That is really interesting and good to know, thank you! Although from what I just read about how anharmonicity affects overtones, they are usually at a lower frequency than a multiple of the fundamental. But that was just from a quick google search, so take it with a grain of salt.
At this point I feel like I'm going way beyond the scope of this exam though, so the overtone explanation is good enough for now. I will look more into this though, it's pretty cool stuff. Thanks again for your help.