Abstract
Pulse is the base timing to which western music is commonly notated, generally expressed by a listener by performing periodic taps with their hand or foot. This cognitive construction helps organize the perception of timed events in music and is the most basic expectation in rhythms. The analysis of expectations, and more specifically the strength with which the beat is felt—the pulse clarity—has been used to analyze affect in music. Most computational models of pulse clarity, and rhythmic expectation in general, analyze the input as a whole, without exhibiting changes through a rhythmic passage. We present Tactus Hypothesis Tracker (THT), a model of pulse clarity over time intended for symbolic rhythmic stimuli. The model was developed based on ideas of beat tracking models that extract beat times from musical stimuli. Our model also produces possible beat interpretations for the rhythm, a fitness score for each interpretation and how these evolve in time. We evaluated the model’s pulse clarity by contrasting against tapping variability of human annotators achieving results comparable to a state-of-the-art pulse clarity model. We also analyzed the clarity metric dynamics on synthetic data that introduced changes in the beat, showing that our model presented doubt in the pulse estimation process and adapted accordingly to beat changes. Finally, we assessed if the beat tracking generated by the model was correct regarding listeners tapping data. We compared our beat tracking results with previous beat tracking models. The THT model beat tracking output showed generally correct estimations in phase but exhibits a bias towards a musically correct subdivision of the beat.
Highlights
We evaluated the model on three aspects: whether an overall pulse clarity metric obtained from the model corresponds with human perception, whether the clarity metric changes on synthetic rhythmic inputs with changing beat scenarios and whether the final beat tracking performed by the model agrees with beat tracking performed by listeners
The model is based on beat tracking models from the Music Information Retrieval field, performing adaptations that allow inspecting the inner workings of the model while it is exposed to a symbolic rhythmic passage
We focused on using the model’s output to produce a pulse clarity metric that develops over time as the model ‘listens’ to the rhythmic passage
Summary
The beat function is filtered to obtain discrete beat times Most of these algorithms analyze the entire signal to estimate the initial parameters of the beat tracking process, which is done in a causal fashion (from beginning to end without using future information). Our proposal is a beat tracking model that continuously produces a pulse clarity metric and can be used for experiments on the relationship of rhythmic expectations with affect. With this in mind, we aim for a simple model that allows understanding how pulse clarity is calculated from the stimulus. The Discussion revises the results in the broader context of analysis of musical affect and proposes further developments for the model and its uses as a tool for experimental designs
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