  Inflation predicts a primordial gravitational wave spectrum that is slightly
``red,'' i.e., nearly scale-invariant with slowly increasing power at longer
wavelengths. In this paper, we compute both the amplitude and spectral form of
the primordial tensor spectrum predicted by cyclic/ekpyrotic models. The
spectrum is blue and exponentially suppressed compared to inflation on long
wavelengths. The strongest observational constraint emerges from the
requirement that the energy density in gravitational waves should not exceed
around 10 per cent of the energy density at the time of nucleosynthesis.
