In a message dated 98-05-08 Ray Fairfield writes:

> The center of gravity of an object can only move if it is acted on
> by an outside force ....

Friends, the principles previously enumerated presume straight-line
acceleration, which is incorrect.  Piano hammers travel in an arc.
While the hammer shank remains attached to it's pivot (the hammer
butt flange), angular acceleration is induced because of the pivots
centripetal force on the hammer.

An apt illustration may be found in outer-space travel which
harnesseses the "sling-shot" affect by approaching a gravitational body
tangentially.  There are plenty of illustrations, such as swinging a
golf club (which has a flexing shank, like a piano hammer shank, which
most definitely does flex).

I cannot state whether the hammer is accelerating at the moment of
impact with the string.  However, it is feasible.  And, I believe, it
is probable that this characteristic is designed into the modern
pianoforte, separating the modern instruments from their primitive
roots.

Ray also writes, "Apparently many of us have too much time on our
hands ... Aren't we really here to enjoy the music? ..."

Guilty on all points!  :-)  But these curious, esoteric factors do
weigh into the musical result.

Regards,
Robert Linnstaedt

 [ Hal Davis applauds: "Music and physics are absolutely inseparable."
 [ Today, just as for thousands of years, the quest continues to
 [ improve traditional instruments and occasionally develop new
 [ instruments.  In every case the goal is ... music!
 [ -- Robbie