Using Trajectory Mapping to Analyze Musical Intervals

Cognitive scientists have often pondered the question of perceptual spaces, that is, the question of how a certain gamut of familiar stimuli might be organized in the mind. We present Trajectory Mapping as an alternative clustering method to the traditional algorithm of Multi-Dimensional Scaling. We suggest that given data about the relationships among stimuli, Multi-Dimensional Scaling provides the one type of information (geometric), while Trajectory Mapping offers a second type (relational). As an illustration we present the initial results of applying both clustering techniques to subjects' perceptions musical intervals. While an interpretation of Multi-Dimensional Scaling requires a priori knowledge of music theory, Trajectory Mapping reveals the music theory that has been internalized by subjects.