This study models the human process of music cognition on the digital computer. The definition of music cognition is derived from the work in music cognition done by the researchers Carol Krumhansl and Edward Kessler, and by Mari Jones, as well as from the music theories of Heinrich Schenker. The computer implementation functions in three stages. First, it translates a musical "performance" in the form of MIDI (Musical Instrument Digital Interface) messages into LISP structures. Second, the various parameters of the performance are examined separately a la Jones's joint accent structure, quantified according to psychological findings, and adjusted to a common scale. The findings of Krumhansl and Kessler are used to evaluate the consonance of each note with respect to the key of the piece and with respect to the immediately sounding harmony. This process yields a multidimensional set of points, each of which is a cognitive evaluation of a single musical event within the context of the piece of music within which it occurred. This set of points forms a metric space in multi-dimensional Euclidean space. The third phase of the analysis maps the set of points into a topology-preserving data structure for a Schenkerian-like middleground structural analysis. This process yields a hierarchical stratification of all the musical events (notes) in a piece of music. It has been applied to several pieces of music with surprising results. In each case, the analysis obtained very closely resembles a structural analysis which would be supplied by a human theorist. The results obtained invite us to take another look at the representation of knowledge and perception from another perspective, that of a set of points in a topological space, and to ask if such a representation might not be useful in other domains. It also leads us to ask if such a representation might not be useful in combination with the more traditional rule-based representations by helping to eliminate unwanted levels of detail in a cognitive-perceptual system.