We present a method for real-time sound propagation that captures all wave effects, including diffraction and reverberation, for multiple moving sources and a moving listener in a complex, static 3D scene. It performs an offline numerical simulation over the scene and then applies a novel technique to extract and compactly encode the perceptually salient information in the resulting acoustic responses. Each response is automatically broken into two phases: early reflections (ER) and late reverberation (LR), via a threshold on the temporal density of arriving wavefronts. The LR is simulated and stored in the frequency domain, once per room in the scene. The ER accounts for more detailed spatial variation, by recording a set of peak delays/amplitudes in the time domain and a residual frequency response sampled in octave frequency bands, at each source/receiver point pair in a 5D grid. An efficient run-time uses this precomputed representation to perform binaural sound rendering based on frequency-domain convolution. Our system demonstrates realistic, wave-based acoustic effects in real time, including diffraction low-passing behind obstructions, sound focusing, hollow reverberation in empty rooms, sound diffusion in fully-furnished rooms, and realistic late reverberation.