Event-based and emergent timing: dichotomy or continuum? A reply to Repp and Steinman (2010)

Sensorimotor synchronization with visual, auditory, and tactile modalities

While it is well known that humans are highly responsive to rhythm, the factors that influence our ability to synchronize remain unclear. In the current study, we examined how stimulus modality and rhythmic deviation, along with the synchronizer's level of musicality, impacted sensorimotor synchronization (SMS). Utilizing a finger-tapping task and three sensory modalities (visual, auditory, and tactile), we manipulated rhythmic deviation by varying the temporal position, intensity, and availability of cues across four deviation levels. Additionally, to determine our participants' musical familiarity and aptitude, we administered the Goldsmiths Musical Sophistication Index (Gold-MSI) questionnaire. We found that SMS to external rhythmic stimuli was significantly more precise for auditory and tactile than for visual sequences. Further, we found SMS consistency significantly decreased in all modalities with increased rhythmic deviation, suggesting rhythmic deviation directly relates to SMS difficulty. Moreover, a significant correlation was found between Gold-MSI scores and SMS consistency in the most rhythmically deviant level, such that the higher one's musical general sophistication score, the greater one's SMS ability. This held for all three modalities. Combined, these findings suggest that rhythmic synchronization performance is affected not only by the modality and rhythmic deviation of the stimuli but also by the musical general sophistication of the synchronizer.

Temporal organization of stride-to-stride variations contradicts predictive models for sensorimotor control of footfalls during walking

Walking exhibits stride-to-stride variations. Given ongoing perturbations, these variations critically support continuous adaptations between the goal-directed organism and its surroundings. Here, we report that stride-to-stride variations during self-paced overground walking show cascade-like intermittency-stride intervals become uneven because stride intervals of different sizes interact and do not simply balance each other. Moreover, even when synchronizing footfalls with visual cues with variable timing of presentation, asynchrony in the timings of the cue and footfall shows cascade-like intermittency. This evidence conflicts with theories about the sensorimotor control of walking, according to which internal predictive models correct asynchrony in the timings of the cue and footfall from one stride to the next on crossing thresholds leading to the risk of falling. Hence, models of the sensorimotor control of walking must account for stride-to-stride variations beyond the constraints of threshold-dependent predictive internal models.

Effects of motor pacing on frontal-hemodynamic responses during continuous upper-limb and whole-body movements

Advances in timing research advocate for the existence of two timing mechanisms (automatic vs. controlled) that are related to the level of cognitive control intervening for motor behavior regulation. In the present study, we used the functional near-infrared spectroscopy (fNIRS) cutting-edge technique to examine the hypothesis that prefrontal inhibitory control is needed to perform slow motor activities. Participants were asked to perform a sensorimotor-synchronization task at various paces (i.e., slow, close-to-spontaneous, fast). We contrasted upper-limb circle drawing to a more naturalistic behavior that required whole-body movements (i.e., steady-state walking). Results indicated that whole-body movements led to greater brain oxygenation over the motor regions when compared with upper-limb activities. The effect of motor pace was found in the walking task only, with more bilateral orbitofrontal and left dorsolateral activation at slow versus fast pace. Exploratory analyses revealed a positive correlation between the activation of the orbitofrontal and motor areas for the close-to-spontaneous pace in both tasks. Overall, results support the key role of prefrontal cognitive control in the production of slow whole-body movements. In addition, our findings confirm that upper-limb (laboratory-based) tasks might not be representative of those engaged during everyday-life motor behaviors. The fNIRS technique may be a valuable tool to decipher the neurocognitive mechanisms underlying naturalistic, adaptive motor behaviors.

Multifractal Dynamics in Executive Control When Adapting to Concurrent Motor Tasks

There is some evidence that an improved understanding of executive control in the human movement system could be gained from explorations based on scale-free, fractal analysis of cyclic motor time series. Such analyses capture non-linear fractal dynamics in temporal fluctuations of motor instances that are believed to reflect how executive control enlist a coordination of multiple interactions across temporal scales between the brain, the body and the task environment, an essential architecture for adaptation. Here by recruiting elite rugby players with high motor skills and submitting them to the execution of rhythmic motor tasks involving legs and arms concurrently, the main attempt was to build on the multifractal formalism of movement control to show a marginal need of effective adaptation in concurrent tasks, and a preserved adaptability despite complexified motor execution. The present study applied a multifractal analytical approach to experimental time series and added surrogate data testing based on shuffled, ARFIMA, Davies&Harte and phase-randomized surrogates, for assessing scale-free behavior in repeated motor time series obtained while combining cycling with finger tapping and with circling. Single-tasking was analyzed comparatively. A focus-based multifractal-DFA approach provided Hurst exponents (H) of individual time series over a range of statistical moments H(q), q = [−15 15]. H(2) quantified monofractality and H(-15)-H(15) provided an index of multifractality. Despite concurrent tasking, participants showed great capacity to keep the target rhythm. Surrogate data testing showed reasonable reliability in using multifractal formalism to decipher movement control behavior. The global (i.e., monofractal) behavior in single-tasks did not change when adapting to dual-task. Multifractality dominated in cycling and did not change when cycling was challenged by upper limb movements. Likewise, tapping and circling behaviors were preserved despite concurrent cycling. It is concluded that the coordinated executive control when adapting to dual-motor tasking is not modified in people having developed great motor skills through physical training. Executive control likely emerged from multiplicative interactions across temporal scales which puts emphasis on multifractal approaches of the movement system to get critical cues on adaptation. Extending such analyses to less skilled people is appealing in the context of exploring healthy and diseased movement systems.

A general procedure to measure the pacing of body movements timed to music and metronome in younger and older adults

Finger-tapping tasks are classically used to investigate sensorimotor synchronization in relation to neutral auditory cues, such as metronomes. However, music is more commonly associated with an entrained bodily response, such as toe tapping, or dancing. Here we report an experimental procedure that was designed to bridge the gap between timing and intervention studies by directly comparing the effects of metronome and musical cue types on motor timing abilities across the three naturalistic voluntary actions of finger tapping, toe tapping, and stepping on the spot as a simplified case of whole body movement. Both pacing cues were presented at slow, medium, and fast tempi. The findings suggested that the task of stepping on the spot enabled better timing performances than tapping both in younger and older adults (75+). Timing performances followed an inverse U shape with best performances observed in the medium tempi that were set close to the spontaneous motor tempo in each movement type. Finally, music provided an entrainment effect in addition to pace setting that enabled better motor timing and greater stability than classically reported using a metronome. By applying time-stamp analyses to kinetic data, we demonstrate that tapping and stepping engage different timing modes. This work details the importance of translational research for a better understanding of motor timing. It offers a simple procedure that strengthens the validity of applying academic work and contributes in knowledge towards a wide range of therapeutic interventions.

Attention Guides the Motor-Timing Strategies in Finger-Tapping Tasks When Moving Fast and Slow

Human beings adapt the spontaneous pace of their actions to interact with the environment. Yet, the nature of the mechanism enabling such adaptive behavior remains poorly understood. The aim of the present contribution was to examine the role of attention in motor timing using (a) time series analysis, and (b) a dual task paradigm. In a series of two studies, a finger-tapping task was used in sensorimotor synchronization with various tempi (from 300 to 1,100 ms) and motor complexity (one target vs. six targets). Time series analyzes indicated that two different timing strategies were used depending on the speed constraints. At slow tempi, tapping sequences were characterized by strong negative autocorrelations, suggesting the implication of cognitive predictive timing. When moving at fast and close-to-spontaneous tempi, tapping sequences were characterized by less negative autocorrelations, suggesting that timing properties emerged from body movement dynamics. The analysis of the dual-task reaction times confirmed that both the temporal and spatial constraints impacted the attentional resources allocated to the finger-tapping tasks. Overall, our work suggests that moving fast and slow involve distinct timing strategies that are characterized by contrasting attentional demands.

Interpersonal Synchronization Processes in Discrete and Continuous Tasks

Three frameworks have been proposed to account for interpersonal synchronization: The information processing approach argues that synchronization is achieved by mutual adaptation, the coordination dynamics perspective supposes a continuous coupling between systems, and complexity matching suggests a global, multi-scale interaction. We hypothesized that the relevancy of these models was related to the nature of the performed tasks. 10 dyads performed synchronized tapping and synchronized forearm oscillations, in two conditions: full (participants had full information about their partner), and digital (information was limited to discrete auditory signals). Results shows that whatever the task and the available information, synchronization was dominated by a discrete mutual adaptation. These results question the relevancy of the coordination dynamics perspective in interpersonal coordination.

Fractal properties and short-term correlations in motor control in cycling: influence of a cognitive challenge

Fluctuations in cyclic tasks periods is a known characteristic of human motor control. Specifically, long-range fractal fluctuations have been evidenced in the temporal structure of these variations in human locomotion and thought to be the outcome of a multicomponent physiologic system in which control is distributed across intricate cortical, spinal and neuromuscular regulation loops. Combined with long-range correlation analyses, short-range autocorrelations have proven their use to describe control distribution across central and motor components. We used relevant tools to characterize long- and short-range correlations in revolution time series during cycling on an ergometer in 19 healthy young adults. We evaluated the impact of introducing a cognitive task (PASAT) to assess the role of central structures in control organization. Autocorrelation function and detrending fluctuation analysis (DFA) demonstrated the presence of fractal scaling. PSD in the short range revealed a singular behavior which cannot be explained by the usual models of even-based and emergent timing. The main outcomes are that (1) timing in cycling is a fractal process, (2) this long-range fractal behavior increases in persistence with dual-task condition, which has not been previously observed, (3) short-range behavior is highly persistent and unaffected by dual-task. Relying on the inertia of the oscillator may be a way to distribute more control to the periphery, thereby allocating less resources to central process and better managing additional cognitive demands. This original behavior in cycling may explain the high short-range persistence unaffected by dual-task, and the increase in long-range persistence with dual-task.

Music and Metronomes Differentially Impact Motor Timing in People with and without Parkinson's Disease: Effects of Slow, Medium, and Fast Tempi on Entrainment and Synchronization Performances in Finger Tapping, Toe Tapping, and Stepping on the Spot Tasks

Introduction

Rhythmic auditory stimulation (RAS) has successfully helped regulate gait for people with Parkinson's disease. However, the way in which different auditory cues and types of movements affect entrainment, synchronization, and pacing stability has not been directly compared in different aged people with and without Parkinson's. Therefore, this study compared music and metronomes (cue types) in finger tapping, toe tapping, and stepping on the spot tasks to explore the potential of RAS training for general use.

Methods

Participants (aged 18–78 years) included people with Parkinson's (n = 30, Hoehn and Yahr mean = 1.78), older (n = 26), and younger adult controls (n = 36), as age may effect motor timing. Timed motor production was assessed using an extended synchronization-continuation task in cue type and movement conditions for slow, medium, and fast tempi (81, 116, and 140 mean beats per minute, respectively).

Results

Analyses revealed main effects of cue and movement type but no between-group interactions, suggesting no differences in motor timing between people with Parkinson's and controls. Music supported entrainment better than metronomes in medium and fast tempi, and stepping on the spot enabled better entrainment and less asynchrony, as well as more stable pacing compared to tapping in medium and fast tempi. Age was not confirmed as a factor, and no differences were observed in slow tempo.

Conclusion

This is the first study to directly compare how different external auditory cues and movement types affect motor timing. The music and the stepping enabled participants to maintain entrainment once the external pacing cue ceased, suggesting endogenous mechanisms continued to regulate the movements. The superior performance of stepping on the spot suggests embodied entrainment can occur during continuous movement, and this may be related to emergent timing in tempi above 600 ms. These findings can be applied therapeutically to manage and improve adaptive behaviours for people with Parkinson's.

Steady-state evoked potentials distinguish brain mechanisms of self-paced versus synchronization finger tapping

Sensorimotor synchronization (SMS) requires aligning motor actions to external events and represents a core part of both musical and dance performances. In the current study, to isolate the brain mechanisms involved in synchronizing finger tapping with a musical beat, we compared SMS to pure self-paced finger tapping and listen-only conditions at different tempi. We analyzed EEG data using frequency domain steady-state evoked potentials (SSEPs) to identify sustained electrophysiological brain activity during repetitive tasks. Behavioral results revealed different timing modes between SMS and self-paced finger tapping, associated with distinct scalp topographies, thus suggesting different underlying brain sources. After subtraction of the listen-only brain activity, SMS was compared to self-paced finger tapping. Resulting source estimations showed stronger activation of the left inferior frontal gyrus during SMS, and stronger activation of the bilateral inferior parietal lobule during self-paced finger tapping. These results point to the left inferior frontal gyrus as a pivot for perception-action coupling. We discuss our findings in the context of the ongoing debate about SSEPs interpretation given the variety of brain events contributing to SSEPs and similar EEG frequency responses.

Manual asymmetries in bimanual isochronous tapping tasks in children

Tapping tasks have been investigated throughout the years, with variations in features such as the complexity of the task, the use of one or both hands, the employ of auditory or visual stimuli, and the characteristics of the subjects. The evaluation of lateral asymmetries in tapping tasks in children offers an insight into the structure of rhythmic movements and handedness at early stages of development. The current study aims to investigate the ability of children (aged six and seven years-old) to maintain a rhythm, in a bimanual tapping task at two different target frequencies, as well as the manual asymmetries displayed while doing so. The analyzed data in this work are the series of the time intervals between successive taps. We suggest several profiles of behavior, regarding the overall performance of children in both tempo conditions. We also propose a new method of quantifying the variability of the performance and the asymmetry of the hands, based on ellipses placed on scatter plots of the non-dominant-dominant series versus the dominant-non-dominant series. We then use running correlations to identify changes of coordination tendencies over time. The main results show that variability is larger in the task with the longer target interval. Furthermore, most children evidence lateral asymmetries, but in general they show the capacity to maintain the mean of consecutive intertap intervals of both hands close to the target interval. Finally, we try to interpret our findings in the light of existing models and timing modes.

Synthesis of asymmetric movement trajectories in timed rhythmic behaviour by means of frequency modulation

Results from different empirical investigations on gestural aspects of timed rhythmic movements indicate that the production of asymmetric movement trajectories is a feature that seems to be a common characteristic of various performances of repetitive rhythmic patterns. The behavioural or neural origin of these asymmetrical trajectories is, however, not identified. In the present study we outline a theoretical model that is capable of producing syntheses of asymmetric movement trajectories documented in empirical investigations by Balasubramaniam et al. (2004). Characteristic qualities of the extension/flexion profiles in the observed asymmetric trajectories are reproduced, and we conduct an experiment similar to Balasubramaniam et al. (2004) to show that the empirically documented movement trajectories and our modelled approximations share the same spectral components. The model is based on an application of frequency modulated movements, and a theoretical interpretation offered by the model is to view paced rhythmic movements as a result of an unpaced movement being "stretched" and "compressed", caused by the presence of a metronome. We discuss our model construction within the framework of event-based and emergent timing, and argue that a change between these timing modes might be reflected by the strength of the modulation in our model.

Influence of pacer continuity on continuous and discontinuous visuo-motor synchronisation

Previous research has reported that synchronising movements with an external pacer, known as sensorimotor synchronisation (SMS), is more stable when the movements are discrete/discontinuous rather than continuous. A standard explanation considers that more efficient mechanisms are involved for regulating synchronisation when producing discontinuous movements. To date, however, only discontinuous pacers (e.g., metronomes) have been investigated to compare discontinuous and continuous SMS. We propose an alternative explanation whereby the discontinuous SMS has benefited from the matching between the (dis)continuous nature of the pacer and the (dis)continuous nature of the movements of synchronisation. The present experiment tested this explanation by examining the relative stability of discontinuous and continuous SMS when synchronising with a continuous pacer. Twelve participants finger tapped (discontinuous SMS) or continuously oscillated their forearm (continuous SMS) in synchrony with an oscillatory visual target. The continuity of the pacer was manipulated by varying the kinematic (harmonic to Rayleigh-like oscillations) and the frequency (0.5 and 1Hz) of the target oscillations. Overall, the results showed a more stable continuous than discontinuous SMS. Furthermore, the stability of the discontinuous SMS improved when increasing the discontinuity of the target displacements (high nonlinear kinematic and low frequency), showing an interaction between movement type and pacer continuity in SMS.

Visual Timing of Structured Dance Movements Resembles Auditory Rhythm Perception

Temporal mechanisms for processing auditory musical rhythms are well established, in which a perceived beat is beneficial for timing purposes. It is yet unknown whether such beat-based timing would also underlie visual perception of temporally structured, ecological stimuli connected to music: dance. In this study, we investigated whether observers extracted a visual beat when watching dance movements to assist visual timing of these movements. Participants watched silent videos of dance sequences and reproduced the movement duration by mental recall. We found better visual timing for limb movements with regular patterns in the trajectories than without, similar to the beat advantage for auditory rhythms. When movements involved both the arms and the legs, the benefit of a visual beat relied only on the latter. The beat-based advantage persisted despite auditory interferences that were temporally incongruent with the visual beat, arguing for the visual nature of these mechanisms. Our results suggest that visual timing principles for dance parallel their auditory counterparts for music, which may be based on common sensorimotor coupling. These processes likely yield multimodal rhythm representations in the scenario of music and dance.

Balancing out dwelling and moving: optimal sensorimotor synchronization

Sensorimotor synchronization is a fundamental skill involved in the performance of many artistic activities (e.g., music, dance). After a century of research, the manner in which the nervous system produces synchronized movements remains poorly understood. Typical rhythmic movements involve a motion and a motionless phase (dwell). The dwell phase represents a sizable fraction of the rhythm period, and scales with it. The rationale for this organization remains unexplained and is the object of this study. Twelve participants, four drummers (D) and eight nondrummers (ND), performed tapping movements paced at 0.5-2.5 Hz by a metronome. The participants organized their tapping behavior into dwell and movement phases according to two strategies: 1) Eight participants (1 D, 7 ND) maintained an almost constant ratio of movement time (MT) and dwell time (DT) irrespective of the metronome period. 2) Four participants increased the proportion of DT as the period increased. The temporal variabilities of both the dwell and movement phases were consistent with Weber's law, i.e., their variability increased with their durations, and the longest phase always exhibited the smallest variability. We developed an optimal statistical model that formalized the distribution of time into dwell and movement intervals as a function of their temporal variability. The model accurately predicted the participants' dwell and movement durations irrespective of their strategy and musical skill, strongly suggesting that the distribution of DT and MT results from an optimization process, dependent on each participant's skill to predict time during rest and movement.

Timing skills and expertise: discrete and continuous timed movements among musicians and athletes

Introduction: Movement-based expertise relies on precise timing of movements and the capacity to predict the timing of events. Music performance involves discrete rhythmic actions that adhere to regular cycles of timed events, whereas many sports involve continuous movements that are not timed in a cyclical manner. It has been proposed that the precision of discrete movements relies on event timing (clock mechanism), whereas continuous movements are controlled by emergent timing. We examined whether movement-based expertise influences the timing mode adopted to maintain precise rhythmic actions.

Materials and Method: Timing precision was evaluated in musicians, athletes and control participants. Discrete and continuous movements were assessed using finger-tapping and circle-drawing tasks, respectively, based on the synchronization-continuation paradigm. In Experiment 1, no auditory feedback was provided in the continuation phase of the trials, whereas in Experiment 2 every action triggered a feedback tone.

Results: Analysis of precision in the continuation phase indicated that athletes performed significantly better than musicians and controls in the circle-drawing task, whereas musicians were more precise than controls in the finger tapping task. Interestingly, musicians were also more precise than controls in the circle-drawing task. Results also showed that the timing mode adopted was dependent on expertise and the presence of auditory feedback.

Discussion: Results showed that movement-based expertise is associated with enhanced timing, but these effects depend on the nature of the training. Expertise was found to influence the timing strategy adopted to maintain precise rhythmic movements, suggesting that event and emergent timing mechanisms are not strictly tied to specific tasks, but can both be adopted to achieve precise timing.

A little elastic for a better performance: kinesiotaping of the motor effector modulates neural mechanisms for rhythmic movements

A rhythmic motor performance is brought about by an integration of timing information with movements. Investigations on the millisecond time scale distinguish two forms of time control, event-based timing and emergent timing. While event-based timing asserts the existence of a central internal timekeeper for the control of repetitive movements, the emergent timing perspective claims that timing emerges from dynamic control of nontemporal movements parameters. We have recently demonstrated that the precision of an isochronous performance, defined as performance of repeated movements having a uniform duration, was insensible to auditory stimuli of various characteristics (Bravi et al., 2014). Such finding has led us to investigate whether the application of an elastic therapeutic tape (Kinesio® Tex taping; KTT) used for treating athletic injuries and a variety of physical disorders, is able to reduce the timing variability of repetitive rhythmic movement. Young healthy subjects, tested with and without KTT, have participated in sessions in which sets of repeated isochronous wrist's flexion-extensions (IWFEs) were performed under various auditory conditions and during their recall. Kinematics was recorded and temporal parameters were extracted and analyzed. Our results show that the application of KTT decreases the variability of rhythmic movements by a 2-fold effect: on the one hand KTT provides extra proprioceptive information activating cutaneous mechanoreceptors, on the other KTT biases toward the emergent timing thus modulating the processes for rhythmic movements. Therefore, KTT appears able to render movements less audio dependent by relieving, at least partially, the central structures from time control and making available more resources for an augmented performance.

Rhythm patterns interaction--synchronization behavior for human-robot joint action

Interactive behavior among humans is governed by the dynamics of movement synchronization in a variety of repetitive tasks. This requires the interaction partners to perform for example rhythmic limb swinging or even goal-directed arm movements. Inspired by that essential feature of human interaction, we present a novel concept and design methodology to synthesize goal-directed synchronization behavior for robotic agents in repetitive joint action tasks. The agents’ tasks are described by closed movement trajectories and interpreted as limit cycles, for which instantaneous phase variables are derived based on oscillator theory. Events segmenting the trajectories into multiple primitives are introduced as anchoring points for enhanced synchronization modes. Utilizing both continuous phases and discrete events in a unifying view, we design a continuous dynamical process synchronizing the derived modes. Inverse to the derivation of phases, we also address the generation of goal-directed movements from the behavioral dynamics. The developed concept is implemented to an anthropomorphic robot. For evaluation of the concept an experiment is designed and conducted in which the robot performs a prototypical pick-and-place task jointly with human partners. The effectiveness of the designed behavior is successfully evidenced by objective measures of phase and event synchronization. Feedback gathered from the participants of our exploratory study suggests a subjectively pleasant sense of interaction created by the interactive behavior. The results highlight potential applications of the synchronization concept both in motor coordination among robotic agents and in enhanced social interaction between humanoid agents and humans.

A Review of Theoretical Perspectives in Cognitive Science on the Presence of 1/f Scaling in Coordinated Physiological and Cognitive Processes

Time series of human performances present fluctuations around a mean value. These fluctuations are typically considered as insignificant, and attributable to random noise. Over recent decades, it became clear that temporal fluctuations possess interesting properties, however, one of which the property of fractal 1/f scaling. 1/f scaling indicates that a measured process extends over a wide range of timescales, suggesting an assembly over multiple scales simultaneously. This paper reviews neurological, physiological, and cognitive studies that corroborate the claim that 1/f scaling is most clearly present in healthy, well-coordinated activities. Prominent hypotheses about the origins of 1/f scaling are confronted with these reviewed studies. It is concluded that 1/f scaling in living systems appears to reflect their genuine complex nature, rather than constituting a coincidental side-effect. The consequences of fractal dynamics extending from the small spatial and temporal scales (e.g., neurons) to the larger scales of human behavior and cognition, are vast, and impact the way in which relevant research questions may be approached. Rather than focusing on specialized isolable subsystems, using additive linear methodologies, nonlinear dynamics, more elegantly so, imply a complex systems methodology, thereby exploiting, rather than rejecting, mathematical concepts that enable describing large sets of natural phenomena.

Sensorimotor synchronization: a review of recent research (2006-2012)

Sensorimotor synchronization (SMS) is the coordination of rhythmic movement with an external rhythm, ranging from finger tapping in time with a metronome to musical ensemble performance. An earlier review (Repp, 2005) covered tapping studies; two additional reviews (Repp, 2006a, b) focused on music performance and on rate limits of SMS, respectively. The present article supplements and extends these earlier reviews by surveying more recent research in what appears to be a burgeoning field. The article comprises four parts, dealing with (1) conventional tapping studies, (2) other forms of moving in synchrony with external rhythms (including dance and nonhuman animals' synchronization abilities), (3) interpersonal synchronization (including musical ensemble performance), and (4) the neuroscience of SMS. It is evident that much new knowledge about SMS has been acquired in the last 7 years.

The role of musical training in emergent and event-based timing

Introduction: Musical performance is thought to rely predominantly on event-based timing involving a clock-like neural process and an explicit internal representation of the time interval. Some aspects of musical performance may rely on emergent timing, which is established through the optimization of movement kinematics, and can be maintained without reference to any explicit representation of the time interval. We predicted that musical training would have its largest effect on event-based timing, supporting the dissociability of these timing processes and the dominance of event-based timing in musical performance.

Materials and Methods: We compared 22 musicians and 17 non-musicians on the prototypical event-based timing task of finger tapping and on the typically emergently timed task of circle drawing. For each task, participants first responded in synchrony with a metronome (Paced) and then responded at the same rate without the metronome (Unpaced).

Results: Analyses of the Unpaced phase revealed that non-musicians were more variable in their inter-response intervals for finger tapping compared to circle drawing. Musicians did not differ between the two tasks. Between groups, non-musicians were more variable than musicians for tapping but not for drawing. We were able to show that the differences were due to less timer variability in musicians on the tapping task. Correlational analyses of movement jerk and inter-response interval variability revealed a negative association for tapping and a positive association for drawing in non-musicians only.

Discussion: These results suggest that musical training affects temporal variability in tapping but not drawing. Additionally, musicians and non-musicians may be employing different movement strategies to maintain accurate timing in the two tasks. These findings add to our understanding of how musical training affects timing and support the dissociability of event-based and emergent timing modes.

A tutorial introduction to adaptive fractal analysis

The authors present a tutorial description of adaptive fractal analysis (AFA). AFA utilizes an adaptive detrending algorithm to extract globally smooth trend signals from the data and then analyzes the scaling of the residuals to the fit as a function of the time scale at which the fit is computed. The authors present applications to synthetic mathematical signals to verify the accuracy of AFA and demonstrate the basic steps of the analysis. The authors then present results from applying AFA to time series from a cognitive psychology experiment on repeated estimation of durations of time to illustrate some of the complexities of real-world data. AFA shows promise in dealing with many types of signals, but like any fractal analysis method there are special challenges and considerations to take into account, such as determining the presence of linear scaling regions.

Effects of accuracy feedback on fractal characteristics of time estimation

The current experiment investigated the effect of visual accuracy feedback on the structure of variability of time interval estimates in the continuation tapping paradigm. Participants were asked to repeatedly estimate a 1-s interval for a prolonged period of time by tapping their index finger. In some conditions, participants received accuracy feedback after every estimate, whereas in other conditions, no feedback was given. Also, the likelihood of receiving visual feedback was manipulated by adjusting the tolerance band around the 1-s target interval so that feedback was displayed only if the temporal estimate deviated from the target interval by more than 50, 100, or 200 ms respectively. We analyzed the structure of variability of the inter-tap intervals with fractal and multifractal methods that allow for a quantification of complex long-range correlation patterns in the timing performance. Our results indicate that feedback changes the long-range correlation structure of time estimates: Increased amounts of feedback lead to a decrease in fractal long-range correlations, as well to a decrease in the magnitude of local fluctuations in the performance. The multifractal characteristics of the time estimates were not impacted by the presence of accuracy feedback. Nevertheless, most of the data sets show significant multifractal signatures. We interpret these findings as showing that feedback acts to constrain and possibly reorganize timing performance. Implications for mechanistic and complex systems-based theories of timing behavior are discussed.