Counter bearing treatment

[Richard Brekne]

Roger Jolly wrote:

> Hi Ron,
>            I've done quite a few measurements on the string coupling effect.
> When an average 3 string unison is tuned for full blush (RCT) on each
> individual string,
> 2 strings played together will show about 0.3 cent flat, 3 strings will
> show 0.5 cent flat.
> I'm not so sure what the imformation is telling me.
> Regards Roger

Grin.. I will venture a few thoughts on this matter if I may be so bold. A few
things are known about this pitch drop, and what I know about these things is
limited to reading about the following factors.



The mode of vibration of the two strings (horizontal vs vertical) is and
important factor. If a second string vibrates asymetrically with the first, then
you get longer decay time, and reduced volume, if they vibrate sysmetrically
then the oposite happens. Also if a second string is allowed to vibrate in
sympathy, but is not struck then there will be a strong tendency towards an
asymetrical mode of vibration.

To some degree the horizontal mode of vibration is determined by the bridge.
Depending on the way its built, some lend themselves better to horizontal motion
of strings then others, which in turn will effect the amount of asymetrical
coupling possible.

A bridge which is "springy" in nature (relatively conducive to sideways motion)
lowers the frequency of a single string. A massy bridge or support does the
opposite. (this also affects the behaviour of longitudenal modes if I am not
mistaken) A support or bridge that is just plain resistive, the frequency of the
string is unneffected, but it will decay quicker.

The presence of a second string effects the imedance of the bridge as seen by
the first string, and this results in a change of frequency in the first string,
depending largely on how far out of tune the two strings are. In reality, it is
no longer the frequency of the first string we are talking about, rather the
frequency of two coupled strings vibrating simultaneously. (presumably
regardless of vibrational mode)

Now... put all this together and we have some interesting possibilities. To name
one... what happens with a bridge that is springy in nature, when two strings
with high stiffness factors relative to their frequencies are coupled in such a
fashion so that they vibrated assymetrically ? And what happens to these same
when they vibrate symetrically ?

I suppose one thing to measure in all this would be to take the left two strings
in a tricord, adjust the relative tuning of the two strings to "close"  "very
very close" and "almost perfect" and measure the frequency of the middle string
for each for the following three conditions. 1) left string muted.  2) left
string unmuted, shift pedal depressed. 3) left string unmuted shift pedal off.

Now I just spent about 4 hours re-reading several articles I have by Conklin and
Weinreich... so I hope at least the effort was worthwhile and I havent made a
complete fool of myself with all this. In anycase.. it was fun and I hope it
helps the old thinking processes out there.  Course in the event I am waaayyy
out in xeno land... please straighten me out.. grin

Richard Brekne
I.C.P.T.G.  N.P.T.F.
Bergen, Norway







>
> Roger Jolly
> Saskatoon, Canada.
> 306-665-0213
> Fax 652-0505