Here is a neat example of overtones on a piano. Depress the G above middle
C (without sounding it) to remove the damper from the strings and hold the
key down. Then hit the C below middle C very hard. You will then faintly
hear the G you are holding down. The G overtones from the C that was hit
are causing the G strings being held down (undampered) to vibrate in
sympathy.An example of overtones and sympathetic vibration in one.
The C will generate the following overtone series
C |C G | C E G (bar denotes a new octave)
The 1st G in the series will cause the G strings, undampered, to sound.
For what its worth,