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Tonal music is a highly structured system that is ubiquitous in our cultural environment. We demonstrate the acquisition of implicit knowledge of tonal structure through neural self-organization resulting from mere exposure to simultaneous and sequential combinations of tones. In the process of learning, a network with fundamental neural constraints comes to internalize the essential correlational structure of tonal music. After learning, the network was run through a range of experiments from the literature. The model provides a parsimonious account of a variety of empirical findings dealing with the processing of tone, chord, and key relationships, including relatedness judgments, memory judgments, and expectancies. It also illustrates the plausibility of activation being a unifying mechanism underlying a range of cognitive tasks. Natural environments contain highly structured systems to which we are exposed in everyday life. The human brain internalizes these regularities by passive exposure, and the acquired implicit knowledge influences perception and performance. Aspects of language and music provide two examples of highly structured systems that may be learned in an incidental manner. In each case, there is a paradox. On the one hand, a thorough formal description of the structure has proven to be extremely challenging. On the other hand, native speakers or nonmusician listeners internalize the regularities underlying linguistic or musical structures with apparent ease. A substantial corpus of research has been devoted to the learning process of language, but little has been devoted to the learning of music. The central purpose of the present article is to investigate how implicit knowledge of some basic features of Western musical grammar may be acquired and mentally represented.Barbara Tillmann, Department of Psychology, Universit6 de Bourgogne, LEAD-CNRS, Dijon, France, and Department of Psychological and Brain Sciences, Dartmouth College; Jamshed J. Bharucha, Department of Psychological and Brain Sciences, Dartmouth College; Emmanuel Bigand, Department of Psychology, Universit6 de Bourgogne, LEAD-CNRS.This research was supported in part by National Science Foundation Grant SBR-9601287 and National Institutes of Health Grant 2P50 NS17778-18 to Jamshed J. Bharucha and by a grant from the International Foundation for Music Research to Emmanuel Bigand. Barbara Tillmann has been supported by the French Ministry of Education and Research and by the Deutsche Akademische Austauschdienst DAAD. We thank Herv6 Abdi, Pierre Perruchet, and Philippe Schyns for insightful comments at different stages of the present work and Carol Krumhansl and Fred Lerdahl for comments on the article.Correspondence concerning this article should be addressed to Barbara Tillmann, Department of Psychological and Brain Sciences, Dartmouth College, 6207 Moore Hall, Hanover, New Hampshire 03755. Electronic mall may be sent to barbara.tillmann@dartmouth.edu. 885We present a connectionist model that (a) simulates the implicit learning of p...

The mind internalizes persistent structural regularities in music and recruits these internalized representations to facilitate subsequent perception. Facilitation underlies the generation of musical expectations and implications and the influence of a musical context on consonance and memory. Facilitation is demonstrated in experiments showing priming of chords: chords that are harmonically closely related to a preceding context are processed more quickly than chords that are harmonically distant from the context. A tonal context enhances intonational sensitivity for related chords and heightens their consonance. Facilitation occurs even when related chords don't share component tones with the context, and even when overlapping harmonics are eliminated. These results point to the indirect activation of representational units at a cognitive level. In a parallel study conducted in India, tones considered to play an important role in a rag but absent from the experimental rendition of that rag were facilitated in the same way. In a connectionist framework, facilitation is a consequence of activation spreading through a network of representational units whose pattern of connectivity encodes musical relationships. In a proposed connectionist model of harmony, each event in a musical sequence activates tone units, and activation spreads via connecting links to parent chord units and then to parent key units. Activation reverberates bidirectionally until the network settles into a state of equilibrium. The initial stages of the activation process constitute the bottom-up influence of the sounded tones, while the later, reverberatory stages constitute the top-down influence of learned, schematic structures internalized at the cognitive level. Computer simulations of the model show the same pattern of data as human subjects in experiments on relatedness judgments of chords and memory for chord sequences.

The cognitive processes underlying musical expectation were explored by measuring reaction time in a priming paradigm. Subjects made a speeded true/false decision about a target chord following a prime chord to which it was either closely or distantly related harmonically. Using a major/minor decision task in Experiment 1, we found that major targets were identified faster, and with fewer errors, when they were related than when unrelated. An apparent absence (and possible reversal) of this effect for minor targets can be attributed to the prime's biasing effect on the target's stability. In Experiments 2 and 3 we tested this hypothesis by employing an in-tune/out-of-tune decision for major and minor targets separately. Both major and minor in-tune targets were identified faster when related than when unrelated. We outline a spreading activation model which consists of a network of harmonic relations. Priming results from the indirect activation of chord nodes linked through the network.

Western tonal music relies on a formal geometric structure that determines distance relationships within a harmonic or tonal space. In functional magnetic resonance imaging experiments, we identified an area in the rostromedial prefrontal cortex that tracks activation in tonal space. Different voxels in this area exhibited selectivity for different keys. Within the same set of consistently activated voxels, the topography of tonality selectivity rearranged itself across scanning sessions. The tonality structure was thus maintained as a dynamic topography in cortical areas known to be at a nexus of cognitive, affective, and mnemonic processing.

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SUMMARYCross-culturally, most music is tonal in the sense that one particular tone, called the tonic, provides a focus around which the other tones are organized. The specific organizational structures around the tonic show considerable diversity. Previous studies of the perceptual response to Western tonal music have shown that listeners familiar with this musical tradition have internalized a great deal about its underlying organization. Krumhansl and Shepard (1979) developed a probe tone method for quantifying the perceived hierarchy of stability of tones. When applied to Western tonal contexts, the measured hierarchies were found to be consistent with music-theoretic accounts.In the present study, the probe tone method was used to quantify the perceived hierarchy of tones of North Indian music. Indian music is tonal and has many features in common with Western music. One of the most significant differences is that the primary means of expressing tonality in Indian music is through melody, whereas in Western music it is through harmony (the use of chords). Indian music is based on a standard set of melodic forms (called rags), which are themselves built on a large set of scales (thats). The tones within a rag are thought to be organized in a hierarchy of importance.Probe tone ratings were given by Indian and Western listeners in the context of 10 North Indian rags. These ratings confirmed the predicted hierarchical ordering. Both groups of listeners gave the highest ratings to the tonic and the fifth degree of the scale. These tones are considered by Indian music theorists to be structurally significant, as they are immovable tones around which the scale system is constructed, and they are sounded continuously in the drone. Relatively high ratings were also given to the vadi tone, which is designated for each rag and is given emphasis in the melody. The ratings of both groups of listeners generally reflected the pattern of tone durations in the musical contexts. This result suggests that the distribution of tones in music is a psychologically effective means of conveying the tonal hierarchy to listeners whether they are familiar with the musical tradition. Beyond this, only the Indian listeners were sensitive to the scales (thats) underlying the rags. For Indian listeners, multidimensional scaling of the correlations between the rating profiles recovered the theoretical representation of scales described by theorists of Indian music. Thus, the empirically measured tonal hierarchy induced by the rag contexts generates structure at the level of the underlying scales or thats, but its internalization apparently requires more extensive experience with music based on that scale system than that provided by the experimental context. There was little evidence that Western listeners assimilated the pitch materials to the major and minor diatonic system of Western music. 394

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