Somewhere I heard or read that a piano is tuned with a cute bit of trickery. The upper half has three strings per note, and they are tuned to concert pitch - 1 of the 3 strings that is; then 1 string 1 Hz lower, and the 3rd string 1 Hz higher.

As an example, A4's three strings are tuned to 439,440,441 Hz.

This means that the first harmonics of A4's 3 strings are at 878,880,882.

Then D4's strings are tuned to 292.66,293.66,294.66.

So the SECOND harmonics of D4 are at 877.99,880.99,884.99

Thus it turns out that the first harmonic of one of A4's strings matches very nearly the second harmonic of one of D4's. When you hit these two notes at the same time, those two strings' vibrations mutually reinforce each other, while the other strings of those notes are vibrating at odds. So those soon die out, while the strings with matching harmonics keep vibrating longer. So the sound begins with a sort of transient noise, but very quickly settles down to a pleasing harmony.

The lower half only has 2 strings per note. I guess this is because the human ear doesn't hear the finer nuances of lower notes so the same trick is used, but it can be done simpler.