But in fact, the impression that different pianists have a distinctive sound in this way is an illusion. On other instruments, a musician can create a characteristic timbre with his or her own playing. Timbre refers to the spectrum of overtones above a fundamental frequency and the variations in the amplitude of these overtones through time. Different spacings of overtones are what give each instrument and each voice its characteristic tone, as well as different members of the same instrument, and different musicians on the same instrument. Different string players vibrate differently; everyone's voice resonates in a body that is slightly different.
Unlike on a string or wind instrument, or voice, though, there's not much a pianist can do with any one note to make it unique in the same way. To understand this, a quick explanation of piano mechanics is necessary. A pianist depresses a note on the piano, which sets in motion two events. First, a damper is lifted from the strings corresponding to that note allowing them to vibrate if struck. Then a felt hammer strikes the strings. When the key is released by the pianist, the damper falls back, stopping the strings' vibrations. There is also the relevant pedal, which, when pressed by the right foot of the pianist, lifts all of the dampers off all of the strings.
If I'm not mistaken, these are the only five "dimensions" along which a note on a piano can vary:
1. the speed with which the hammer hits the string (this determines, among other things, the initial volume of the sound).
2. The duration of hammer to string contact.
3. how many other strings are allowed to vibrate and to what degree (i.e. how many other notes are simultaneously held down, or how far are the dampers lifted off the strings by the pedal).
4. time elapsed before the damper hits the string again.
5. the manner in which the damper comes back into contact with the string (fast vs. slow), and the length of time between the initial contact and the final silencing of the sound.
Categories 1, 3, and 4 are simple continuous categories which every pianist, from the relative beginner to the experienced professional, all utilize from one of the spectrum to the other. Everyone can play loud and soft, with lots of pedal and no pedal, long notes and short notes. Two and five are somewhat more mysterious, but not, I think, extremely important. I'll come back to them.
It's always a shock for me to think about these things, because the illusion that everything we as pianists do to affect the sound of the notes we play could hardly be any more compelling. All our lives, we're taught that the amount of arm weight, or the amount of the finger action, or the looseness of our wrists all contribute to the sound of the individual notes we play. And they do, in a way, but only indirectly, by correlating with one of the dimensions noted above.
The more important point is that almost everything a pianist does to make his or her sound unique largely depends on how the notes are put together, and not about the individual notes themselves. There are about five pianists whose playing I can generally recognize and distinguish very quickly, not by style, but by "sound" (though to be fair I've never submitted to a blind test). But for only one of them is that judgment based on anything I could easily describe in words, or attribute to quality of the playing (Ivan Moravec). For the others, (Gould, Richter, and Serkin) it's something more mysterious. More on that another time.
One caveat: a friend pointed out that a lot of what I hear as different pianists could also be reflections of their different piano selections. Richter, unlike every other pianist who ever lived, famously played on Yamahas, rather than Steinways. However, there's much more to it than that: Gould may have been picky about his pianos, but among all the ones he used over the years, they couldn't all have been that different from the others we're used to hearing. Serkin, with a much more extensive career as a chamber musician, would not have had the privilege of being so picky all the time.