Beyond velocity and acceleration: jerk, snap and higher derivatives (2016)

For people who understand sound - how much can acceleration, jerk and snap affect the tone a piano creates?

A (mis)conception of the piano is that it is purely percussive and velocity is the only parameter you control for voicing on the piano but professionals would beg to differ...

For playing a note on a piano and doing nothing more, I'd like to suggest that the velocity of the hammer as it strikes a string is the only variable that can be adjusted by the player.

A hammer in a piano always moves on a fixed path. It always strikes the same part of the string, and it always does so in the same orientation. And after it strikes that string, it always falls away from it. That's how that part works.

Striking a percussion instrument with a stick (such as a wooden block) has more variables to toy around with than playing a note on a piano does.

But there's a lot more going on in a piano than striking strings: Strings are also muted, and the degree of muting can be manipulated. It is not binary.

And, of course, pianos are polyphonic: With ten fingers, we can strike ten different [sets of] strings at different velocities and at different times, and we can even mute them to individually-different degrees.

And then, there's also the pedals...