In general, transformations will conserve interior relations of objects, but not their ‘absolute’ position, or site, in the ambient space. This aspect is covered by the topological perspective. In its infancy, mathematical topology was in fact called “analysis situs”. It deals with the general question of what it means to be in the vicinity of an object. In music, topological considerations are of central importance since slight deformations of objects to neighboring objects are standard identification concepts|though never handled with the necessary care. The point in making these structures precise lies in the sharpening of a fundamental descriptive tool, and in the semantic potential which topology induces. We make explicit the latter topic in a discussion of the problem of topological classification of sounds.