# At what rate does the volume (velocity) of a note decay?

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?

Thank you!

• It's nowhere near that simple. Quick experiment. hit the top note & bottom note... which decays first? – Tetsujin Jul 27 at 16:20
• "what is the rate of decay in volume (aka velocity)?" For a start, volume isn't velocity. – Laurence Payne Jul 27 at 17:00
• Velocity is basically how fast you hit the note. The way the sensors work that's all it can do - times how long it takes for the note to travel from rest to pressed. That is translated to 'weight'. Once the note is then generated, real or imaginary, what you then hear is 'volume'. – Tetsujin Jul 27 at 17:18
• Velocity is "the rate at which a keyboard controller key is pressed" according to a paper about how to interpret and implement it. pdfs.semanticscholar.org/92a7/… – Camille Goudeseune Jul 27 at 17:19
• Once you're in the realm of actual sound, midi then has no job to do until you let go of the note, at which point the processor then determines what should occur [good ones have all kinds of ancillary functions at that point - sympathetic resonance, mechanical noise, subtle stuff, but that's why the Avants are expensive] – Tetsujin Jul 27 at 17:25