure there must be some offset allowed, were there no need
for it acoustically, to counteract the relaxation, some degree of
compression set, in my opinion much smaller than generally claimed,
and plastic reponse of the board after loading by the strings. This is
an utterly paramount, particularly as regards terminations, but,
nevertheless mechanical consideration in a new soundboard, but which,
as most know, must be accomplished effectively if there is to be a
functional soundboard for any length of time after manufacture. This
is another consideration in design discussions, which seems to have
been generally disregarded here on the list. <br>
As I have said above these factors convienently serve control of
energy resistance, itself the heart of acoustic function, which
modulates the nature, along with reflection and superposition, of the
coupled string/soundboard/ rim/case system as well. Where energy
resistance is lessened the system easily absorbs energy from the string
and feeds this energy right back into the vibrating string itself, the
two become a dynamic whole. This, again, is a kind of circle of
sound. It is easily seen that it differs entirely from attributing
power and sustain solely to the degree of transmittivity and
reflectivity resulting from wave activity at an impedance discontinuity
which is expressed by the impedance ratio of the two media.
Obviously, the interplay of these variables, alone, affords a
considerable range of design flexibility, as long as energy resistance
is controlled, which, again, requires equalization of stress
distribution, that is manipulation of both volume and stress levels in
a coordinated fashion. As volume varies as the cube slight changes
in dimension, for example, the soundboard, ribbing, or rib taper, may
cause substantial effects, equalities or inequalities, in the stress
distribution, for better or worse insofar as absorption is concerned.
<br>
The board, of course is highly anistropic, which requires
structural alterations the purposes of which are also those of energy
control, such as board thinning, ribs and rib tapering. These, along
with downbearing pressure allow for some level of equalization of
stress. It is entirely possible, as crown lessens, where such does
occur, over time, that these changes actually result in more, rather
than less, equalization, with a probable result being a better sound,
and this may account for the better sound some find in old boards. I
don't urge this as a mechanism I am certain of but, merely, a possible
explanation. Ribbing, with or without crown, lessens the anistropy
of the board. As the speed of sound is much greater along the grain
the ribs, crossing the grain as they do, in at least one functional
sense, lessen this anistropy by providing a sound path which allows the
sound to more effectively travel into the board, where it does it's
superpositional thing, than it could do by simply crossing the grain,
arriving late and attenuated. As it is late, I will not, at the
moment take up the last of the functions I indicated, which is acoustic
radiation from the board itself. <br>
Regards, Robin Hufford <br>
<br>
<a class="moz-txt-link-abbreviated" href="mailto:Erwinspiano@aol.com">Erwinspiano@aol.com</a> wrote:<br>
<br>
<blockquote type="cite" cite="mida1.56dc1f41.2f26c8e1@aol.com">
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<div> Ron</div>
<div> Yes & I happen to agree with you. Mysteries are after
all............still mysteries?</div>
<div> Dale</div>
<blockquote
style="border-left: 2px solid blue; padding-left: 5px; margin-left: 5px;"><font
style="background-color: transparent;" face="Arial" color="#000000"
size="2">I strongly suspect that there is some sort of important
relationship <br>
between mass/stiffness/soundboard area which fundamentally influences <br>
the tonal qualities of an instrument. Please don't ask me to <br>
elaborate on this matter at this time. This theory remains just that, <br>
at present.<br>
<br>
Ron O.<br>
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