Ron N, Ron O,. and Del, ,
The quote from Seely is Chapter XI, section 98. The book I have is the
second (1935) edition. He has, at least,
another book on the same subject, which is ADVANCED STRENGTH OF MATERIALS. I've
not seen it but hope to acquire it. The book in its second edition reasons
mostly through the use of algebraic expressions, taking recourse to calculus only
in a limited fashion; this may be somewhat different as regards the other one.
Aware, as I have been that I am presenting a view that is substantially
different than that of many, I have repeatedly attempted to make clear that I am
not criticising the results obtained by the methods you refer to and which Ron
claims that I am eager to dismiss. On the contrary, I am eager to hear a piano in
which they have been employed. Even though I have not heard the sound of a piano
resulting from such methods my arguments are as to particulars of, apparently, the
models that have inspired these methods and the generalizations that have been
offered, it seems, from them. As I have said, I do believe it likely that they
be very nice sounding pianos, especially, again, as regards transition problems.
In my post on the Sound Waves thread, dated 16 Dec. 2001, one will find :
"I believe, however, judging from the quality of argument of its proponents
that when their newly
installed soundboards, rescaled and remanufactured, glistening in the light
are heard they probably sound pretty good, and may well be extremely good
particularly as regards transition problems, and I look forward to an
opportunity to hear one or more them. I applaud their efforts, respect them
for it, and am more than happy to see such things.
However, what I take issue with in the discussion of these subjects in
the last year or two is the implication that all other methods, including
the vast compendium of practical knowledge acquired through the painstaking
efforts of ten or fifteen generations who, in the aggregate have produced far
more pianos than the present generation, and certainly filled the world with
a variety of remarkable designs and hi-quality instruments which represent
original, remarkable and unique solutions to the problems of piano design
whatever they are but of which there must be some consensus as we are able to
recognize them as pianos, has in fact been superseded and the efforts of the
designers of the past are all obsolete, irrelevant and inferior."
It would obviously be foolish of me to claim any such inadequacy for the
results obtained by yourselves and Ron O., operating on what appears to be the
deflection model of soundboard behavior, as I have no direct data upon which to
base any observations at all. I do not. On the contrary, I am much more inclined
to believe that your results will produce very nice sounding pianos, for a variety
of reasons as I have said above. I think, that your methods are, however,
essentially traditional, regardless of the applicability of the model and your
claims of modernity notwithstanding. Insofar as scaling is concerned,
obviously, there is a new element due to the much greater computational ability
now routinely available. Its importance, although real, is generally exaggerated
from my point of view. I question at times the relative importance placed upon
this. I am grateful, as I am sure others are for your willingness to share your
views. Judging from the tenor of commentary which I have noted expressed here on
the list, and in your words and those of Ron O. you both have arrived,
independently at similar conclusions and have publicly claimed so. Part of the
issue here is the so-called modernity and exclusivity of these methods, to the
degree that I can infer them from the commentary on the list and the implied
futility of other approaches in analysis and design of pianos, particularly older
instruments.
I do not, as I said in the post "Confessions" install soundboards as I am
satisified with the results obtained by more conservative rebuilding techniques,
whether the operations have been performed by myself or by certain other
rebuilders. I have no objection whatsoever to those whose views are different;
should they wish to do so for whatever reason and firmly believe they should have
at it. As to its fundamental necessity, however, I am in substantial disagreement
with you that claim or imply that it is impossible or even difficult to achieve
similar results otherwise.
As to the usefulness of older soundboards, some of my view is expressed in
the post indicated above. However, in spite of an occasional disclaimer otherwise
the general tenor of commentary by those advocating your point of view is that
pianos are, essentially, left incomplete unless a new board is installed by the
methods which you share; that the scaling of past and present production is
everywhere obsolete, that older pianos are compromised by defective soundboards as
a result of accumulating compression set; that the sound of the instrument, holding
constant numerous other variables, will deteriorate thereby; that the
possibilities of improving sound occuring naturally in an aging instrument are
non-existent with regard to that part of the full sound of the instrument
attributable to the board only, and that pianos with traditional scales are,
somehow, inferior if not rescaled, among other things. Even though I find this
simply not to be the case in my own experience and that of others, should I then
simply disregard my own and their experience and concede these points to a kind of
authoritarian prescription of view? Particularly in regard to one whose model of
soundboard behavior appears, to me at least, substantially inadequate and of which
the proponents advocate something completely contrary to my own observations and
analysis? By this I mean the subject of the intense controvery of the last two or
three weeks, namely, bridge rocking and its implications.
It is easy to see, by calculating vectors, as I indicated earlier, that the
forces at work on the soundboard in reponse to the vibrations of strings SHOULD
produce a fluctuation in downbearing pressure; that this fluctuation SHOULD rock
the board, and then to arrive at the conclusion that such happens and that the
transfer of energy from string to board is essentially described by this model,
that is, that the rocking and flexing of the bridge is driving the soundboard. All
three of you have been explicit on this point. However, this is not the only way
to calculate such transfer of energy and is, in fact, correct only to describe the
deflection of the bridge/ board under a slow application of load such as applying
tension to the system after restringing. The description of a dynamic loading,
such as is the case with the vibrating strings requires a different method. This is
not a dogmatic theory as one of you claim, but an important subtlety of the Theory
of Elasticity. There are significant and profound implications for analysis of
piano design inherent in these differences.
John Delacour's model, for one, has plainly shown, that the bridge could
not possibly move simultaneously with the strings, due to inertia if nothing else.
He has shown that the bridge cannot instantaneously repond to the forces exerted on
it by the vibrating string and in so doing intimated substantially the difference
in dynamic and gradual loading. Your camp, apparently dismisses this as irrelevant
and in so dismissing this dismisses the critical distinctions of loading, something
I am not sure you will continue to insist upon.
In the function of the piano critical distinctions must be made if the
analysis is to be accurate. Some of these, in particular, are: the mechanical
stabilization of the vibrations of the string through creation of boundary
conditions, that is string terminations, which must impose conditions that force
the string to vibrate at a stable, constant frequency, as nearly as possible; the
acquisition of the energy by the string, which. also is a problem in dynamic
loading, the transduction of the energy of the vibrating string, its dispersion to
and radiation from the soundboard. These processes are best described by methods
appropriate to the nauture of loading, which is, as I say, a distinction long
absent here and in the PTG Journal.
Should the distinctions arising from the nature of loading be given their
due, then it will be seen that the acquisition and termination/ reflection of
energy in the string is a dynamic problem and the static loading method is
inadequate for its description, , the transduction of this energy is a dynamic
problem; the reflection of superposition of this energy in the soundboard is also a
dynamic problem and finally, the radiation of sound from the board into the air is
a problem partaking of both aspects: those that are dynamic problems are best
analized by the energy load method.
Taking note of the flexing of the board when a string is pressed by a
finger, the flexing of the engine block by hand pressure given by Ron O, the
requisite "physical, substantial motion," as being necessary to move the board, the
measured flexion of the plate and rim under static loading of ten pounds, and
such, proceeds, evidently, from a view of the flexion of the system as being
paramount. As these examples do not address the real question which is the
loading of the bridge/soundboard by the strings correctly, then so is their utility
as a refutation of the something that is in fact the consequence of this loading
suspect. Of course flexion is important for many reasons. But it is only
paramount in the context of what in reality it is - that is the flexural behavior
of the board operating in a diaphragmatic way to radiate sound. This is not
necessary, as you seem to believe for the system to acquire energy from the
strings. There is another question of equal importance and that is, as I have
said, the nature of the loading of the system by the strings. These things seem
plainly to me to have been considered heretofore part and parcel of the same
problem. My view is that they are not and that different methods are necessary
to properly understand them. This view is, as I have said earlier, well grounded
in physical prinicples.
On the one hand one must consider the vibratory behavior of the
soundboard/piano system; on the other one must consider the mechanism of transfer
of energy from the strings to the radiating system. These functions are distinct.
I have called the transfer function, if you will, stress transduction. Label it
as you will, it nevertheless exists. In all of the examples offered by you and
your co-proponents a gradual load is applied hence its relevance to the loading
of the bridge/soundboard by the strings is questionable as are the conclusions
drawn thereby.
What these examples indicate is a miscontruction of the concepts underlying
these processes, at least from my point of view, and an erroneous imputation of
the inseparability of these processes when, they are, in fact, necessarily
separate due to the nature of loading. To state the matter simply: the
soundboard/bridge/string interaction has a dual function - on the one hand it must
terminate the speaking length of the string and provide the mechanism for
transduction of the energy of the vibrating string; on the other it must then
disperse this acoustic pressure, stress wave, strain energy (however one wishes)
through the soundboard for superposition and radiation to occur. These functions
are mutually contrary - that is one may be made greatly efficient at the expense
of the other or vice versa. The way this is resolved is part of the characteristic
sound produced by a given manufacturer. Mechanical loading of the soundboard
system by the strings and the ensuing deflection is distinct from the dynamic
loading applied by the string under vibration. This is the critical point and if
properly understood the local stress and deformation of the areas in contact, that
is the localized mutual strain of the string, bridge and bridge pin is not
synonymous with a generalized, bodily, physical, substantial motion such as I take
rocking must be for it to be capable of physically, substantially moving the
soundboard as you claim. In point of fact not only is it not necessary to
energize the system but would be detrimental if it existed in any appreciable
degree, something, not to be repetitious, I have asserted before.
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 these relations is the
one used in energy loading and that is the modulus of resilience which is half of
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 piano
soundboard assemblies are profound as it can be used as a predictor for the
absorbtion of energy or energy resistance of a member and therefore models the
transfer relations between string and bridge, among others.
Critical implications of the modulus of resilience and energy loading arise
in comparison to the methods of static loading. Static loading, whether flexion
or axial, manner 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 on the maximum unit-stress,
s, but also (1) on the distribution of the stress through the body, since the
energy absorbed by a given unit of volume is ((the modulus of resilience is
quoted,rh)), and hence depends on the degree to which that VOLUME ((caps mine rh))
is stressed and,(2) 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 the 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 rim 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 absorbtive 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.
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 the 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 under struts, etc.
It is plainly evident to me, being aware of these distinctions and having
seen, played, rebuilt and performed upon thousands of older pianos, that the
designers of these so-called obsolete pianos, in particular the high quality ones,
of the past had an understanding of these matters, and of others pertinent things
not yet discussed, which appears not to have been taken into account in the view
of some participating in this discussion, and that they understood other
implications of the nature of loading whether calculated or not, and that they did
not consider these dogmatic irrelevant theories, and incorporated them into the
the designs of the instruments they produced.
Regards, Robin Hufford
> >These involve calculation of the forces and displacements using
> >vector
> >methods as you also indicate below: a part of this is the application of
> these
> >methods to calculate the varying downbearing load on the bridge and soundboard
> >produced as you and others say, through cyclic behavior of the strings;
> >calculations would indicate flexion of the bridge under the strings as being
> >the
> >principal motion along with that of "fore and aft:" and otherwise as Del has
> >indicated. The use of deflection mechanics and various forms of the flexure
> >formula are employed enabling one to calculate, approximately, these
> >deflections
> >or to design new soundboards, rib scalings, string scalings, bridges designs,
> >etc. etc. Inherent in this model is the notion of motion(!) at the bridge,
> >its
> >interactive behavior with the strings,(compliance); and the idea that the
> >bridge
> >then moves the soundboard hence sound. This method is presented as the best
> >thing
> >since sliced bread, entirely novel and of such import as to completely
> >supersede
> >the efforts of all previous periods of piano work.
>
> In the entire bulk of any of the writing that Del, Ron O, or I have
> presented on this list or anywhere else that I know of, you will not find
> anything remotely resembling a claim that any soundboard motion other than
> simple beam deflection of the ribs from static downbearing load is
> calculated by any of the three of us to design soundboards. I wrote that I
> not only didn't know, but didn't care what contribution to the overall
> sound a rocking motion in the bridge produced. I currently have no way to
> quantify it, encourage it, or prevent it in soundboard design, so it is
> beyond my control. It is not even considered in my design process. It
> happens, so be it. Do I want it to happen or not, and to what degree?
> Lacking the means to quantify it, I don't know. I've said something to this
> effect more than once already.
>
> And have you actually heard any of these designs you are so quick to
> dismiss? Have you designed and built a few soundboards of your own using
> the ideas and assembly and crowning methods we have discussed on the list?
> If we hadn't found our concepts and methods to produce what we consider
> more dependably high performance results than the traditional concepts and
> methods we all started out with, you would never have heard of them. The
> published information didn't have to be shared.
>
> > However, the use of this method in the analysis of the dynamics of
> >energy
> >transfer from string to bridge/soundboard and from soundboard to air, and the
> >resultant vibration of members of the system , is inadequate, except in
> >the most
> >vague and diffuse sense, to well describe the processes involved. It is the
> >nature of the load itself in the system, in this case a piano, which
> determines
> >how best to approach such an analysis.
>
> And as I have said, direct measurement with appropriate equipment is the
> only way to prove anything. Even then, there will be another crop of more
> minute hairs to split by opinion.
>
> > The rate of loading is a critical matter to these issues. Relatively
> >slowly
> >applied loads result in stress/strain relationships that are susceptible to
> >analysis using the methods of statics which the deflection model employs; it
> >then
> >works well. However, in rapid loading such as, I believe, occurs in
> >connection
> >with a vibrating string transfering energy, that is an energy load, into a
> >bridge/soundboard assembly, these stress/strain relationships are not the
> same,
> >the analysis is incorrect and its conclusions such as bridge rocking, bridge
> >motion, however phrased, are flawed, even if they can be calculated.
>
> I addressed this with the blanket analogy.
>
> >requires methods that are somewhat different. To quote from THE
> RESISTANCE OF
> >MATERIALS by Seely, second edition, "the dimensions of the resisting
> member and
> >the properties of the material in the member that give it maximum resistance
> >to an
> >energy load are quite different from those that give the member maximum
> >resistance
> >to a static load". This matter has been thoroughly confused, as far as I can
> >see, for some years now on this list.
>
> Again, see the blanket analogy.
>
> By the way, what's the chapter and heading reference on the quote from the
> Seely?
>
> Ron N
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