Weighty Problem

Robert Scott rscott@wwnet.net
Thu, 12 Mar 1998 14:18:00 -0500


Don wrote:

>When you remove weight you change the moment of inertia. Therefore less
>*energy* is required to play.

That's right.  But the effect depends somewhat on the way you play (loud
or soft).  When you play a note, the resistance felt by your finger has two
components - static and dynamic.  The static component is the constant
resistance
due to the downweight.  This component is the same regardless of how hard you
play the note. The other component is the dynamic reaction to inertia.  This
component is directly proportional to rate at which you make the key accelerate.

When you remove weights from front of the front of a key, you increase the
downweight and decrease the inertia.  Therefore the static component of force
on your finger goes up while the dynamic component goes down.  When can we
say that the net effect is to reduce total force on your finger?  If we assume
that the weights are essentially at the same distance from the balance rail as
the finger pressing the note, the answer is "almost always".  In order for
the missing front weights to actually increase the total force on the finger,
one would have to be playing so as to induce an acceleration in the key that
is less than the acceleration due to gravity.  If we assume a 3/8" touch, then
such soft playing would mean playing so that it takes over 44 milliseconds for
the key to travel down to the front rail.  I believe that in most playing the 
keys move faster than this, and to the extent that they do, the reaction to
inertia will be more significant than the static downweight.

Bob Scott
Ann Arbor, Michigan



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