Expanding on my earlier posts on this topic (as it keeps me up at night more and more often):
After doing some basic research, it seems that there is a fair amount of scholarly work on physical modeling of the piano, attempting to figure out exactly what physical parameters affect the production of sound. Most of this work has to do with the physics of damped string oscillations and the acoustics of the soundboard, etc. etc., i.e., what is common to all piano tones. This is all very interesting, but comes at the issue from an altogether different perspective from what is, practically speaking, most useful to pianists and musicians.
The big question for me remains: how much do variations in "touch," or the pianist's physical approach, affect variation in the sound spectra of individual notes? In particular, after glossing through some articles, one specific question seems particularly urgent and no one seems to be close to answering it: In affecting the timbre of a sustained note, can a pianist vary anything other than the velocity of the hammer just before it hits the string?
When the hammer hits the string, the interaction is actually quite complex. In the few milliseconds that the hammer is actually in contact with the string, it exerts a variable force on the string, which affects the vibration of the string and therefore the spectrum of the sound, but it's extremely hard to measure how this force varies over that small time. And, apparently, it's unclear whether anything farther up the stream of the piano action systematically varies the time-varying force that the hammer exerts on the string.
First, before proposing how to actually answer this question, I can't help but express my complete and utter astonishment that no one (to my knowledge) has studied it closely, nor can anyone support a solid argument on either side of the proposition. It's one of those questions that lots of people pretend they satisfactorily understand. I recently learned about the history of this "debate" in a lecture (that's right, I still learn things at school!). From one perspective--the "artistic"--pianists assume they can affect the tone of individual notes based on experience. But based on my earlier post, this experience could well be an illusion created by the presence of other notes, both simultaneously and through time, and pedal. From the more scientific perspective, it's generally assumed that there's no nuance at all to the sound produced; with the keystroke, the pianist can only control loudness through controlling hammer velocity.
Next time: how can one approach this problem experimentally, rather than through dynamic modelling?
Also, I realize this question is analogous to another aspect of music in that the traditional position of music theorists is so wildly off-base, and that everyone assumes they sort of understand, and that is, perception of musical form. For another day.