Hi Vladan, I think your options 1 - 3 pretty much describe it. I'm an Option 3 (combo mode), playing mostly in Option 1 mode. Adaptation time to a strange piano is a few notes long -- a few measures if the piano is really screwy. Warm-up time dramatically reduces the required adaptation time. I would only add that the relevant dimension to your model should be slow/soft vs. rapid/loud. Slow/loud involves a very rapid keystroke. Rapid/soft involves "playing the tops of the keys." Either way, the duration of the keystroke is very short. Only slow/soft involves a slow keystroke. Your mathematical model: Do I understand correctly that the force on the key is the same between the red and blue curves? If so, the acceleration will not be the same, and the terminal velocity of the hammer will be less with the higher-friction system. I think you must have found that, because you say you normalized the curves for comparison of response time. But yes, it would take longer (and more key dip and hammer travel) for the same force to accelerate the hammer to the same velocity. Of course if you're a pianist and want to play a note at a given amplitude, you would apply whatever force is necessary to achieve that amplitude. That force would be higher if there's more friction to fight. In fact it would be higher by exactly the additional frictional force that must be overcome. The resultant force that accelerates the system would be the downward key pressure, minus the frictional force, as measured at the key. It is that resultant force that would have to be equalized between the two systems to achieve the same terminal hammer velocity and note amplitude. If these resultant forces are the same between the lower and higher friction systems playing the same amplitude of note, then the rates of hammer acceleration and key stroke will also be the same. IMO, all friction buys you is... friction. If I may apply a new term here, it increases the required "bias force" on the system, this being the force needed to move the action. On a plot of terminal hammer velocity, vs. applied downwards key force, it offsets the curve along the y axis. My own (admittedly atypical) feeling about this bias force is that it doesn't really do anything useful for me during slow, soft play, when I use muscle tone to regulate finger/wrist/arm velocity anyway. However, during rapid, hard play, it's a bit like running in the sand (with greater exertion and slower key return). I can run much faster on pavement! ;-) Perhaps I'm different from high-performance concert pianists, in that I don't have their stamina or arm weight. My fingers are also relatively short, so perhaps they're not prone to the same jumps and jerks. (Of course I'd LOVE to have longer fingers.) Dunno... I think the difference may be that I don't have a lot of upper end on my own, personal power curve, and I have pretty good control over the lower end of my curve. Other pianists may have little control over the lower end but may max out at a much higher end. Perhaps differences in friction is one of the ways we seek out the dynamic range that we find most comfortable. Other differences would be SWR and SW and DW. I think it's a Goldilocks sort of thing. There are no "wrong" beds -- only beds that are too hard, too soft, and just right. Peace, Sarah PS My reaction time, college years, of 65 msec: Hmmmm... This seems awfully fast. Perhaps I'm remembering my fastest reaction times. Average reaction time was surely slower. Or perhaps I'm suffering from OldTimer's disease, and my memory is in error. If reaction times are indeed longer than this, that would imply still less opportunity for fine control of key movement. PPS For lack of time that I should be spending on other things, I'll probably want to bow out of this discussion now... ;-) ----- Original Message ----- From: "V T" <pianovt@yahoo.com> To: <pianotech@ptg.org> Sent: Monday, August 30, 2004 10:53 PM Subject: Pinning on new flanges > 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 > > > > > > > _______________________________ > Do you Yahoo!? > Win 1 of 4,000 free domain names from Yahoo! Enter now. > http://promotions.yahoo.com/goldrush ---------------------------------------------------------------------------- ---- ---------------------------------------------------------------------------- ---- > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives >
This PTG archive page provided courtesy of Moy Piano Service, LLC