Look for film footage of nyiregyhazi on youtube and listen to mosonyis funeral March and the Liszt rhapsody no 3. I don't believe that's only down to illusions and nothing else. He made almost every sound from contact. He plays louder than most people could play by punching the keys. And he makes a huge sound before he even starts trying. Sometimes his very loudest gets percussive, but the sounds that fascinate me are the effortlessly massive ones that he makes without even coming close to his limits. Those who try to recreate such depth almost always start trying trying to hit or to move as faster. But they get a percussive tone and simply max out, before even approaching the level of volume or resonance that he reaches in his moderate dynamics, with no effort at all. I don't see any explanation at all other than the pacing of acceleration.
I don't see how one can judge loudness via a youtube clip played through a computer. But no matter; I agree with you that one pianist can create a greater psychological impression of loudness than another, playing the same passage of music on the same piano in the same room. However, I think it's perfectly possible to explain this via control of velocity alone (plus of course legato, pedalling etc. that I think we all agree on as factors but see as separate from the argument about the keystroke itself).
It comes down to control of dynamic range.
Anyone who has put a highly produced pop music CD in their player and played it, after playing a classical CD and not changing the volume, will understand this. The pop CD sounds many times louder even though, if you look at the very loudest sounds, it can't be. Both CDs are normalised to 0db and there's simply no way they can be louder than that. The difference is that the classical CD has an enormous dynamic range from PPP to fff, whereas the pop CD has been compressed to all hell to bring the softer sounds up to near the level of the louder ones. Anyone who's worked in music technology will tell you that one of the functions of such compression (when done in certain ways) is not just to make the music sound louder, but to make it sound "warmer", "richer", or "smoother" - terms that correspond pretty well to what most people here probably mean by "good tone".
Suppose you get someone to play a big, thundering piece of romantic music on a Steinway grand in a particular concert hall. Now suppose that we could analyse the velocity of every keystroke, and map them on a scale from 1 - 100 (rounding them off to the nearest integer). Suppose we find that some impression of harshness starts to happen at around 85, and becomes very noticeably and unpleasant above about 90.
Now, your highly skilled famous concert pianist playing the piece, will aim to get most of the loudest notes at about 84, maybe occasionally exceeding that a little and allowing a tiny bit of harshness judiciously placed according to the phrasing. Just as importantly, they will aim to get most of the
other notes not too far below that, using just enough variation to obtain the sense of phrasing and dynamic shading that they need, while maintaining a consistently loud sound (plus of course any sections or voices that are deliberately intended to sound very soft, and don't contribute to the sense of loudness).
If OTOH you get a second rate amateur to play the same piece, they will probably AIM to do the same thing. But instead of getting the louder notes right at 84, many of them will come out at 90 or higher and sound harsh, due to the player's lack of control. And instead of getting the softer notes at 75-80, many of them will come out at 60, 50 or lower for the same reason. The effect will be much "looser" and less consistent.
Returning to the pop music compression example, one thing we know about psychoacoustics is that tightly controlled sounds within a narrow dynamic range give a greater subjective impression of "loudness" (AND of "warmth", "richness" etc.) than less controlled sounds over a wider range. In this case as well, the
average dynamic of the amateur will surely be lower for the simply reason that if you're aiming for 75-84, and 100 corresponds to how hard it's realistically possible to thump a key in an actual playing situation, there is more scope for accidentally obtaining a lower dynamic due to poor technique, than a higher one. When the amateur hears harshness, he'll back off, but unlike the professional he won't have the control to back off by exactly the right amount and still sound loud.
There are of course other factors involved too, like the professional's control of the pedal etc. And of course as soon as you are talking about chords (ie, nearly all the time) then control of different simultaneous dynamics comes into play as well as sequential ones. Harshness is something we mostly experience in higher frequencies, and the extent to which a higher note sounds harsh will be mitigated by being supported by simultaneous lower notes. Someone with the precision of technique to get those lower notes to exactly the right level of support will be better placed to raise the level of the higher notes a bit further.
You suffer here from the same problem that your claim always seems to suffer from. You have made a claim about the nature of individual keystrokes, but you are illustrating it with an example of the playing of an actual piece, with many keystrokes interacting. Once you consider such interaction, it's perfectly possible to explain the phenomenon you're talking about without recourse to unfounded voodoo about hammer flexion, which may or may not even be happening to a significant degree in the first place.
These things - the psychological effect of dynamic compression; the more precise technique of the better player - these are known phenomena for which there is clear evidence. They are perfectly sufficient (along with the other factors I mentioned) to explain the difference in
subjective impression of loudness when hearing two different pianist play the same
piece, and Occam's razor tells us not to multiply explanatory phenomena beyond necessity.
To actually prove your point, you'd need to get nyiregyhazi to play a SINGLE NOTE at a loud dynamic but without "harshness", and then fashion some kind of mechanism that could reproduce exactly the same hammer velocity but with a quick, sudden stroke of the key from above. If there were a discernible difference to the listener in double blind tests, in nyiregyhazi's favour, then you'd have a case.
To speak of him moving keys "faster" than other pianists couldn't explain the first thing and neither could anyone recreate his sound with such a mindset. Pianists who think it's about moving faster hit their upper limit without getting anywhere near how far a piano can go (while still avoiding the hard percussive thuds). Volodos is another excellent example of a pianist who can play far louder than the point where most people assume it will sound percussive.
Clearly it's not all about moving faster
overall, but about fine control of fast movements and how they interact in the piece. Again, when you make this judgment of Volodos you are judging the overall effect of a piece, not the specific effect of a single note.