Jon Teske wrote:

If you touch one note above that (B natural on the E string) the
result is a not an octave and a fifth (or high B) above the
fundamental frequency, because lightly stopping the B and causing
it to vibrate on both side of the stop divides the string into thirds.


Jon Teske, W3JT and concert violinist.

And this is why pianos are arranged to strike the string at a point
which suppresses a harmonic which is dissonant. (I think it's the 7th
harmonic which is suppressed)


The choice of where the hole you blow over in a flute has similar things
going on. As do the locations of the holes on any wind instrument.

That musical instrument design thing is not as simple as it might seem
in first year physics class.