You can use a fundamental mode crystal as an overtone oscillator, but
even if you can get it to oscillate, it won't be generating an
overtone at 100MHz, since overtone modes of oscillation aren't
harmonically related to the fundamental.

There is a related phenomenon in the field of piano tuning. It has
long been known that overtones (called "partials" by piano people) of
piano notes are not exactly related to pitch of the fundamental
frequency by whole numbered ratios. Instead they are related by
factors like

1.000
2.003
3.007
4.018
5.039
6.092
7.211
etc.

The amount by which this series deviates from the ideal whole-numbered
ratios is called "inharmonicity" and it differs from one string to
another. The stiffer the string, the more inharmonicity. Long thin
strings, as are found on harpsichords, have almost no inharmonicity.
Short strings in the highest section of the piano have the most
inharmonicity. Since one of the goals of piano tuning is to make
partials of different notes come out the same, this phenomenon of
inharmonicity makes piano tuning inherently more difficult than
instruments that have no inharmonicity, like pipe organs.

What is perhaps more like quartz crystals is carillon bells. They are
tuned at the factory, and each partial is tuned independently and
separately by grinding away metal from different levels on the bell.
In view of these related phenomena, it is no wonder that overtones of
quartz crystals are independent of each other and from the
fundamental.


-Robert Scott
Ypsilanti, Michigan