At 6:34 PM +1100 12/26/01, Ron Overs wrote:
>I haven't got figures for bridge rocking at present. However, since
>this appears to have become such a hot issue, I will try to devote
>some attention to it when I return from holidays (by getting some
>real figures). I have no desire to get into a full blown debate on
>the issue since I am not concerned if others don't share my view,
>but I would be prepared to derive a few figures on the matter.
Ron, this is not the "hot issue" at all. If you have read this
thread from the beginning, you will see that I have provided a simple
demonstration with a graphic illustration showing that the bridge can
indeed rock. Here is an extract from that message
At 10:55 AM +0000 12/24/01, John Delacour wrote:
>This message shows a model that demonstrates very simply, without
>lasers or pianos, exactly the phenomenon you are talking about,
>about which there is no argument. Any continuous force, however
>slight, acting on a system in equilibrium will, by well-known
>physical laws, cause that system to change position until an equal
>and opposite force is encountered.
>
>I have said from the outset and have been forced to repeat numerous
>times, in response to suggestions that I have denied it, that the
>movement of the bridge occurs. By the same token the bridge in
>rocking will obey the same physical laws. How can you still pretend
>that there is any argument about this.
>
>My model was designed so that those unfortunate people without
>lasers and mirrors could see for themselves what it is not possible
>to see with the naked eye and furthermore carry out tests that would
>be impossible on a strung grand without highly sophisticated
>measuring equipment.
Similarly I would ask you not to pretend there is an argument about
the rockability of the bridge. In this context it would be pointless
to provide exact figures, which in any case would be practically
impossible to obtain. What I think I have demonstrated is a general
principle, which can be observed directly in the simplified model,
that the frequency at which the bridge rocks, however slightly, bears
no relation to the frequency of the string's vibrations
RO
>...the apparent stiffness of the bridge will not prevent it from
>rocking as some have asserted (particularly if the bridge height is
>not too low). A bridge will 'rock' just as a relatively stiff rim
>will flex...One could conclude from this that rigidity is and will
>always be relative.
Ditto.
At 4:15 PM +0000 12/25/01, John Delacour wrote:
>there is no dispute concerning the flexibility (i.e. mobility) of
>the soundboard/rib/bridge system and that the degree of flexibility
>at different locations is critical to the efficient production of
>the sound and acoustic radiation of the various frequencies.
RO:
> Therefore, when the vibrating string goes through a cycle, its
>tension (which varies slightly as the speaking length is offset from
>its resting position) will cause the bridge to flex slightly
>backwards and forwards (in a vector direction parallel to the axis
>of the speaking length) in response to the speaking length
>deflection also. Because the vector force on the sound board panel
>is a product of the string tension times the SIN of the string
>deflection angle, the downbearing force will vary similarly to that
>of the speaking length during the cycle. Therefore, the board will
>respond to the position of the speaking length string segment at
>each point in the cycle. This is I believe the most important
>physical factor which causes the sound board to respond to the
>vibration of the speaking length segment.
At last some meat! This finally is what the argument IS about. That
the downbearing in the static system is as you say is undisputable
and a matter of the simplest trigonometry, so I'll pass that over.
If the tension on the speaking length is increased or the downbearing
angle increased, again it is quite obvious that there will be
additional downward force on the system tending to compress it and
also a force acting at the bridge tending to tip it towards the
speaking length. The first purpose of my model was to provide a
visual demonstration of this latter fact, as though any were needed.
So much for that ... now for the points at issue:
a) "the board will respond to the position of
the speaking length string segment at each
point in the cycle."
Using my model to demonstrate this visually or imagining the same in
the piano itself; if I pull the string up and down slowly it is clear
that two things will happen: 1) the tension of the speaking length
will rise and fall and tend to tip the bridge back and forth, and 2)
the downward pressure on the bridge will rise and fall; though these
changes will not be quite instantaneous.
The faster I pull the string up and down, the more apparent will
become the fact that the phenomena are not instantaneous and it will
be seen that the fluctuations in the bridge position (as well as the
up and down position) do not follow the movements of the string. If
there were no mass and no inertia in the system, they would, but we
are dealing with a real physical system.
There is thus a _resistance_ on the part of the bridge to respond to
the forces imposed on it by the movements of the string and it takes
a measurable time for a state of equilibrium to establish itself.
Already with a very slow frequency of manual movement of the string,
this resistance will be apparent. If I now twang the string (of the
model) and cause it to move at an audible frequency, it will be seen
that the bridge is in no way "responding to the position of the
speaking length at each point in the cycle" as you say. Instead it
is rocking in another fashion which is determined by _all_ the forces
acting on it according to its mass and inertia. The forces imposed
by the string's tension and position are introducing a stress; in
other words the bridge and the string are quite unable to agree about
the frequency of their respective oscillations.
The main purpose of my model ends there, but its utility can be
extended a little further. If the "rocking bridge" is tightened up
by some means, either by adding weight to it or sticking the curved
base to a thinkness of rubber or by adding more strings, it will be
observed that it will become less mobile and that the string will
oscillate for a longer time. However, no matter how much I stiffen
up the bridge, it will never rock at the same frequency as the string.
To translate the observable model to a real piano in which the same
phenomena are at work, the movements of the bridge/soundboard will
NOT "respond to the position of
the speaking length string segment at each point in the cycle." What
will cause the sound excited in the string to propagate through the
system is quite the opposite of what you say. The more
"disagreement" there is between the string and the bridge, the more
stress will exist between them, to use a figurative metaphor, and
this stress will be exerted at the point where they meet, which is to
say at the termination of the speaking length.
The above resistance on the part of the bridge/soundboard to conform
to the dictates of the string constitutes acoustic impedance --
resistance and impedance both having originally similar meaning, but
I have used the word resistance simply to make the idea more
generally understandable.
While the bridge is flexible and mobile, it is unable to impede in
any useful way the movements that the string is trying to dictate.
Everything is flapping about and neither the string nor the bridge is
getting its own way.
As the system is stiffened up (I am deliberately using language that
I hope is generally understandable) so stress or pressure increases
at the point where the string meets the bridge. The pressure
increases and the movement decreases. It is the ratio between these
two quantities that constitutes "acoustic impedance" and any movement
of the bridge/soundboard system plays no part in the propagation of
the sound except in so far as it creates the necessary environment
for that propagation to take place. The sound is propagated through
the bridge and the soundboard in the same way as sound is always
propagated and the bodily movement of things is not involved.
RO:
>Now Robin, I do not at this time have numbers to support my
>philosophy here....I suspect that Charles Darwin had a strong idea
>...voyage on the Beagle ... I have carried the 'rocking' theory with
>me for at least fifteen years ... Even Bösendorfer seem to be
>demonstrating an understanding of the principle in their later
>pianos by undercutting their dog-leg breaks to allow a more uniform
>bridge stiffness. The 'dog-leg's wider footprint, if not undercut,
>will tend to 'close' the sound at the breaks (this is just one more
>piece of evidence which supports the bridge-rocking theory - perhaps
>not to everybody's satisfaction but ah well).
Again you are claiming some denial that does not exist! If
Bösendorfer have only just discovered this, then it might explain a
lot about the performance of their pianos. These principles have
been practised by good makers for well over a century. It's a pity I
have to be constantly wasting time refuting false imputations....
At 4:15 PM +0000 12/25/01, John Delacour wrote:
>I think there is no dispute concerning the flexibility (i.e.
>mobility) of the soundboard/rib/bridge system and that the degree of
>flexibility at different locations is critical to the efficient
>production of the sound and acoustic radiation of the various
>frequencies.
At 12:24 AM +0000 12/8/01, John Delacour wrote:
>And when the treble bar of an upright necessitates the cutting away
>of the bridge, we need to make up for this either behind the board
>or by splinting (rare) the bridge.
>
>We cut large holes in bass bridges and cant the long bridge in the treble etc.
At 9:24 PM +0000 12/18/01, John Delacour wrote:
>If the problem is in the bridge, then there are relatively simple
>tricks to try with laths or cutting away, but these are more radical
>approaches, and the strings themselves should be optimized first.
At 5:55 PM +0000 12/2/01, John Delacour wrote:
>In most straight-strung grands and early overstrungs you will find
>the edge of the board detached from the rim for a length of a foot
>or so and provided with a lath of maple or beech for firmness. This
>frees up the board to respond better to the low notes on the bass
>bridge which, or whose apron, is fixed quite near the rim. In my
>experience the effect of this is wholly successful. 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.
JD
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