Categorical time production: evidence for discrete timing in motor control.

Subjects performed a repetitive manual tapping task, attempting to match a given rate of auditory stimulus pulses, first with the pulses audible (synchronization) and then with the pulses turned off (continuation). In different sessions, the interstimulus interval (ISI) was selected from the range 175 to 825 msec in steps of 25 msec, with different ISI values presented in a random order. Across this range of ISI conditions, interresponse intervals (IRIs) exhibited alternating positive bias (too slow) and negative bias (too fast). We interpret this pattern of bias in terms of a discrete, or categorical, timing mechanism in motor timing. Categorical time production can be viewed as extending our conception of the timekeeper in Wing's (Wing & Kristofferson, 1973a, 1973b) two-process model of motor timing and may be related to the system of multiple clocks proposed by Kristofferson (1980) to explain a categorical pattern of variability measures in duration discrimination.     

Motor timing deficits in children with Attention-Deficit/Hyperactivity disorder

Children with Attention-Deficit/Hyperactivity Disorder (ADHD) are thought to have fundamental deficits in the allocation of attention for information processing. Furthermore, it is believed that these children possess a fundamental difficulty in motoric timing, an assertion that has been explored recently in adults and children. In the present study we extend this recent work by fully exploring the classic Wing and Kristofferson (1973) analysis of timing with typically developing children (n=24) and children with ADHD (n=27). We provide clear evidence that not only do children with ADHD have an overall timing deficit, they also time less consistently when using a similar strategy to typically developing children. The use of the Wing and Kristofferson approach to timing, we argue, will result in the discovery of robust ADHD-related timing differences across a variety of situations.     

Timing and trajectory in rhythm production

The Wing-Kristofferson movement timing model (A. M. Wing & A. B. Kristofferson, 1973a, 1973b) distinguishes central timer and motor implementation processes. Previous studies have shown that increases in interresponse interval (IRI) variability with mean IRI are due to central timer processes, not motor implementation. The authors examine whether this is true with IRI duration changes in binary rhythm production. Ten participants provided IRI and movement data in bimanual synchronous tapping under equal (isochronous) and alternating (rhythm) interval conditions. Movement trajectory changes were observed with IRI duration (300, 500, or 833 ms) and for 500-ms IRIs produced in rhythm contexts (300/500 ms, 500/833 ms). However, application of the Wing-Kristofferson model showed that duration and context effects on IRI variability were attributable largely to timer processes with relatively little effect on motor processes.     

Comparison of variance and covariance patterns in parallel and serial theories of timing.

Parallel and serial timing processes are analyzed for their account of the dynamics of intertrial responding in the peak procedure. A strictly serial model, such as the behavioral theory of timing (Killeen & Fetterman, 1988), does not fit the dynamic correlation pattern in the location and duration of the middle high-rate responding portion of peak trials. In contrast, the parallel scalar expectancy theory model, with a sample for memory and threshold, does fit this pattern. A modification of the serial model is presented that also accommodates the within-trial covariance pattern. The modification, which is formally equivalent to a model for human tapping (Wing & Kristofferson, 1973), entails the addition of concurrent processes operating in parallel with serial timing.     

Detrended windowed (lag one) autocorrelation: a new method for distinguishing between event-based and emergent timing

The aim of this study was to test different methods for distinguishing between two known timing processes involved in human rhythmic behaviours. We examined the implementation of two approaches used in the literature: the high-frequency slope of the power spectrum and the lag one value of the autocorrelation function, ACF(1). We developed another method based on the Wing and Kristofferson (1973a) model and the predicted negative ACF(1) for event-based series: the detrended windowed (lag one) autocorrelation (DWA). We compared the reliability and performance of these three methods on simulation and experimental series. DWA gave the best results, and guidelines are given for its appropriate use for identifying underlying timing processes.     

Delayed auditory feedback in repetitive tapping: A role for the sensory goal

The open-loop model by Wing and Kristofferson has successfully explained many aspects of movement timing. A later adaptation of the model assumes that timing processes do not control the movements themselves, but the sensory consequences of the movements. The present study tested direct predictions from this “sensory-goals model”. In two experiments, participants were instructed to produce regular intervals by tapping alternately with the index fingers of the left and the right hand. Auditory feedback tones from the taps of one hand were delayed. As a consequence, regular intervals between taps resulted in irregular intervals between feedback tones. Participants compensated for this auditory irregularity by changing their movement timing. Compensation effects increased with the magnitude of feedback delay (Experiment 1) and were also observed in a unimanual variant of the task (Experiment 2). The pattern of effects in alternating tapping suggests that compensation processes were anticipatory—that is, compensate for upcoming feedback delay rather than being reactions to delay. All experiments confirmed formal model predictions. Taken together, the findings corroborate the sensory-goals adaptation of the Wing–Kristofferson model.     

Timing precision in continuation and synchronization tapping

 Wing and Kristofferson (1973) have shown that temporal precision in self-paced tapping is limited by variability in a central timekeeper and by variability arising in the peripheral motor system. Here we test an extension of the Wing–Kristofferson model to synchronization with periodic external events that was proposed by Vorberg and Wing (1994). In addition to the timekeeper and motor components, a linear phase correction mechanism is assumed which is triggered by the last or the last two synchronization errors. The model is tested in an experiment that contrasts synchronized and self-paced trapping, with response periods ranging from 200–640 ms. The variances of timekeeper and motor delays and the error correction parameters were estimated from the auto-covariance functions of the inter-response intervals in continuation and the asynchronies in synchronization. Plausible estimates for all parameters were obtained when equal motor variance was assumed for synchronization and continuation. Timekeeper variance increased with metronome period, but more steeply during continuation than during synchronization, suggesting that internal timekeeping processes are stabilized by periodic external signals. First-order error correction became more important as the metronome period increased, whereas the contribution of second-order error correction decreased. It is concluded that the extended two-level model accounts well for both synchronization and continuation performance. Received: 16 November 1998 / Accepted: 21 April 1999     

Adding drift to the decomposition of simple isochronous tapping: an extension of the Wing-Kristofferson model

The Wing-Kristofferson model (A. M. Wing & A. B. Kristofferson, (1973a, 1973b) decomposes the variance of isochronous finger tapping into 2 components: a central clock component and a peripheral motor component. The method assumes that there is no drift in the intertap intervals. A new method is introduced that further decomposes the clock component drift and drift-free clock variance. The method was studied through simulation and empirical analyses. Clock variance was the most prominent, followed by drift, and then motor variance. Individual and group differences were larger for the motor and drift variances than for the drift-free clock variance, so that group differences observed in the past may have been partially due to the failure to fully remove drift. The authors argue that the methods presented and extensions thereon show great promise in extending a method in wide use since 1973.     

Temporal control and motor control: two functional modules which may be influenced differently under microgravity.

Three subjects performed sequences of periodic movements by synchronizing their movements (button pressing with the thumb) to a series of visual stimuli (induction phase), and by continuing to produce the movements with the same rhythm after the metronome had been switched off (continuation phase). The required inter-response intervals (IRIs) were 450, 550 or 650 ms. Two subjects were members of the EUROMIR 94 spaceflight mission. The inter-response intervals of the continuation phase were analyzed in terms of mean and variability. The mean inter-response intervals did not differ systematically during spaceflight from the pre- and post-flight values. The variability of the inter-response intervals significantly increased during the flight with both experimental subjects. The total variance of the inter-response intervals was partitioned into variance due to the internal timekeeper and variance due to the motor implementation processes, following the method proposed by Wing, A.M., Kristofferson, A.B., 1973. Response delays in the timing of discrete motor responses. Perception and Psychophysics 14, 5-12. The variance attributed to the timekeeper showed a significant increase with both subjects, whereas the variance attributed to the motor processes showed inconsistent trends during the spaceflight. It is concluded that during spaceflight, the functioning of the internal timing module may undergo some changes, as the result of which the regularity of the motor timing is slightly impaired.     

FTAP: A Linux-based program for tapping and music experiments

This paper describes FTAP, a flexible data collection system for tapping and music experiments. FTAP runs on standard PC hardware with the Linux operating system and can process input keystrokes and auditory output with reliable millisecond resolution. It uses standard MIDI devices for input and output and is particularly flexible in the area of auditory feedback manipulation. FTAP can run a wide variety of experiments, including synchronization/continuation tasks (Wing & Kristofferson, 1973), synchronization tasks combined with delayed auditory feedback (Aschersleben & Prinz, 1997), continuation tasks with isolated feedback perturbations (Wing, 1977), and complex alterations of feedback in music performance (Finney, 1997). Such experiments have often been implemented with custom hardware and software systems, but with FTAP they can be specified by a simple ASCII text parameter file. FTAP is available at no cost in source-code form.     

Temporal organization of pattern structure

Two pattern reproduction experiments examined the relations among the figural goodness of a pattern, the organization of two parts within the pattern, and the interpart interval (ISI), which ranged from 40 to 200 msec. If the parts contained connected line segments, performance was slightly better (3%-5% gain in accuracy) at a 40-msec ISI than at a 200-msec ISI. If the parts contained unconnected line segments, reproduction accuracy of the first part declined sharply between 40 and 200 msec. These results were interpreted by assuming that the parts were perceived as a single whole pattern at a 40-msec ISI but as two separate patterns at a 200-msec ISI. One surprising finding, the lack of an interaction between figural goodness and ISI, was explained in terms of a response bias in favor of figural good patterns. A secondary manipulation revealed that a part was more accurately reproduced in a good figure context than in a poor figure context but was most accurately reproduced when it appeared alone.     

Bloch’s law and a Poisson counting model for simple reaction time to light

A series of three experiments was conducted with identical design as an earlier series (Hildreth, 1973). Its purpose was (1) to determine whether Bloch’s law holds for simple reaction time (RT) to still lower intensity visual stimuli, and (2) to provide data for testing a stochastic generalization of the temporal integration model (TI-ED) reported earlier. RT means were found to agree with Bloch’s law for durations below 48 msec. By a statistical test, Bloch’s law was shown to hold for both means and standard deviations below about 65 msec. Latency statistics—means and standard deviations—were predicted by a Poisson process counting model. This model assumes that a number of identical, parallel Poisson processes, activated by light, with pulse interarrival times decreasing with light intensity, trigger light detection when a critical number of pulses arrive at a counting center. For the intensities investigated, both the estimated number of Poisson processes and critical number of pulses required for detection range between 8 and 13. The model predicts the Broca-Sulzer effect for mean RTs which is observed in several of these experiments.     

Ultrastable stimulus-response latencies: Acquisition and stimulus control

Modifications were made to Kristofferson’s (1976) response-stimulus synchronization procedure which resulted in a further reduction in the estimate of minimum S-R latency variance. Minimum variances near 50 msec² were obtained whether mean latency was 310 or 550 msec. Within this range, latency distributions were the same, symmetrical and sharp-peaked, and unlike typical RT. All responses fell within a 50-msec time window. This independence of mean latency and latency variance was present throughout acquisition. A special technique allowed isolation of the controlling stimulus for synchronization timing, and showed that subjects were able to transfer control to another modality with no loss of performance. Results are discussed in terms of support for the notion of nonvariable, internally timed delays which can be inserted in the S-R chain. These delays are easily adjustable, but, once set, are deterministic. The role of feedback in acquisition and maintenance of synchronization performance is also examined.     

Preferred rates of repetitive tapping and categorical time production

In a constrained finger-tapping task, in which a subject attempts to match the rate of tapping responses to the rate of a pacer stimulus, interresponse interval (IRI) was a nonlinear function of interstimulus interval (ISI), in agreement with the results of Collyer, Broadbent, and Church (1992). In an unconstrained task, the subjects were not given an ISI to match, but were instructed to tap at their preferred rate, one that seemed not too fast or too slow for comfortable production. The distribution of preferred IRIs was bimodal rather than unimodal, with modes at 272 and 450 msec. Preferred IRIs also tended to become shorter over successive sessions. Time intervals that were preferred in the unconstrained task tended to be intervals that were overproduced (IRI > ISI) when they were used as ISIs in the constrained task. A multiple-oscillator model of timing developed by Church and Broadbent (1990) was used to simulate the two tasks. The nonlinearity in constrained tapping, termed theoscillator signature, and the bimodal distribution in unconstrained tapping were both exhibited by the model. The nature of the experimental results and the success of the simulation in capturing them both provide further support for a multiple-oscillator view of timing.     

A quantal step function in duration discrimination

The difference threshold for duration, for the case of empty time intervals bounded by brief auditory pulses, is an increasing function of base duration. For base durations between 100 and 1,480 msec, Weber’s law describes the function quite well and a Weber ratio of .05 is obtained. These results in the present paper conform closely to results that have been reported by others. However, it is further shown that the function changes as the amount of practice is increased at each specific base duration: steps unfold from the linear function, and these steps are clearly evident after 17 consecutive sessions at each base duration. Expressing threshold in terms of the apparent magnitude of the “time quantum,” it is found that q is about 13 msec when base duration is 100 msec and that it jumps to 25 at 200, to 50 at 400, and to 100 at 800. Between the abrupt risers in this step function, the treads are not quite flat, perhaps because the amount of practice was insufficient. It is concluded that the time quantum can be doubled and halved, at least within the doubles set 13, 25, 50, and 100 msec. It is not restricted to the single value of 50 msec as initially proposed (Kristofferson, 1967).     

Retention of time information in forced-choice duration discrimination

We explore the effect on performance in a forced-choice duration-discrimination task of varying the interstimulus interval (ISI) from 0 to 2 sec. The durations were brief empty intervals (115–285 msec) bounded by very brief auditory pulses. Performance improved as the ISI increased from 0 to 1/2 sec, but a further increase in ISI up to 2 sec resulted in little further change in performance. The “time information” derived from a brief interval bounded by auditory pulses does not appear to be susceptible to the very short-term perceptual memory loss inferred in other auditory discriminations.     

Modification of muscle activation patterns during fast goal-directed arm movements

The motor programming of fast goal-directed arm movements was studied in a tracking task. A target jumped once or twice randomly to the left or right direction with an interstimulus interval (ISI) in a range between 50 and 125 msec. Double step stimuli were either two steps in the same direction (C-trial) or in opposite direction (R-trial). Tracking results show that at the beginning average EMG-activity is the same for responses to single step trials, R-trials and C-trials. Differences set in after some time equal to or somewhat shorter than ISI. It was concluded that muscle activation patterns of fast goal-directed movements are not preprogrammed but that they can be modified during the movement. The time interval between second target step and the moment when EMG activity of the double step response deviates from the EMG activity of a single step (RT2) could be smaller than the time interval between first target displacement and EMG onset. (RT1). If modification of the muscle activation pattern required a longer or larger activation of the active muscle, RT2 tended to be smaller than RT1, whereas RT2 was about equal to RT1 if the new muscle activation required a termination of the ongoing muscle activation pattern and the activation of another muscle.     

Variability of timing in expressive piano performance increases with interval duration

In simple motor tasks such as finger tapping at different constant rates, within-trial variability of response interonset intervals (IOIs) increases with IOI duration (which varies between trials). In expressive piano performance, the rate of key depressions is not constant, in part due to compositional structure and in part due to expressive timing, so that IOIs of many different durations occur within a single “trial.” Nevertheless, across repeated performances of the same music (Schumann’s “Träumerei” and Debussy’s “La fille aux cheveux de lin”) at the same intended tempo, the standard deviations of individual IOIs tend to increase linearly with their average duration. This is also true when the variation is due to expressive timing alone and when unintended differences in basic tempo between performances are taken into account. In the music studied here, at least, there was no evidence of compensatory timing. The results suggest that the pianists employed a continuously variable tempo governed by a flexible internal timekeeper whose variability follows a generalized Weber’s law (for IOIs longer than about 300 msec).     

Timing in trace conditioning of the nictitating membrane response of the rabbit (Oryctolagus cuniculus): scalar, nonscalar, and adaptive features

Using interstimulus intervals (ISIs) of 125, 250, and 500 msec in trace conditioning of the rabbit nictitating membrane response, the offset times and durations of conditioned responses (CRs) were collected along with onset and peak latencies. All measures were proportional to the ISI, but only onset and peak latencies conformed to the criterion for scalar timing. Regarding the CR's possible protective overlap of the unconditioned stimulus (US), CR duration increased with ISI, while the peak's alignment with the US declined. Implications for models of timing and CR adaptiveness are discussed.     

Fluctuations and phase symmetry in coordinated rhythmic movements

Pendular, clocking movements typify mammalian terrestrial locomotion. They can be investigated with a procedure in which people swing hand-held pendulums at the wrists, comfortably and rhythmically. Pendular, clocking behavior was examined for in-phase and out-of-phase coordinations. The periodic timing and powering of rhythmic movements in the comfort state follow from different laws (Kugler & Turvey, 1986). One law guides the assembling of the reference frame for "clocking." Another law guides the assembling of the muscular, escapement processes determining the cycle energy. Wing and Kristofferson's (1973) method for parsing periodic-timing variance into independent "clock" and "motor" sources was applied. Mean periodicity was unaffected by phase. "Clock" fluctuations, however, were larger out of phase than in phase. "Motor" fluctuations were indifferent to phase but reflected the departures of individual wrist-pendulum systems from their preferred periods. It appears that an intended phase relation is realized as a constraint on "clock" states. These states are more stable under the in-phase constraint than under the out-of-phase constraint.