The cognitive representation of harmonic and tonal structure in Western music is investigated using a tone-profile technique. In this method listeners rate how well single tones (any one of the 12 tones of the chromatic scale) follow a musical element such as a scale, chord, or cadence. Very stable rating profiles reflecting the tonal hierarchies in major and minor keys are obtained, which, when intercorrelated and analyzed using multidimensional scaling, produce a four-dimensional spatial map

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... f the distances between keys. The keys are located on the surface of a torus, in which the circle of fifths and the parallel and relative relations between major and minor keys are represented. In addition, single chords (major, minor, diminished, and dominant seventh) are found to be closely associated with the major and minor keys in which they play harmonic functions. The developing and changing sense of key during sequences of chords is traced by obtaining probe tone ratings following each chord in 10 different sequences, 8 of which contain modulations (changes) between keys. Modulations between closely related keys are found to be effected more immediately than are modulations between relatively distant keys. In all cases beyond the initial chord, the sense of the prevailing key is stronger than that produced by the last heard chord in isolation. Thus, listeners integrate harmonic functions over multiple chords, developing a sense of key that may need to be reevaluated as additional chords are sounded. It is suggested that the perceived relations between chords and keys and between different keys are mediated through an internal representation of the hierarchy of tonal functions of single tones in music. Music consists of tones varying in pitch, serve to highlight rhythmic patterns, further duration, loudness, and timbre, but the per-emphasize phrase structure, and distinguish ception of music extends well beyond the between tones constituting the primary meregistration of these physical attributes of lodic line and tones serving more ornamental the musical stimulus. Indeed, music contains or harmonic functions. Timbral characterconsiderable structure even in the relations istics may additionally provide important that obtain among the individual tones. For cues for the overall structure of the musical example, the durations are such that metri-composition. cal and rhythmic patterns emerge from the l n Western music pitch relationships are succession of tones, and these patterns in probably the most developed and essential combination with other features define nat-to defining organization. Despite the treural boundaries, or phrases, within the mu-mendous variation found in the selection and sical composition. Variations in loudness ordering of pitches in the musical literature, certain underlying regularities can be ob-This research was supported in part by a grant from served and described The perception of muthe National Science Foundation (BNS-81-03570) to gical structure de pends on the processing of the first author. The authors are grateful to David M. . , . , ,. ... e * 7 Green for the use of the facilities in the Psychophysics P ltc h information with reference to a system Laboratory at Harvard University, to Murray Spiegel of knowledge about the conventional USCS of and David Wilson for technical advice and assistance, pitches within the musical tradition. Thus, and to Roger N. Shepard and an anonymous reviewer cogn j t ive processes are significantly involved