You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
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.

Cited Abstract(s):
[1]: 

[2]: 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

[3]: 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.

[4]: 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.

[5]: 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.
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 [4] [3] , others focus more strongly on the role of long-term memory in tonal perception [1] [2] [4]0 .