A non-Brownian, inertialess, dense suspension of rigid hollow glass spheres is studied with time sweep oscillatory experiments. The measured apparent complex viscosity is shown to depend on the amplitude of the applied strain, in agreement with the literature, and, unexpectedly, also on the angular frequency. Two different regimes are individuated depending on the applied strain. For values smaller than 1, when the structure evolution is driven by the shear-induced diffusion, the complex viscosity depends on the frequency, for values larger than 1, it is rate independent. In the first regime, the dependence on the applied strain amplitude and the angular frequency can be lumped into a single parameter: The maximum shear rate, the applied strain amplitude times the angular frequency. The results obtained are quite surprising since in a non-Brownian, inertialess, dense suspension, the particle interactions do not have a characteristic time scale and, consequently, the governing equations of motion result rate independent. Only the presence of a nonhydrodynamic force can introduce a characteristic time. We observe that this nonhydrodynamic force must be so small to be neglected in simple shear, since the behavior of the investigated suspension in the steady shear flow is found to be rate independent, and it must show its effects only in oscillatory experiments with strain amplitude smaller than 1. The frequency dependence is also observed with two less concentrated suspensions and all the data collapse on a single master curve, proving that the physics underneath the rate dependence is independent of the concentration.