Key Leads and Inertia

Sarah Fox sarah@gendernet.org
Tue, 29 Apr 2003 19:16:48 -0400


Hi Del,

I was going to reply to this earlier today, but my 'puter died.  New power
supply, and I'm up and running again -- back from the dead.  ;-)

> Most of the energy lost between the key end and the hammer goes into
bending
> the key. At action saturation the front of the key fully bottoms before
the
> hammer starts to move. I'm not sure how much key leading contributes to
this
> but I shouldn't think it was all that much.

OK, if it were possible (which it is not), consider a key of 100 kg mass
(the equivalent of a rather large person), but with the same relative
balance and flexibility as an adjacent key of normal mass.  Experiment 1:
Move the heavy key downwards at the same velocity as a neighboring, normal
key, and the two respective hammers will move up with the same velocity and
produce roughly the same sound amplitude.  However, how much energy did you
expend in order to move the heavy key, as compared to the light one?  Much
more, I venture.  Obviously it takes much more energy to accelerate a heavy
key.

So where did all the extra energy go that was put into moving the heavy key?
Obviously the extra energy didn't go into the action/hammer/strings, or else
the sound would be much louder.  The answer lies in experiment 2:  Remove
the keyslip.  Insert pinky finger of one hand under the heavy key and pinky
finger of the other hand under the light key.  Repeat Experiment 1, playing
a good strong note on each key.  Remove bloodied pinky from underneath heavy
key, bandage carefully, and go see an orthopedist.  The answer is that the
extra energy is wasted when the key collides with the front rail and
punching.  Depending on the elasticity of the punching and the rapidity of
relaxation of the pianist's finger, the "rebound" of the key from the front
rail might assist the pianist in lifting his finger, but beyond that feeble
prospect, the energy is all wasted in the form of friction and dissipated in
the form of heat (albeit not much heat).

How this effect varies from pp to ff is elucidated by experiment 3:  Move
both keys downwards at such a slow velocity that time lapse photography
would be needed in order to detect movement.  Very little of the energy
would be put into the kinetic energy of either key.  The primary expenditure
of energy would be in moving the key aganist the forces produced by
gravity's effects on the action, any spring action, and friction (i.e.
energy = force * distance).  The slower the movement, the more equal the
energy expenditure between the light and heavy key.

Possibly also consider experiment 4:  a completely massless action, massless
hammers, etc. (which would of course move but produce no sound).  Because
this action is massless, the effects of gravity would have to be simulated
with springs.  The end result is a key that requires a fixed amount of
energy (force * distance) to depress it.  The velocity of the key would be
irrelevant, since there is no inertia.  (I'm assuming the pianist also has a
massless hand.)

We can see from these conceptual experiments that greater mass in a key
results in greater energy wastage at higher key velocities.  The lower a
key's mass is, the more of the pianist's effort that can be put into moving
the hammer.  Ideally, if all of the mass were in the hammer, and if the key
and action were completely massless, then the maximum kinetic energy could
be delivered into the strings from the pianist's hands (now depending on the
characteristics of the hammer and strings).  This would be uniform from pp
to ff and would, in my estimation, result in a far more responsive and
"intuitive" instrument.

There are other issues at play as well.  If the hammer (barely) moves before
the key hits the punching during a hard blow, there is an important ceiling
effect to consider.  I'm rather surprised at this assertion, by the way, but
I certainly take your word for it.  I tried depressing a key somewhat hard
while holding the capstan end in place and produced about 1/8" of dip from
flexion.  Wow!  I guess the remainder is flexion in the action, which can
certainly be tested statically by depressing the key while holding the
hammer in place.  What sort of force is required for such a thing?  (I'm not
willing to try it on my piano. <grin>)  Anyway, I digress...

If this effect does in fact occur, even an 800 lb gorilla with a sledge
hammer couldn't produce a louder note than someone capable of bottoming out
the key without the hammer moving (much).  The maximum amount of energy that
can be delivered into the action is, again, force times distance -- the
integral sum of the force applied against the key at each given position,
times the tiny distance increment traveled -- with the hammer held
stationary.  To hear this "loudest" note, just lock the hammer in place,
depress the key completely, thereby "winding up" the system, and release the
hammer.

Could Mr. Olmsted (COWABUNGA BACK, DUDE! ;-) achieve a higher hammer
velocity and louder note, given that he does a ff workout 1 hr/day?  Almost
definitely.  However, someone is going to have to design him a stiffer
action.  Could an amateur such as myself, similarly, produce a louder ff?
Probably, but someone is going to have to reduce the mass of my keys and
action parts and increase the mass of my hammers.  (And do we REALLY want to
do all this ear-splitting banging anyway?  With all all respect to your
feelings about "LOUD" pianos, many pieces do legitimatelly require some
banging.  Sorry, Del! <grin>)

I think what pianists *really* want, above all, is control.  Control means
not only consistency from key to key but also an intuitive feel that yields
a predictable dynamic range.  In my own case, I like a heavy hammer.  That's
probably because I find it easier to regulate how much force I put on a key
than the velocity at which I move it.  I would conjecture that the "comfort
factor" that Isaac refers to (regarding a heavier key) is attributable to
exactly that.  Heavier keys have enough inertia that they resist movement
enough that one can regulate the force applied to a key, rather than the
velocity.  Still, doesn't it make more sense to put greater inertia in the
hammer, and not in the key?  At least it's doing something there.

Why force and not velocity???  Putting on my neurobiologist hat for a
moment, I think there is a very good reason for this.  (Those with headaches
can skip this paragraph and the next one.)  Controlling key velocity is a
slow process.  It requires proprioceptive input to the brain (i.e. finger
position information), which must be coordinated with motor output through
the basal ganglia -- a slow, neurologically "clumsy", and inherently
inaccurate process.  Did I mention SLOW?  I can't overemphasize this.  When
I'm playing something that has a lot of fast pp stuff, there's simply no
time for nerve impuses to make the round trip in order to regulate key
velocity.  (Yes, I've calculated!)  However, there is time to "regulate" the
amount of force I apply against a key.

Regulation of force against a key is an output-only process.  It relies on
output from the cerebellum, which is the part of the brain that learns
complex and elaborate movements, such as are required for learning piano
fingerings.  The force applied against a key is directly proportional to the
strength of muscle contraction, which is directly proportional to the number
of nerve impulses (action potentials) reaching the muscle.  (A bit of an
oversimplification, but roughly accurate.)  Therefore, relative force is
directly controllable from the brain without *any* proprioceptive or even
tactile feedback.  It works as fast as I can move my fingers (which is
actually as fast as my brain can send bursts of nerve impulses, barring
tetany.)  What feedback does occur (tactile, proprioceptive, auditory,
visual) is still important, of course, but it is incorporated into "fine
tuning" the motor program, much like a machinist on a factory floor tweaks
an adjustment on a running machine to shave another 1/1000" off of the parts
that are shooting through it.

Sorry for the digression.  I think I would really love working with some
team to redesign the piano action.  There are so many things that could be
done with modern materials, acceleration optimization through jerk
reduction, etc., etc.  This begs the question of whether a redesigned piano
would be adored or despised on the basis of its "different" feel.  I was
really interested in Mr. Olmsted's comments about adapting to the piano and
about uniformity of action, but that's another post.

Peace,
Sarah

(Sorry for the rambling, but this is a topic I find particularly
interesting.)


This PTG archive page provided courtesy of Moy Piano Service, LLC