Perceptual Tests of an Algorithm for Musical Key-Finding Mark A. Schmuckler and Robert Tomovski University of Toronto at Scarborough Perceiving the tonality of a musical passage is a fundamental aspect of the experience of hearing music. Models for determining tonality have thus occupied a central place in music cognition research. Three experiments investigated 1 well-known model of tonal determination: the Krumhansl–Schmuckler key-finding algorithm. In Experiment 1, listeners’ percepts of tonality following short musical fragments derived from preludes by Bach and Chopin were compared with predictions of tonality produced by the algorithm; these predictions were very accurate for the Bach preludes but considerably less so for the Chopin preludes. Experiment 2 explored a subset of the Chopin preludes, finding that the algorithm could predict tonal percepts on a measure-by-measure basis. In Experiment 3, the algorithm predicted listeners’ percepts of tonal movement throughout a complete Chopin prelude. These studies support the viability of the Krumhansl–Schmuckler key-finding algorithm as well as a model of listeners’ tonal perceptions of musical passages. Keywords: music cognition, tonality, key-finding As a subdiscipline with cognitive psychology, music perception provides a microcosm for investigating general psychological functioning (Schmuckler, 1997b), including basic psychophysical processing, complex cognitive behavior (e.g., priming, memory, category formation), issues of motor control and performance, and even social and emotional influences on musical behavior. Within this broad range, the apprehension of music has been most vigor- ously studied from a cognitive standpoint. One example of the type of insights into basic cognitive function afforded by such research is found in work on the psychological representation of pitch in a tonal context (e.g., Krumhansl, 1990; Schmuckler, 2004). A fundamental characteristic of Western music is that the indi- vidual tones making up a piece of music are organized around a central reference pitch, called the tonic or tonal center, with music organized in this fashion said to be in a musical key or tonality. Tonality is interesting psychologically in that it represents a very general cognitive principle: that certain perceptual and/or concep- tual objects have special psychological status (Krumhansl, 1990). Within psychological categories, for example, there is a gradient of representativeness of category membership, such that some mem- bers are seen as central to the category, functioning as reference points, whereas other members are seen as more peripheral to the category and, hence, function as lesser examples (see Rosch, 1975). This characterization is particularly apt for describing mu- sical tonality. In a tonal context, the tonic note is considered the best exemplar of the key, with the importance of this tone indicated by the fact that it is this pitch that gives the tonality its name. The remaining pitches (with the complete set composed of 12 pitches called the chromatic scale) then vary in terms of how representa- tive they are of this tonality relative to this reference pitch. Within Western tonal music, there are two categories of musical key—major and minor tonalities. For any given reference pitch, it is possible to produce a major and a minor tonality, with each tonality establishing a unique hierarchical pattern of relations among the tones. Moreover, major and minor tonalities can be built on any chromatic scale tone; thus, there are 24 (12 major and 12 minor) tonalities used in Western music. For all of these keys, however, the theoretical pattern of note relations holds, with the tonic functioning as the reference pitch and the remaining tones varying in their relatedness to this reference pitch. Table 1 presents this theoretical hierarchy for the 12 semitones (the smallest unit of pitch change in Western music) for both major and minor tonalities. Krumhansl and colleagues (Krumhansl, 1990; Krumhansl, Bha- rucha, & Castellano, 1982; Krumhansl, Bharucha, & Kessler, 1982; Krumhansl & Kessler, 1982; Krumhansl & Shepard, 1979) have provided psychological verification of this theoretical hier- archy, using what is known as the probe-tone procedure. In this procedure, a listener hears a context passage that unambiguously instantiates a given tonality. The context is then followed by a probe tone, which is a single tone from the chromatic scale, and listeners provide a goodness-of-fit rating for this probe relative to the tonality of the previous context. By sampling the entire chro- matic set, one can arrive at an exhaustive description of the perceptual stability of these individual musical elements vis-a `-vis a given tonality. The ratings for these 12 events with reference to a key is known as the tonal hierarchy (Krumhansl, 1990). The top panel of Figure 1 shows the ratings of the probe tones relative to a major and minor context, with the note C as the tonic (C major and C minor tonalities, respectively); for comparison with Table 1, the semitone numbering is also given. These ratings Mark A. Schmuckler and Robert Tomovski, Department of Life Sci- ences, University of Toronto at Scarborough, Toronto, Ontario, Canada. Portions of this work were presented at the 38th Annual Meeting of the Psychonomic Society, Philadelphia, Pennsylvania, November 1997. This research was supported by a grant from the Natural Sciences and Engi- neering Research Council of Canada to Mark A. Schmuckler. Correspondence concerning this article should be addressed to Mark A. Schmuckler, Department of Life Sciences, University of Toronto, 1265 Military Trail, Scarborough, Ontario M1C 1A4, Canada. E-mail: marksch@utsc.utoronto.ca Journal of Experimental Psychology: Copyright 2005 by the American Psychological Association Human Perception and Performance 2005, Vol. 31, No. 5, 1124 –1149 0096-1523/05/$12.00 DOI: 10.1037/0096-1523.31.5.1124 1124