Phil,
I was aware they were sharing the view of some authorities in the field, even
though it had been claimed that these views were arrived at independently.
Incidentally, as I have said, I once was, at least to some degree, a proponent of this
view myself but certain problems left this an unsatisfactory answer as far as I was
concerned and led me to other views. I am quite behind on my reading on the posts on
this matter for this week, even though I have just hurriedly run through some them to
get a sense of their contents. I will post other observations about this matter and
try, as best I can, to answer the questions you posted for me, I think, later this week,
as I fear I will have to be out of town all weekend on business. I want to, briefly,
touch upon an illustrative point which, I am sure will be ignored by many, or possibly
create more howls of outraged commentary that this has no connection to the
soundboard/string interface even though it is an illustration of a general principle.
There is a problem that can occur in an internal combustion engine that will
illustrate some of the importance that must be laced upon loading. When an engine in
some cars is revved up or redlined to about 6000 RPM., a condition can be created
which the valves are said to "float". Normally, the valves are connected through
various linkages to the crankshaft. Motion of the piston drives the crank to which a
sprocket or pulley is attached. The timing chain or belt drives the cam pulley and
camshaft which in turn, drive the rocker arms and they, in turn, move the valves
against at spring which results in them opening or closing, as the case may be in the
cylinder. This is the normal process by which the valves are opened or closed and it is
easy to see the straightforward, linear relation between the angle of rotation of the
crankshaft and the mechanically imposed position of the remaining components of the
valve train system.
This system operates, of course, by direct mechanical connections created in
various ways which impose a dependency and interconnectedness of one part of the system
on the other. These ultimately push against the valve spring which provides the
restoring force to return the valve to a closed position. The harmonic motion, as it
were, of the piston drives the system and results in an output that is motion of the
valves that is also harmonic, although, or course, the periods of the two are not the
same. If you turn the crank you will move a valve, very simple, very straightforward.
So far so good.
However, if is possible to perturb this simple relationship and, in fact, the
timing relationship established between the crank and valves is progressively altered as
the RPM of the engine is increased. That is, as the rate of loading of the valve train
by the pistons increases there is a progressively non linear reponse in the system due
to inertia of the parts and the inability of the spring to maintain the original
relative conformations of the parts one to another. Eventually, a point is reached
where the valves are floating. When this happens the pistons will come up and hit the
valves, who are no longer able to move fast enough to get out of the way and are bent
and damaged as a result.
The point I am making is that one has a simple, linear system which progressively
becomes non-linear as the rate of loading increases. Far greater forces are at work in
an engine than those putative "forces" said to be moving the soundboard directly as a
result of the transverse behavior on the string, . Stipulating that these "forces" in a
piano are in fact moving the soundboard, then then their magnitudes relative to that
which they must operate upon, namely, the soundboard/bridge/rim system are greatly
different from the relative magnitudes of the piston and valve train, the gap is
greater. The valve train system, which, even though operating at vastly greater levels
of energy overall than those of the soundboard system, nevertheless, exhibits increasing
non-linearity to the point that the system ceases to operate roughly somewhere in the
region of a mere 100 cycles per second, a frequency that is a pittance to a piano.
Those that have complete faith and make a religion of the view that the board
drives the piano, linearly, that is at identical frequencies as the standing waves on
the string, and causes a flexing motion of the bridge which directly imposes upon the
soundboard these frequencies should test their generalized theories of linearity by
going out and revving up the engines in their Mercedes and Jaguars, holding the RPM up
high enough and observing the results. A four or five thousand dollar repair bill will
likely be far more persuasive than anything I could have to say.
Incidentally, I don't believe that I have implied or said anything relative to the
proponents of the contrary view of the nature as suggested by you below. Nor would I.
In fact, I have been insistent in urging civilty in this controversy as I know emotions
are necessarily attached to these opinions.
As to the question of whether my view is right or wrong, in the context of this
discussion,.this is, as I have said, of no consequence to me. I simply prefer to
understand the facts and their implications as they are. Were my view incorrect, then I
would prefer to be brought to understand that by recourse to facts and reasoned
commentary, something in poor supply heretofore; an involuntary change of view would
then ensue. However, loud shouting, petty inuendo, patronizing lectures as to the
nature of science and the outraged insistence upon the sanctity and inviolabilty of
one's view, however buttressed by others opinions, cannot successfully masquerade
itself, to me at least, as reasoned argument. The invigorating and instructive aspect
of this discussion which by its clarification of ideas and analysis, should lead to a
better understanding, has only strengthened my belief that the model of
soundboard/bridge behavior propounded by the Ripple Theorists, a term to which I would
also happily claim credit for although it did not originate with me, is wrong.
Regards, Robin Hufford
Phillip L Ford wrote:
> On Wed, 23 Jan 2002 01:07:22
> Robin Hufford wrote:
> > I have owned the Five Lectures on the Acoustics of the Piano for some 8 or 10
> >years now, and been through it many times.
>
> > In general, though, the tenor of the book, here and there when the
> >subject is taken up, is that the bridge is moved by the strings. Some may consider
> >this temerity on my part, but my position was taken with a ready familiarity to
> >the views expressed in this collection of lectures, and I maintain it still.
>
> I do think it's temerity on your part. But, I don't have a problem with that.
>
> > I am sure many of the conventional thinkers so antagonized by any other
> >point of view will find themselves vindicated here; they could have quoted from
> >the book to support their position that some motion occured at the bridge; but
> >that would not have been convincing to me as to the origin, periodicity and extent
> >of this motion and the nature of energy transfer at the string/bridge interface.
>
> >Regards, Robin Hufford
>
> I don't think that the conventional thinkers were antagonized by another point of
> view. I think they were antagonized by the tone of some of the posts on this thread
> and by the implication or outright statement that they were stupid or deluded for
> holding their point of view. Now it seems that they were simply sharing the view
> held by (at least some) acknowledged authorities in the field.
>
> Phil F
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