Keyweights and moment of inertia

[Robert Scott]

Richard,

You asked what use it is to measure the moment of inertia of a key
and its associated action parts.  If you vigorously play the lowest 
few notes on the piano and compare them to the highest few notes, 
you will notice the difference in feel.  That difference is almost 
entirely due to the greater inertia in the bass because of the 
heavier hammers.  Anything that can cause such an effect on the 
feel of the keyboard certainly seems like a parameter worthy of study.

We don't have to go into Newton's laws to appreciate moment of
inertia.  It is enough to just treat it as a force that resists
your fingers when you play forte.  When you say "But here acceleration 
is zero", I don't agree.  When you play a note, the key and its 
associated action parts are initially not moving.  Then you get them 
moving by striking the key.  That is change in velocity. That is 
acceleration.

I agree when you say "Where ever the weight is placed on the key, 
I suspect these "laws" would predict an effect close to zero."
And that was exactly the point of my previous posting.  But instead
of guessing, I tried to deduce it from known facts.  That is the value
of physics as applied to piano technology.  It is not that we are
trying to win the "plaudits of physicists", as you say.  Rather we
are trying to use physics to understand how to achieve our goals,
which are ultimately artistic.

You will notice that I qualified my analysis of moment of inertia
saying that it is not obvious what the relationship is between
moment of inertia and the artist's perception of the feel of the
keyboard.  But it is reasonable to suppose that there is some
relationship.

Rob,

In regard to why your keyboard felt easier to play after you moved
the weights forward, I have another speculation.  When the weights
are moved forward, they are also reduced.  This reduces the total
key weight supported at the balance rail.  If the bushing and pin
alignment is such that a heavier key causes more binding at the 
pin, then perhaps that could cause a heavier feel.  If that were
the case, it would also increase the difference between down-weight
and up-weight, so it should be easy to check.

Robert Scott
Ann Arbor, Michigan