bridges/seating

[Ron Nossaman]

Jon & all,

Re Bob Scott: So single direction terminations at agraff and capo wouldn't=
 cause false beats by virtue of not being on the sound production end of the=
 string huh? OK, fair enough, but I just went out in the shop for more=
 ammunition. I've got a Baldwin SF ready to go with re-notched bridges, new=
 bridge pins (CA'd in) sounds clean and nice (except for final tuning) from=
 one end to the other. OK, here goes. With back lighting along the strings,=
 it's obvious that the string excursion is not purely vertical. They go all=
 over the place without false beats. Doesn't compute. I'm still holding out=
 for the loose bridge pin theory because with the string stuck off the=
 bridge, you wouldn't have the horizontal motion anchor of the bridge=
 surface allowing the pin to flex in a loose hole with the horizontal phase=
 of string excursion. Seating the string on the bridge would help in the=
 cases where the resulting horizontal friction overcomes the leverage of=
 horizontal string movement. What do you think?

Regards, Ron Nossaman  =20

=20


At 10:43 AM 4/13/97 -0400, you wrote:
>This appeared in rmmp. back in December.=20
>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>Bob Scott wrote:
>
>An easy way to understand false beats is to imagine the piano string
>just after it is struck.  It is vibrating essentially up and down.
>But it doesn't continue to vibrate that way.  It begins drifting
>towards a side-to-side vibration.  When it vibrates like that there is
>less coupling to the sound board.  Then the vibration continues to
>drift to an up and down motion - this time upside down from the
>original motion.  Now it is producing sound 180 degrees out of phase
>with what it was doing originally.  If it goes through this cycle once
>per second you will hear a once per second fluctuation in the loudness
>of the note.  It is not like vibrato, which is a fluctuation in the
>pitch of a note.  Now what makes the string decide to start vibrating
>sideways?  Lots of various imperfections in the string or its seating
>can cause that.  But the effect is a cyclic fluctuation in the
>loudness of the note which is indistinguishable from the sound made
>from two strings tuned slightly off from each other.
>
>   -Bob Scott  (rscott@wwnet.com)
>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>At 03:39 AM 4/13/97 +0000, you wrote:
>>Ron & list:
>>
>>I'm on my way out of town for two weeks, but this was an interesting=
 thread,
>>and I wanted to at least give a swag, in case the thread has died by the=
 time I
>>get back.
>>Frictional force is equal to the normal force times the coefficient of
>>friction (Ff=3DFn x u).  I'm not a piano technician, so I will assume some
>>values for discussion purposes, but I think the logic will hold.  The
>>downbearing force is a function of=20
>>the angle across the bridge versus the string tension.  The side force
>>against the bridge pin is a function of the side angle against the pin and
>>the string tension.
>>The string tension being a constant for a particular string the forces
>>involved (down
>>force versus side force against the bridge pin) are a ratio of the angles
>>down and sideways on the pin.  I looked at my piano and it looks like
>>typical ratios would be:
>>down force .1 inch down over a 30 inch length or a tangent of 1/300 versus=
 a
>>side angle force of .1 inch sideways over a .75 inch length or a tangent=
 of
>>1/7.5 (depending of course on what note you are looking at).  Please=20
>>note that I am just wildly estimating, but the differences are so great=
 that
>>the argument will hold with a large estimation error.   Anyway..... the
>>sideward force on
>>the bridge pin relative to the down force will be a ratio of the above=
 numbers.
>>In our hypothetical example above, down force would only be 7.5/300 of the
>>side force on the pin.  With a friction coefficient of approximately .1 to
>>.15 for lubricated copper alloy versus steel, it looks like the bridge=
 pins
>>could definitely hold a displaced string off of the bridge, even with the
>>negative angle the bridge pins have.  If this thread is still going when I
>>get back I'll take some measurements, and can calculate the angle a bridge
>>pin would have to be at to prevent this from happening. Of course a
>>microscopic burr or imperfection on the pin will also lead towards causing
>>the string to stay up off of the bridge when displaced.
>>
>>As to this causing false beats, I don't pretend to know the answer; but=
 will
>>ask a
>>naive question (I don't have any acoustic background knowledge):  When the
>>string is seated against the bridge it has one degree of freedom (it can
>>move up and down, it seems sideways would be rapidly damped).  If it is=
 held
>>off the bridge up on the pin it can vibrate in a more 360 degree mode -
>>could this cause false beats?)
>>
>>Well, I've got to run - please forgive me for the above "off the top of my
>>head"=20
>>comments;  I like to think things through more thoroughly, but wanted to
>>answer before I left!
>>
>>                                                   Regards,  Mike =20

<****** history deleted ******> Ron Nossaman