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.
Another limitation of most long-term memory models for tonal learning is that they work with stimuli that are reduced in one or more ways. For example, the input may consist of discrete representations of tones such as MIDI note numbers @cite_20 , pitch classes @cite_1 , artificial harmonic representations @cite_0 , or of artificial harmonic sounds such as Shepard tones @cite_2 . Furthermore, the musical material that a model is exposed to may be limited to monophonic melodic lines @cite_20 , sets of chords or harmonic cadences @cite_2 , or even a set of probe-tone profiles @cite_22 . A notable exception to this is @cite_36 , which uses an audio recording of Bach's Well Tempered Clavier (WTC), performed on a harpsichord, to train a SOM by converting the acoustic signal to . The work of @cite_21 also takes an ecological approach by using real audio and plausible psychological representations, with multiple representations along the sensory-cognitive spectrum, to better account for human tonal expectation.
@cite_22 @cite_36 @cite_21 @cite_1 @cite_0 @cite_2 @cite_20
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We examined a variety of real-time responses evoked by a single piece of music, the organ Duetto BWV 805 by J S Bach. The primary data came from a concurrent probe-tone method in which the probe tone is sounded continuously with the music. Listeners judged how well the probe tone fit with the music at each point in time. The process was repeated for all probe tones of the chromatic scale. A self-organizing map (SOM) (Kohonen 1997 Self-organizing Maps (Berlin: Springer)) was used to represent the developing and changing sense of key reflected in these judgments. The SOM was trained on the probe-tone profiles for 24 major and minor keys (Krumhansl and Kessler 1982 Psychological Review 89 334^368). Projecting the concurrent probe-tone data onto the map showed changes both in the perceived keys and in their strengths. Two dynamic models of tonality induction were tested. Model 1 is based on pitch class distribu- tions. Model 2 is based on the tone-transition distributions; it tested the idea that the order of tones might provide additional information about tonality. Both models contained dynamic components for characterizing pitch strength and creating pitch memory representations. Both models produced results closely matching those of the concurrent probe-tone data. Finally real- time judgments of tension were measured. Tension correlated with distance away from the predominant key in the direction of keys built on the dominant and supertonic tones, and also correlated with dissonance. 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. We consider the problem of transcribing polyphonic piano music with an emphasis on generalizing to unseen instruments. We use deep neural networks and propose a novel approach that predicts onsets and frames using both CNNs and LSTMs. This model predicts pitch onset events and then uses those predictions to condition framewise pitch predictions. During inference, we restrict the predictions from the framewise detector by not allowing a new note to start unless the onset detector also agrees that an onset for that pitch is present in the frame. We focus on improving onsets and offsets together instead of either in isolation as we believe it correlates better with human musical perception. This technique results in over a 100 relative improvement in note with offset score on the MAPS dataset.