As Jan already mentioned an ordinary piece of matter does not necessarily show harmonic 'overtones', when oscillating. In fact, most shapes show inharmonic overtones. To make them sound "harmonically" they must be brought into the right shape. A very nice example is the marimba:

http://www.lafavre.us/tuning-marimba.htm

Quartzes behave similar, they aren't precisely harmonic. I once had a nice article about this issue. Must search a bit...

Kai