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.)
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