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Interpersonal coordination during musical joint action (e.g., ensemble performance) requires individuals to anticipate and adapt to each other’s action timing. Individuals differ in their ability to both anticipate and adapt, however, little is known about the relationship between these skills. The present study used paced finger tapping tasks to examine the relationship between anticipatory skill and adaptive (error correction) processes. Based on a computational model, it was hypothesized that temporal anticipation and adaptation will act together to facilitate synchronization accuracy and precision. Adaptive ability was measured as the degree of temporal error correction that participants (N = 52) engaged in when synchronizing with a ‘virtual partner’, that is, an auditory pacing signal that modulated its timing based on the participant’s performance. Anticipation was measured through a prediction index that reflected the degree to which participants’ inter-tap intervals led or lagged behind inter-onset intervals in tempo-changing sequences. A correlational analysis revealed a significant positive relationship between the prediction index and temporal error correction estimates, suggesting that anticipation and adaptation interact to facilitate synchronization performance. Hierarchical regression analyses revealed that adaptation was the best predictor of synchronization accuracy, whereas both adaptation and anticipation predicted synchronization precision. Together these results demonstrate a relationship between anticipatory and adaptive mechanisms, and indicate that individual differences in these two abilities are predictive of synchronization performance.

In: Timing & Time Perception

The mechanisms that support sensorimotor synchronization — that is, the temporal coordination of movement with an external rhythm — are often investigated using linear computational models. The main method used for estimating the parameters of this type of model was established in the seminal work of Vorberg and Schulze (), and is based on fitting the model to the observed auto-covariance function of asynchronies between movements and pacing events. Vorberg and Schulze also identified the problem of parameter interdependence, namely, that different sets of parameters might yield almost identical fits, and therefore the estimation method cannot determine the parameters uniquely. This problem results in a large estimation error and bias, thereby limiting the explanatory power of existing linear models of sensorimotor synchronization. We present a mathematical analysis of the parameter interdependence problem. By applying the Cramér–Rao lower bound, a general lower bound limiting the accuracy of any parameter estimation procedure, we prove that the mathematical structure of the linear models used in the literature determines that this problem cannot be resolved by any unbiased estimation method without adopting further assumptions. We then show that adding a simple and empirically justified constraint on the parameter space — assuming a relationship between the variances of the noise terms in the model — resolves the problem. In a follow-up paper in this volume, we present a novel estimation technique that uses this constraint in conjunction with matrix algebra to reliably estimate the parameters of almost all linear models used in the literature.

In: Timing & Time Perception

Linear models have been used in several contexts to study the mechanisms that underpin sensorimotor synchronization. Given that their parameters are often linked to psychological processes such as phase correction and period correction, the fit of the parameters to experimental data is an important practical question. We present a unified method for parameter estimation of linear sensorimotor synchronization models that extends available techniques and enhances their usability. This method enables reliable and efficient analysis of experimental data for single subject and multi-person synchronization. In a previous paper (Jacoby et al., ), we showed how to significantly reduce the estimation error and eliminate the bias of parameter estimation methods by adding a simple and empirically justified constraint on the parameter space. By applying this constraint in conjunction with the tools of matrix algebra, we here develop a novel method for estimating the parameters of most linear models described in the literature. Through extensive simulations, we demonstrate that our method reliably and efficiently recovers the parameters of two influential linear models: Vorberg and Wing (), and Schulze et al. (), together with their multi-person generalization to ensemble synchronization. We discuss how our method can be applied to include the study of individual differences in sensorimotor synchronization ability, for example, in clinical populations and ensemble musicians.

In: Timing & Time Perception


We report an experiment to investigate possible vestibular effects on finger tapping to an auditory anapaest rhythm. In a sample of 10 subjects, index finger acceleration and tapping force were recorded along with extensor/flexor activity and the associated electroencephalographic activity measured at central and cerebellar surface electrodes. In a prior session with a standard short air-conducted 500-Hz pip, vestibular evoked myogenic potential thresholds were measured and subsequently used to set the acoustic intensity. During the main experiment subjects were asked to synchronise tapping to the pips arranged in the anapaest at two different frequencies, 500 Hz vs 5 kHz, so that only the low-frequency high-intensity condition was a vestibular, as well as an auditory stimulus. We hypothesised that a vestibular effect would manifest in an interaction between the frequency and intensity factors for a range of dependent measures of tapping performance. No clear evidence was found for vestibular effects, but this was likely due to the confounding effects of an independent effect of intensity and the relative weakness of the acoustic vestibular stimulus. However, the data did show novel evidence for two distinct timing processes for the flexion and extension stages of a tap cycle and two distinct timing strategies, which we refer to as ‘staccato’ and ‘legato’, characterised by different profiles of force and extension.

Open Access
In: Timing & Time Perception