Here's an audio demonstration of the structure of the E44 note on a Steinway grand piano.
A psychoacoustically important part of the sound is the transient at the beginning of the sound, which is essentially the percussive sound of the felt hammer striking the string.
After the initial transient, the tone of the piano note is a sound recipe consisting of ingredients, or partials, that approximate to a harmonic series. The note we are going to look at is this one (E44):
If we take away the transient it sounds like this:
What we are going to do is hear how this tone is made up from the partials. We're only going to include the first 15 partials (the 14th is absent in the recipe), which is sufficient to make the point.
From top to bottom in the following sound clips, we introduce the partials one at a time into the recipe, so that you can hear how the recipe builds up into the actual sound of the piano note. This experiential demo gives a better insight than theory alone, into this aspect of the nature of the piano tone.
If your ear is quick you may sometimes hear what seems to be a pre-emptive part of each new partial, sounding before the main burst of sound. That's not the partial from the piano string, but the effect of the frequency filter on the transient, which itself contains some components at the same frequencies as the partials being filtered.
Listen to them from 1 to 15 and you will hear how the recipe is made. If you actually go though every one and do this, it will probably change how you hear the piano tone itself.
The E44 note itself: