Data are embedded in an audio signal for watermarking, steganography, or other purposes. The audio signal is divided into time frames. In each time frame, the relative phases of one or more frequency bands are shifted to represent the data to be embedded. In one embodiment, two frequency bands are selected according to a pseudo-random sequence, and their relative phase is shifted. In another embodiment, the phases of one or more overtones relative to the fundamental tone are quantized.