Forgive me if this is more a physics question than a music question! My question is: When a note is struck on a piano and held down (or a tuning fork is struck, or any instrument where there is just a one-time impact that then rings until dampened), what is the rate of decay in volume (aka velocity)? I strongly suspect that it is not linear; that the volume after two seconds is not half the volume after one second.
By extension, is it possible to calculate, or even just estimate, how long a note continues to reverberate on a piano if struck at maximum impact, versus lightly pressed, when held down in both cases?
Background, not essential:
I have a beautiful AvantGrand N2, which includes a standard MIDI output via a UX16 capble that allows one to record on a computer when and how forcefully a note was struck. While MIDI will never capture the complete soul of a piano, I want to use this just to see how accurately I'm expressing certain notes in a chord versus others.
The way MIDI works, it just sends a signal when a note was struck and how forcefully (known as "velocity"), and a second signal when that note was released, even if one removes one's finger 30 seconds later, long after the note has decayed. (It can read the pedals too, but that's a future endeavor.) So my question is: When a note is struck, and I want to visualize the velocity over time, what sort of function should I apply to the initial velocity?