A little research has pretty much definitively answered the question from my last post: in terms of the vibration of the string, the only thing a pianist has any control over is the speed with which the hammer hits the string (and the pedal...). It turns out, this was a simple physical problem, solved by learning about piano action. The relevant fact is this: after you push down a piano key, but before the hammer actually hits the string, it loses all contact with the rest of the action, so that the
only force on the hammer for some duration of time before it hits the string is gravity. Then the only forces on the hammer during contact are gravity and the force of the string itself; nothing with the piano action is involved anymore at all. Therefore, if the hammer strikes the same string twice with the same velocity, it will produce the same sound spectrum.
Okay, but there's still more to it, because there's also, surprisingly, a lot of white noise that goes into piano playing. This includes not only finger to key white noise, but more importantly, the noise all the stuff bouncing around inside the piano, which resonates on the soundboard just as the string vibrations do.
Without getting into that too much for now, let me re-state an important question: Who cares? Well, okay, here's something that will never apply to most people, but applies to me: should pianists play chamber music with the lid of the piano raised, or not?