  We have generated frequency combs spanning 0.5 to 20 GHz in superconducting
half wave resonators at T=3 K. Thin films of niobium-titanium nitride enabled
this development due to their low loss, high nonlinearity, low frequency
dispersion, and high critical temperature. The combs nucleate as sidebands
around multiples of the pump frequency. Selection rules for the allowed
frequency emission are calculated using perturbation theory and the measured
spectrum is shown to agree with the theory. The sideband spacing is measured to
be accurate to 1 part in 10 million. The sidebands coalesce into a continuous
comb structure that has been observed to cover at least 6 octaves in frequency.
