Measuring self-similarity in empirical signals to understand musical beat perception

Experiencing music often entails the perception of a periodic beat. Despite being a widespread phenomenon across cultures, the nature and neural underpinnings of beat perception remain largely unknown. In the last decade, there has been a growing interest in developing methods to probe these processes, particularly to measure the extent to which beat-related information is contained in behavioral and neural responses. Here, we propose a theoretical framework and practical implementation of an analytic approach to capture beat-related periodicity in empirical signals using frequency-tagging. We highlight its sensitivity in measuring the extent to which the periodicity of a perceived beat is represented in a range of continuous time-varying signals with minimal assumptions. We also discuss a limitation of this approach with respect to its specificity when restricted to measuring beat-related periodicity only from the magnitude spectrum of a signal, and introduce a novel extension of the approach based on autocorrelation to overcome this issue. We test the new autocorrelation-based method using simulated signals and by re-analyzing previously published data, and show how it can be used to process measurements of brain activity as captured with surface EEG in adults and infants in response to rhythmic inputs. Taken together, the theoretical framework and related methodological advances confirm and elaborate the frequency-tagging approach as a promising window into the processes underlying beat perception and, more generally, temporally coordinated behaviors.