False beats - a correction

[Robert Scott]

There have several postings recently about false beats and their cause.
One of them was by me back in December.  Now that I read it over,
especially in view of Gabriel Weinreich's article about the physics of
piano strings, I think my December posting was misleading.

In that posting I tried to describe how false beats could be explained
in terms of precession from vertical string vibration to horizontal
string vibration.  Then Ron Nossaman observed:

>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.

That's right, Ron.  It doesn't compute.  String vibration never stays in
a vertical plane indefinitely.  Even when there are no false beats, the
string still precesses within 1-2 seconds into vibration that has both
vertical and horizontal components.  But if there are no false beats,
then the string motion becomes a very static round-and-round
motion where the vertical and horizontal components of the vibration
gradually decayed together, staying in approximately the same proportion
to each other.

If there are false beats, then the vertical component of the string vibration
would have to vary cyclically.  It probably would not be as simplistic as
my December description, but the horizontal and vertical components would
no longer be proportionaly to each other in amplitude.

Of course, all this discussion is only about the symptoms, not the
causes.  I'm afraid I can't shed any light on the mechanism by which
a non-uniformity in the string or its mounting brings about false beats.

Bob Scott