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Comments and reviews What are comments? Add a comment. We also consider the evolutionary status of the auditory features over which musical expectations operate. Fundamental pitch features in human music e. Other musical dimensions, e.
Rhythmic cognition in humans and animals: distinguishing meter and pulse perception
This work inspired interest in information theory throughout the s, in fields ranging from psychology e. The information content can be interpreted as the contextual unexpectedness or surprisal associated with an event. These early studies ran into difficulties Cohen, The first is the estimation of probabilities from the samples of music Cohen, However, it remains unclear whether the method could be implemented and generalized beyond their simple examples. Third, except for Hiller and Fuller , the music representations were exclusively simple representations of pitch Cohen, , ignoring other musical dimensions.
Even Hiller and Fuller considered each dimension separately, as they had no way of combining the derived information.
This was because of objective inadequacies of basic Markov chains as models of psychological representations, particularly for language Chomsky, ; it may also have been due to limitations in corpus size and the processing power of contemporaneous computers. These trends in cognitive science affected research on music. However, with a few isolated exceptions e. By way of explaining our approach to the study of information dynamics and the associated experience of expectation, we now present an overview of the Information Dynamics of Music IDyOM model of musical melody processing.
So there is evidence that broadly the same kind of model can capture at least two different aspects of music melody and harmony but also that they predict the expectations of untrained listeners as well as specialist theoreticians. The aim, then, was to construct a computational system embodying these theories and to subject them to rigorous testing. We have supplied a mechanism for learning enabling this overall structure Pearce, , and we hypothesize that it approximates the human mechanism at the level illustrated.
We aim to understand the relationship between auditory stimuli bottom of Fig. The results in the rest of this section are summarized from other more detailed publications, citations of which are given throughout. An abstract layered map, locating our model in a larger cognitive system. The various layers, which are delineated by horizontal lines, and some of which are elided by …, contain processes in squared boxes and phenomena in rounded boxes. These are connected by information flow, denoted by arrows.
As IDyOM encounters the musical corpus from which it learns, it creates a compact representation of the data Pearce, , facilitating matching of new note sequences against previously encountered ones. Second, the model is multidimensional, in two ways. The second multidimensional aspect is within each model, where there are multiple distributions derived from multiple features of the data, as detailed in Fig.
Schematic diagram of the viewpoint models, showing a subset of available viewpoints. D i are distributions across the alphabets of viewpoints, w i are the entropic weights introduced in Section 3. It is crucial that the model is never given the answers that it is expected to produce, nor is it optimized with reference to those answers.
Understanding Music with AI: Perspectives on Music Cognition
Thus, its predictions are in a sense epiphenomenal, and this is the strongest reason for proposing IDyOM, and the strong statistical view in general, as a veridical mechanistic model of music cognition at this level of abstraction: It does what it is required to do without being told how. IDyOM operates at the level of abstraction described above: Its inputs are note percepts described in terms of pitch and time. These dimensions, however, engender multiple features of each note, derived from pitch or time or both.
Added to these percept representations is an explicit representation of sequence in time: Sequence is the fundamental unit of representation. Given a sequence of percepts, we define functions, viewpoints , that accept initial subsequences of a sequence and select a specific dimension of the percepts in that sequence. For example, there is a viewpoint function that selects values of pitch from melodic data; given a sequence of pitches, it returns the pitch of the final note. However, it is most often convenient to think of viewpoints as sequences of these values.
The model starts from basic viewpoints, literal selections of note features as presented to the system, including 3 pitch, notestarttime, duration , and mode. Further viewpoints are derived , such as pitch interval the distance between two pitch es. Finally, threaded viewpoints select elements of a sequence, depending on an external predicate: for example, selecting the scale degree of the first note in each bar of a melody, if metrical information is given see Fig.
Each viewpoint models a percept, which is expressed and used in music theory and hence there is clear, careful motivation for each feature.
How those properties arise is not our focus of interest in the current presentation, but it will be the object of future work. The system itself selects which of the available representations is actually used , as described in the next section. The learning system is enhanced by an optimization step, based on the hypothesis that brains compress information, and that they do so efficiently.
For example, imagine two pitch viewpoints representations of pitch are available, one in absolute terms and the other in terms of the difference interval , in musical terms between successive notes. The system chooses the relative representation and discards the absolute one, because the relative representation allows the music to be represented independently of musical key, and this requires fewer symbols by a factor of Thus, the data itself determines the selection of the viewpoints best able to represent it efficiently; a level playing field for prediction is provided by the fact that each viewpoint distribution is converted into a basic one before comparison: Thus, is computed from the pitch distribution of each model.
A general mechanism by which this may take place in our statistical model is a focus of our current research, beyond the scope of the current paper.
Chapter 9, Music and Consciousness
This model is the first stage of an extended research program of cognitive modeling. In this context, it is important that we note its shortcomings as well as its successes and potentials. We do so at this point to make a clear distinction between the issues, which are outstanding for IDyOM as a model, and those which are relevant to the discourse on expectation presented in the next sections. First, the model is currently limited to monodic melodic music, which is only one aspect of the massively multidimensional range of music available; while our focus on melody is perceptually, musicologically, and methodologically defensible, the other aspects need to be considered in due course.
Second, and more fundamentally, the memory model used here is inadequate: The model exhibits total recall and its memory never fails. There is work to do on the statistical memory mechanism currently based on exact literal recording and matching by identity to model human associative memory more closely.
Options include pruning the leaves of the tree e. Third, as explained above, the viewpoints used in the system are chosen from music theory and must be implemented by hand. This is useful for the purposes of research, because we are able to interpret, to some extent, what the model is doing by looking at the viewpoints it selects.
This would greatly increase the power of the system, because it would be able to determine its own representation, by reflection. Our approach invokes a cognitive learning process through which expectations contribute to accurate predictions about the auditory environment. Here, we study pitch expectations in melody, where evidence exists for learning. However, these rules would be unnecessary if the aspects of expectation they cover can be learned through exposure to music.
In these studies, melodies were paused to allow listeners to respond. Cognitive neuroscientific studies of musical expectations have tended to focus on EEG and MEG, which have far superior temporal resolution to other methods such as fMRI. A The correlation between the mean expectedness ratings of the listeners for each probed note ordinate and the information content of IDyOM abscissa. The notes were divided into two groups: high information content black circles and low information content red squares. Grouping and boundary perception are core functions in many areas of cognitive science, such as natural language processing e.
The segmentation of a sequence of musical notes into contiguous groups occurring sequentially in time e. Narmour proposed that grouping boundaries are perceived where expectations are weak: No particularly strong expectations are generated beyond the boundary. Therefore, we hypothesize that musical grouping boundaries are perceived before events for which the unexpectedness of the outcome h and the uncertainty of the prediction H are high.
We tested this in two experiments using the IDyOM model trained on Western tonal melodies; Pearce, to predict perceived grouping boundaries at peaks in the information content profile for a melody. For example, Jamshed Bharucha and Peter Todd have modeled music perception in tonal music with neural networks. Within cognitive psychology , among the most prominent researchers is Diana Deutsch , who has engaged in a wide variety of work ranging from studies of absolute pitch and musical illusions to the formulation of musical knowledge representations to relationships between music and language.
Patel, whose work combines traditional methodologies of cognitive psychology with neuroscience. Patel is also the author of a comprehensive survey of cognitive science research on music. Sign In Don't have an account? AI and music: A cornerstone of cognitive musicology. Balaban, K. Laske Eds. Journal of Educational Technology Systems , 38 2 , New York: Greenwood Press.
Tracing the dynamic changes in perceived tonal organisation in a spatial representation of musical keys. Otto Laske , Westport: Greenwood Press.