The rule is that if you have a classical source with frequency f, the outgoing radiation is a superposition of frequencies f,2f,3f, etc, according to the Fourier decomposition of the source frequency.
If you write Maxwell's equation in Lorentz gauge:
$$ \partial_\mu \partial_\mu A = J $$
And assume that J is periodic, by Fourier tranform:
$$ k^2 A(k,\omega) = J(k,\omega) $$
So that the fourier transform of A is supported on the same frequencies as J. This is obvious--- a periodic source gives rise to a periodic wave with the same period.
The rule is correct quantum mechanically too in the correspondence limit: the emission between level n and n-k is at a frequency which is k times the inverse classical orbital frequency at level n. You can see how Borh used this to derive the quantization rule here: Bohr Model of the Hydrogen Atom - Energy Levels of the Hydrogen Atom .