Tonal structure is in part conveyed by statistical regularities between musical events, and research has shown that computational models reflect tonal structure in music by capturing these regularities in schematic constructs like pitch histograms. Of the few studies that model the acquisition of perceptual learning from musical data, most have employed self-organizing models that learn a topology of static descriptions of musical contexts. Also, the stimuli used to train these models are often symbolic rather than acoustically faithful representations of musical material. In this work we investigate whether sequential predictive models of musical memory (specifically, recurrent neural networks), trained on audio from commercial CD recordings, induce tonal knowledge in a similar manner to listeners (as shown in behavioral studies in music perception). Our experiments indicate that various types of recurrent neural networks produce musical expectations that clearly convey tonal structure. Furthermore, the results imply that although implicit knowledge of tonal structure is a necessary condition for accurate musical expectation, the most accurate predictive models also use other cues beyond the tonal structure of the musical context.
The computational models proposed in the literature tend to emphasize one of various different factors that are thought to play a role in tonal perception. Whereas some works seek to explain empirical results mainly by a computational account of the lower levels of the auditory system @cite_2 @cite_3 , others focus more strongly on the role of long-term memory in tonal perception @cite_36 @cite_1 @cite_20 .
@cite_36 @cite_1 @cite_3 @cite_2 @cite_20
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Listeners' expectations for melodies and harmonies in tonal music are perhaps the most studied aspect of music cognition. Long debated has been whether faster response times (RTs) to more strongly primed events (in a music theoretic sense) are driven by sensory or cognitive mechanisms, such as repetition of sensory information or activation of cognitive schemata that reflect learned tonal knowledge, respectively. We analyzed over 300 stimuli from 7 priming experiments comprising a broad range of musical material, using a model that transforms raw audio signals through a series of plausible physiological and psychological representations spanning a sensory- cognitive continuum. We show that RTs are modeled, in part, by information in periodicity pitch distributions, chroma vectors, and activations of tonal space-a representation on a toroidal surface of the major minor key relationships in Western tonal music. We show that in tonal space, melodies are grouped by their tonal rather than timbral properties, whereas the reverse is true for the periodicity pitch representation. While tonal space variables explained more of the variation in RTs than did periodicity pitch variables, suggesting a greater contribution of cognitive influences to tonal expectation, a stepwise selection model contained variables from both representations and successfully explained the pattern of RTs across stimulus categories in 4 of the 7 experiments. The addition of closure-a cognitive representation of a specific syntactic relationship- succeeded in explaining results from all 7 experiments. We conclude that multiple representational stages along a sensory- cognitive continuum combine to shape tonal expectations in music. © 2014 American Psychological Association. The perception of tonal structure in music seems to be rooted both in low-level perceptual mechanisms and in enculturation, the latter accounting for cross-cultural differences in perceived tonal structure. Unsupervised machine learning methods are a powerful tool for studying how musical concepts may emerge from exposure to music. In this paper, we investigate to what degree tonal structure can be learned from musical data by unsupervised training of a Restricted Boltzmann Machine, a generative stochastic neural network. We show that even based on a limited set of musical data, the model learns several aspects of tonal structure. Firstly, the model learns an organization of musical material from different keys that conveys the topology of the circle of fifths (CoF). Although such a topology can be learned using principal component analysis (PCA) when using pitch-only representations, we found that using a pitch-duration representation impedes the extraction of the CoF topology much more for PCA than for the RBM. Furthermore, we replicate probe-tone experiments by Krumhansl and Shepard, measuring the organization of tones within a key in human perception. We find that the responses of the RBM share qualitative characteristics with those of both trained and untrained listeners. In this paper, a model for tone-center perception is developed. It is based on an auditory model and principles of schema dynamics such as self-organization and association. The auditory module simulates virtual-pitch perception by transforming musical signals into auditory images. The schema- based module involves data-driven long-term learning for the self-organization of a schema for tone-center perception. The focus of this paper is on a retroactive process (called perceptual interpretation) by which the sense of tone center is adjusted according to a reconsideration of preceding perceptions in view of new contextual evidence within the schema. To this purpose, a metaphor is introduced, in which perceptual interpretation is described as the movement of a snaillike object in an attractor space. Additionally, the mathematical details of the model are presented, and the results of computer simulations are discussed. Science since antiquity has asked whether mathematical relationships among acoustic frequencies govern musical relationships. Psychophysics rejected frequency ratio theories, focusing on sensory phenomena predicted by linear analysis of sound. Cognitive psychologists have since focused on long-term exposure to the music of one’s culture and short-term sensitivity to statistical regularities. Today evidence is rapidly mounting that oscillatory neurodynamics is an important source of nonlinear auditory responses. This leads us to reevaluate the significance of frequency relationships in the perception of music. Here, we present a dynamical systems analysis of mode-locked neural oscillation that predicts cross-cultural invariances in music perception and cognition. We show that this theoretical framework combines with short- and long-term learning to explain the perception of Hindustani rāgas, not only by encultured Indian listeners but also by Western listeners unfamiliar with the style. These findings demonstrate that intrinsic neurodynamics contribute significantly to the perception of musical structure.