[pianotech] Key weights, was Best way to change touch on Yamaha Grand

[William Monroe]

All good and well, and I agree with what you've put forth.  But your example
isn't really representative of the suggestion I was making.  My suggestion,
(to follow your hypothetical example further) is more well represented by an
example in which we have a single key stick in two different
configurations.  In these two key sticks, one with a 1lb. weight at 10
inches, the other with a 0.75lb. weight at 10 inches.  In this case, we
achieve lower moments of inertia and a slightly higher (but not
unacceptable) DW in the key with weight removed.  The suggestion I made in
the original post was that slightly lower moments of inertia with a slightly
higher DW might be favorable to a slightly higher moments of inertia and
slightly lower DW.

So, in the case of the scenario I was trying to put forth, the heavier key
will resist the repeated changes of direction, yes?

It's a bit of a red herring at this point, as I don't think any of us are
suggesting isolating the leading at the front of the key above all else.

WRM



On Thu, Jan 7, 2010 at 10:05 PM, George F Emerson <pianoguru at cox.net> wrote:

>  This thread has taken off in different directions.  Good advice has been
> offered for other approaches to solving the specific original problem.
> Still I cannot leave the issue of key leads and moments of  inertia without
> further comment.  I hate to even use the term "inertia."  It is moments of
> inertia in piano action considerations.
>
> William Monroe wrote:
>  heavier key stick would "resist" that initial change of direction that
> starts the key moving (and all subsequent changes in direction) more than a
> lighter key stick, right?
>
> Wrong! .... if you accept as a precondition that you must end up with a
> reasonable touch weight.  In fact the opposite is true.  A heavier key with
> the same static balance characteristics will have less moments of inertia
> than a lighter key.  It doesn't make sense intuitively, but again, we are
> talking about moments of inertia, not linear inertia.
>
> Let's put it in more familiar units and unrealistic round numbers, to make
> it easier to calculate.  Suppose we have a 1lb. weight added at 10 inches
> from the fulcrum. yielding a perfect DW, unrealistic numbers, but easy to
> calculate.  That represents 10 in/lb of torque (10in x1lb) to achieve the
> desired static balance and DW.  Then suppose we put a 2lb weight at 5 in.
> from the fulcrum in an identical key just next to it.  The torque is the
> same, 10in/lb (2lb x 5in).  The static balance and DW are both the same.
> The moments of inertia are not the same.  In the first case, moments of
> inertia (MR^2) is 100 (!lb x 10in x10in).  In the second, it is 50 (2lb x
> 5in x 5 in).  Which key will depress more easily, and which will return more
> quickly .... the one with a value of 50 or 100 for moments of inertia?
>
> There is a secondary benefit to twice the weight at half the distance.  It
> is far less likely that the added weight at half the distance will achieve
> the acceleration of gravity, than half the weight at twice the distance.  In
> the first key, with the weight added near the end of the key, the added
> weight will likely achieve the acceleration of gravity at a volume level of
> *mf*.  At higher volumes, the added weight become counterproductive.  In
> the second key, the weight is added closer to the fulcrum and it is more
> likely that one could play *fff* before the added weight accelerates to
> the acceleration of gravity.  In the first key, the added weight begins to
> work against you at high volume levels.  In the second case, you can produce
> the maximum volume that the acoustic sytem is capable of delivering before
> the added weight begins to work against you.
>
> Frank Emerson
>
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