Frames provide redundant but stable basis-like expansions in Hilbert and Banach spaces. Gabor and wavelet frames are among the most useful examples. Gabor frames in particular provide representations of signals closely analogous to the representation of music by a musical score. This representation is known to possess a particular uniformity, which is stated precisely in the Homogeneous Approximation Property (HAP) for Gabor frames. We present the HAP and examine its implications for Gabor frames. We then show that the HAP and its implications are not merely features of the particular rigid structure of Gabor frames but rather are consequences of more general considerations. In particular, we show that Nyquist density phenomena are not limited to the Gabor setting but occur in a large class of abstract frames.