If one stimulus pattern is transposed to another, and if the two are recognizably the same, then they are said to be perceptually invariant. Usually, transpositions that lead to perceptual invariance involve changes on a ratio scale between the stimuli comprising the two patterns. In this paper, we survey the literature with a view to the conditions of pitch structure (melody and harmony), spectral structure (timbre), intensity structure (loudness), and temporal structure (rhythm, meter, and tempo) that produce perceptual invariance. The review compares perceptual invariance for human infants, young children, and adults and nonhuman animals. For the most part, perceptual invariance holds at all levels of development and for all species throughout the acoustic dimensions surveyed. However, for melody perception, there is evidence that humans go through a stage in early childhood in which absolute (as distinguished from relative) pitch perception plays a role. Without doubt, absolute pitch is important in perception of serial acoustic (melodic) structures by animals. For both humans and nonhumans, melody perception appears to be governed by a hierarchy of perceptual strategies that includes both absolute and relative pitch. The survey suggests the value of a comparative perspective in understanding the perceptual principles underlying music perception in humans and the principles by which human infants and nonhuman animals process acoustic information.