Abstract: Perceptual similarity underlies a number of important psychological properties of musical materials, including perceptual invariance under transformation, categorization, recognition, and the sense of familiarity. Mental processes involved in the perception of musical similarity may be an integral part of the functional logic of music composition and thus underly important aspects of musical experience. How much and in what ways can musical materials be varied and still be considered as perceptually related or as belonging to the same category? The notions of musical material, musical variation, perceptual similarity and invariance, and form-bearing dimensions are considered in this light. Recent work on similarity perception has demonstrated that the transformation space for a given musical material is limited by several factors ranging from degree of match of the values of auditory attributes of the events composing the sequences to their relations of various levels of abstraction and to the degree that the transformation respects the grammar of the musical system within which the material was composed. These notions and results are considered in the light of future directions of research, particularly concerning the role of similarity and invariance in the understanding of musical form during listening.