Inertia, was "Grand Touch"

[Stéphane Collin]

Hi Vladan.

Most interesting comments from you, as always.

Reading this, I have some intuitive reactions that I would like to share, 
for the case it can rise a better understanding of the matter.

How does moment of inertia relate to work ?  I would have thought that 24 
gram moved (was it in a circular way) by 5 mm (or an arc of circle whose ray 
would be 5 mm) needs the same work as 12 gram moved by 10 mm.  Is this right 
? Does this apply to our key weight matter ? Isn't it the work to accomplish 
that causes fatigue to the pianist ?  I thought, ok, if there is much lead 
in the key, there is much work to accomplish, thus the heavy feel.  But I'm 
still to understand why the same [weight/distance from balance] figure would 
give a different feel.  It is the square of ray parameter that I fail to 
figure out.
Now, from a pianist point of view, I have thought uptill now that as long as 
the action has a decent repetition capability and an acceptable heavyness 
feel, the more inertia would be the better (up to a certain point) as this 
inertia helps alot smoothing out the minute discrepancies between the 
pianist's fingers, by giving all along the 10 mm dip some feedback 
information to the pianist's finger about how much force he is really 
applying to the key, and letting him (intuitively) adapt this, in order to 
produce the exact desired sound, favouring for example perfect legato, and 
avoiding the "ow, I didn't want this" effect.
But then, at what point does the extra inerty start to impede repetition (by 
making the change of direction of move of the key more difficult) ?  I want 
the key to stick to my finger for the fastest that I can repeat the note 
with that finger.  But I heard comments from other pianists that this is 
already too much for good feel.

Any comments about all this ?

Best regards.

Stéphane Collin.


----- Original Message ----- 
From: "V T" <pianovt at yahoo.com>
To: <pianotech at ptg.org>
Sent: Wednesday, July 12, 2006 7:13 AM
Subject: Inertia, was "Grand Touch"


> Jude,
>
> I need to correct something you wrote;  mass x
> velocity is momentum rather than inertia.
>
> There are a few important things to know about lead
> placement.  We are interested in something called
> "moment of inertia" which is a measure of how hard it
> is to set the key, or for that matter the entire
> mechanism including the hammer into motion.
>
> For simplicity, let's look only at the key stick with
> one lead in it.  Let's also make the extreme
> simplification that the wood in the key doesn't weigh
> anything at all, and so we are looking only at the
> effect of the one piece of lead.  The moment of
> inertia caused by that lead is equal to:
>
> I=m*r^2
>
> I=moment of inertia
> m=mass of the lead
> r=distance from the balance rail hole to the lead
>
> Note that the formula takes the square of "r".
>
> Now, let's look at our options for lead placement.
> Suppose that we can use a 12 gram weight placed 10 cm
> away from the balance rail hole to get the desired
> balance weight.  As an alternative, we could also use
> a 24 gram weight placed 5 cm away from the balance
> rail hole and still have the same balance weight.  Is
> there a difference between the two?
>
> Yes, there is.  Looking at the formula above, the
> inertia increases with "r" squared.  In the first
> case, the inertia will be 12*10*10=1200 gcm.  In the
> second case, the inertia will be 24*5*5=600 gcm.
> Placing the 24g weight 5cm away from the balance rail
> hole reduced the moment of inertia by 50%.  That's a
> lot.  You can minimize the inertia by placing the
> weights closer to the balance rail hole and increasing
> the amount of lead accordingly so that the balance
> weight meets the target.
>
> There is a fundamental trade-off between balance
> weight and key stick inertia.  If we add a lot of lead
> to make the balance weight low, the action will feel
> very light, but only when you move the key slowly.  If
> you try to play a loud note, all that lead will have
> to be accelerated and the key will feel heavy.
>
> If you put very little (or no) lead into the key and
> accept a high balance weight, the action will be heavy
> when you measure it with your weights, but it will
> feel light when you play fast/hard/loud.
>
> The question is: What is better?  My own preference is
> for a heavier balance weight with less inertia.
>
> Vladan

>