Pinning on new flanges

V T pianovt@yahoo.com
Mon, 30 Aug 2004 19:53:15 -0700 (PDT)


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Hello Sarah, Ric and Friction Thread,

For the sake of keeping the discussion on target,
let's assume for a moment that we have no way of
finding out what exactly is going on in the pianists
body/mind as he tries to control the pressure on the
key.

To summarize, there are at least three options
available:

Option 1.  The pianist does not have any time to react
to his movement once he starts pushing the key down. 
He is playing "open loop" and acts from some previous
knowledge of what might work well.  Depending on how
well he knows the piano and his skill level, he gets
it more or less right.  Maybe he is really great and
learns very quickly, so after playing a new piano for
a short while he figures the instrument out.

Option 2.  On slow passages, he has enough time to
adjust his touch, and that in combination with his
general pianistic skill gets him through.  On fast
passages, there is no time to react and dynamics take
the back seat.

Option 3.  Some combination of the above.

Going back to mechanical systems with mass,
springiness and friction, I have made a plot of two
theoretical scenarios.  The plots are attached (I hope
they get posted correctly).  The plots are pure math,
showing two systems which are equal, except for the
friction.  In other words, the inertia and the
springiness are unchanged.  This mathematical concept
is universal in nature and can be found just about
everywhere.

The horizontal axis represents time.  The vertical
axis represents the momentum in the hammer.  The red
trace represents a system with more friction than the
blue trace.  I have normalized them so that they
coincide in time at about 90% of the final momentum
value.  This means that both pianos will sound the
note at the same time, assuming that the jack releases
at about 90% of the available momentum.  For the sake
of this discussion, that number can be 95% or 99% - I
just had to pick a number - it doesn't really matter
much.

The important thing to notice is that for a constant
force on the key, the system with more friction will
take more time to get the hammer to the required
momentum.  It takes about 2.4 units of time for the
blue trace to go from 10% to 90%, but it takes about
3.5 units of time for the red (higher friction) trace.

Back to the issue of control: Up to a point, if the
musician has more time to push the key (for a given
required momentum), he will probably be in more
control.  If there is too much friction, things will
not be so pleasant, as he will have to push harder, or
else he will run out of time.  If the action has less
friction, he will have to be more nimble - there will
not be much time between the pressing and the
releasing.

Also note that the piano with the higher friction will
require the pianist to start with the note just a
little sooner so that the note can sound on time; in a
sense he too has to be fast.  It's just that on the
higher friction piano he has to be faster moving his
hands/fingers between notes.

I think that this is fundamentally the first order
effect we are discussing.  It gets more complicated,
of course, but I hope the description sheds some
light!

Vladan





		
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