“One-thousand<Emphasis Type="Italic">one</Emphasis> … one-thousand<Emphasis Type="Italic">two</Emphasis> …”: Chronometric counting violates the scalar property in interval timing

Medical College of Wisconsin, Milwaukee, Wisconsin Weber’s law applied to interval timing is called thescalar property. A hallmark of timing in the secondsto-minutes range, the scalar property is characterized by proportionality between the standard deviation of a response distribution and the duration being timed. In this temporal reproduction study, we assessed whether the scalar property was upheld when participants chronometrically counted three visually presented durations (8, 16, and 24 sec) as compared with explicitly timing durations without counting. Accuracy for timing and accuracy for counting were similar. However, whereas timing variability showed the scalar property, counting variability did not. Counting variability across intervals was accurately modeled by summing a random variable representing an individual count. A second experiment replicated the first and demonstrated that task differences were not due to presentation order or practice effects. The distinct psychophysical properties of counting and timing behaviors argue for greater attention to participant strategies in timing studies.     

A componential analysis of pacemaker-counter timing systems

Why does counting improve the accuracy of temporal judgments? Killeen and Weiss (1987) provided a formal answer to this question, and this article provides tests of their analysis. In Experiments 1 and 2, subjects responded on a telegraph key as they reproduced different intervals. Individual response rates remained constant for different target times, as predicted. The variance of reproductions was recovered from the weighted sum of the first and second moments of the component timing and counting processes. Variance in timing long intervals was mainly due to counting error, as predicted. In Experiments 3-5, unconstrained response rate was measured and subjects responded at (a) their unconstrained rate, (b) faster, or (c) slower. When subjects responded at the preferred rate, the accuracy of time judgment improved. Deviations in rates tended to increase the variability of temporal estimates. Implications for pacemaker-counter models of timing are discussed.     

Benefits and limits of explicit counting for discriminating temporal intervals.

Segmenting information into smaller parts helps to process it, and this is also true for temporal information. The aim of the present article is to compare the benefits of using explicit counting in a temporal discrimination task under various marker-type conditions and to show the limits of this strategy. In Experiment 1, conditions with and without counting were compared for two implicit standard durations, .8 and 1.6 s, in connection with three marker-type conditions, which were intervals marked by: 1) two brief auditory signals (Auditory-Auditory); 2) two brief visual signals (Visual-Visual); and 3) one auditory signal followed by a visual signal (Auditory-Visual). At .8 s, marker-type differences are significant (best in audition, worse with a bimodal sequence), and remain present with an explicit counting strategy. At 1.6 s, explicit counting provides clear improvements of performance in all marker-type conditions and annihilates marker-related differences. Experiment 1 also suggests that standard deviation remains constant from .8 to 1.6 s in the counting condition, while Experiment 2 shows that when standard intervals are extended up to 4 s, explicit counting does not totally prevent variance from increasing as base duration becomes progressively longer. The benefits derived from using explicit counting in duration discrimination are argued to depend (1) on a reduction of variance in the memory process involved in the timing mechanism, and (2) on a change in the decisional process.     

To count or not to count: the effect of instructions on expecting a break in timing

When a break is expected during a time interval production, longer intervals are produced as the break occurs later during the interval. This effect of break location was interpreted as a result of distraction related to break expectancy in previous studies. In the present study, the influence of target duration and of instructions about chronometric counting strategies on the break location effect was examined. Using a strategy such as chronometric counting enhances the reliability of temporal processing, typically in terms of reduced variability, and could influence how timing is affected by break expectancy, especially when relatively long target durations are used. In two experiments, results show that time productions lengthened with increasing value of break location at various target durations and that variability was greater in the no-counting than in the counting instruction condition. More important, the break location effect was stronger in the no-counting than in the counting instruction condition. We conclude that chronometric counting orients attention toward timing processes, making them less likely to be disrupted by concurrent nontemporal processes.     

The intrinsic link between motor behavior and temporal cognition

The debate about the cognitive mechanisms behind human temporal processing has raged for decades without a clear resolution. The theory presented here describes a different perspective to the traditional accounts on the issue, namely, that motor behaviors or sequences of motor behaviors provide a means of reproducing time intervals. Evidence behind this perspective includes tapping strategies (exemplified by musicians), counting strategies, and neuropsychological results showing activation of motor areas during temporal cognitive tasks. I propose that motor behaviors aid human timing by offering a set of processes that consistently take a set amount of time to accomplish. Motor behaviors also allow segmentation of larger intervals into smaller intervals that are easier to estimate. I conclude with a discussion of implications of this perspective on temporal cognition.     

Mechanisms of perceptual timing: Beat-based or interval-based judgements?

Summary What is the nature of the human timing mechanism for perceptual judgements about short temporal intervals? One possibility is that initial periodic events, such as tones, establish internal beats which continue after the external events and serve as reference points for the perception of subsequent events. A second possibility is that the timer records the intervals produced by events. Later, the stored intervals can be reproduced or compared to other intervals. A study by Schulze (1978) provided evidence favoring beat-based timing. In contrast, our two experiments support an interval theory. The judgements of intervals between tones is not improved when the events are synchronized with internal beats established by the initial intervals. The conflict between the two sets of results may be resolved by the fact that an interval timer can recycle from one interval to the next, thus operating in a beat-like mode. However, a timer of this sort is just as accurate when comparing intervals that are off the beat.     

Timing variability in circle drawing and tapping: probing the relationship between event and emergent timing

R. Ivry, R. M. Spencer, H. N. Zelaznik, and J. Diedrichsen (2002) have proposed a distinction between timed movements in which a temporal representation is part of the task goal (event timing) and those in which timing properties are emergent. The issue addressed in the present experiment was how timing in conditions conducive to emergent timing becomes established. According to what the authors term the transformation hypothesis, timing initially requires an event-based representation when the temporal goal is defined externally (e.g., by a metronome), but over the first few movement cycles, control processes become established that allow timing to become emergent. Different groups of participants (N = 84) executed either 1 timed interval, 4 timed intervals, or 2 timed intervals separated by a pause. They produced the intervals by either circle drawing, a task associated with emergent timing, or tapping, a task associated with event timing. Analyses of movement variability suggested that similar timing processes were used in the 2 tasks only during the 1st interval. Those results are consistent with the transformation hypothesis and lead to the inference that the transition from event-based control to emergent timing can occur rapidly during continuous movements.     

Differences in duration discrimination of filled and empty auditory intervals as a function of base duration

In the present experiments, participants were presented with two time intervals that were marked by auditory signals, and their task was to decide which of the two was longer in duration. In Experiment 1, the base durations were 50 and 1,000msec, whereas in Experiment 2, seven different base durations ranging from 50 to 1,000 msec were employed. It was found that filled intervals (continuous tones) were discriminated more accurately than empty intervals (with onset and offset marked by clicks) at the 50-msec base duration, whereas no performance differences could be shown for longer ones. The findings are consistent with the notion of a unitary timing mechanism that governs the timing of both filled and empty auditory intervals, independent of base durations. A likely conceptual framework that could explain better performance with filled as compared with empty intervals represents an information-processing model of interval timing that evolved from scalar timing theory. According to this account, a performance decrement observed with empty intervals may be due to a misassignment of pulses generated by an internal pacemaker.     

The effects of ongoing activity on time estimation in prospective remembering

Two experiments examined whether time‐based prospective memory performance is influenced by the continuous or discontinuous nature of an ongoing activity. The first experiment demonstrated that prospective memory performance was not influenced by the engagement in continuous or discontinuous ongoing activity. The second experiment demonstrated that a discontinuous ongoing activity negatively affected prospective memory performance when participants had to execute two time‐based tasks for which the retention intervals partially overlapped. The results suggest that when individuals are engaged in multiple time‐based tasks, a general timing disruption occurs, with a proactive interference effect resulting in costs that are detrimental to prospective timing. Copyright © 2009 John Wiley & Sons, Ltd.     

时间分层加工研究述评

为了探讨数秒内不同层级时间加工的特性,研究者分别从“时间信息加工”和“信息加工的计时特性”角度开展了一系列研究。Münsterberg (1889)、Michon(1985) 、Lewis 和 Miall(2003) 及Vierodt(1868)从前一角度,分别指出1/3秒、1/2秒、1秒及3秒可能是数秒以内时距加工机制的分界点,分界点以下与以上的加工机制存在差异。P?ppel(1997, 2009)则从后一角度指出限制信息加工过程的两类时间窗,一类时间窗是以20-60毫秒振荡周期运行的高频系统,属于初级整合单元;另一类时间窗主要是处理2-3秒以内事件系列的低频系统,属于高级整合单元。前一类时间窗可以为信息加工整合基本的心理事件,后一类时间窗则是把2-3秒内的心理事件整合为基本知觉单元。基于以往研究的剖析,我们认为1/3秒、1/2秒及1秒等分界点的真伪性尚需进一步验证,并进一步假设40毫秒以内时间不能觉察为时距;40毫秒至3秒之间,随着长度增加,自动化加工减弱,控制性加工增强;3秒以上主要为控制性加工,涉及记忆过程。     

The Timing Effects of Accent Production in Periodic Finger-Tapping Sequences

When subjects are required to produce short sequences of equally paced finger taps and to accentuate one of the taps, the interval preceding the forceful tap is shortened and the one that immediately follows the accent is lengthened. Assuming that the tapping movements are triggered by an internal clock, one explanation attributes the rnistiming of the taps to central factors: The momentary rate of the clock is accelerated or decelerated as a function of motor preparation to, respectively, increase or decrease the movement force. This hypothesis predicts that the interresponse intervals measured between either tap movement onsets or movement terminations (taps) will show the same timing pattern. A second explanation for the observed interval effects is that the tapping movements are triggered by a regular internal clock but the timing of the successive taps is altered because the forceful movement is completed in less time than the other tap movements are. This "peripheral" hypothesis predicts regular timing of movement onsets but distorted timing of movement terminations. In the present study, the trajectories of the movements performed by subjects were recorded and the interresponse intervals were measured at the beginning and the end of the tapping movements. The results of Experiment 1 showed that neither model can fully explain the interval effects: The fast forceful movements were initiated with an additional delay that took into account the small execution time of these movements. Experiment 2 reproduced this finding and showed that the timing of the onset and contact intervals did not evolve with the repetition of trial blocks. Therefore, the assumption of an internal clock that would trigger the successive movements must be rejected. The results are discussed in the framework of a modified two-stage model in which the internal clock, instead of triggering the tapping movements, provides target time points at which the movements have to produce their meaningful effects, that is, contacts with the response key. The timing distortions are likely to reflect both peripheral and central components.     

The Timing Effects of Accent Production in Periodic Finger-Tapping Sequences

When subjects are required to produce short sequences of equally paced finger taps and to accentuate one of the taps, the interval preceding the forceful tap is shortened and the one that immediately follows the accent is lengthened. Assuming that the tapping movements are triggered by an internal clock, one explanation attributes the mistiming of the taps to central factors: The momentary rate of the clock is accelerated or decelerated as a function of motor preparation to, respectively, increase or decrease the movement force. This hypothesis predicts that the interre-sponse intervals measured between either tap movement onsets or movement terminations (taps) will show the same timing pattern. A second explanation for the observed interval effects is that the tapping movements are triggered by a regular internal clock but the timing of the successive taps is altered because the forceful movement is completed in less time than the other tap movements are. This “peripheral” hypothesis predicts regular timing of movement onsets but distorted timing of movement terminations. In the present study, the trajectories of the movements performed by subjects were recorded and the interresponse intervals were measured at the beginning and the end of the tapping movements. The results of Experiment 1 showed that neither model can fully explain the interval effects: The fast forceful movements were initiated with an additional delay that took into account the small execution time of these movements. Experiment 2 reproduced this finding and showed that the timing of the onset and contact intervals did not evolve with the repetition of trial blocks. Therefore, the assumption of an internal clock that would trigger the successive movements must be rejected. The results are discussed in the framework of a modified two-stage model in which the internal clock, instead of triggering the tapping movements, provides target time points at which the movements have to produce their meaningful effects, that is, contacts with the response key. The timing distortions are likely to reflect both peripheral and central components.     

Limits of rhythm perception

To what extent are listeners sensitive to the time intervals separating non-consecutive events in sound sequences? The subjects of Experiment 1 were presented with sequences of 20 identical tones in which the 10 odd-numbered tones or the 10 even-numbered tones made up an isochronous sub-sequence (with a periodicity of 0.5-1 s) whereas the other tones, acting as distractors, occurred at random moments. Such sequences appeared to be very difficult to discriminate from sequences without any timing regularity, which revealed a lack of perceptual sensitivity to their "second-order" intervals. Experiment 2 employed repetitive sequences in which the first-order intervals (separating consecutive tones) took two possible values, forming a ratio that subjects had to classify as larger or smaller than 2. The results of this experiment suggest that subjects were able to make use of second-order intervals in their task, but mainly due to the predictable nature of the sequences; the relative positions of subjective accents (Povel & Essens, 1985) had no significant effect on performance. It is concluded that the perception of subtle timing details in "ordinary" music may rest on nothing more than a sensitivity to the relations between first-order intervals (within a given auditory stream).     

Dynamics of waiting in pigeons

Two experiments used response-initiated delay schedules to test the idea that when food reinforcement is available at regular intervals, the time an animal waits before its first operant response (waiting time) is proportional to the immediately preceding interfood interval (linear waiting; Wynne & Staddon, 1988). In Experiment 1 the interfood intervals varied from cycle to cycle according to one of four sinusoidal sequences with different amounts of added noise. Waiting times tracked the input cycle in a way which showed that they were affected by interfood intervals earlier than the immediately preceding one. In Experiment 2 different patterns of long and short interfood intervals were presented, and the results implied that waiting times are disproportionately influenced by the shortest of recent interfood intervals. A model based on this idea is shown to account for a wide range of results on the dynamics of timing behavior.     

Does expressive timing in music performance scale proportionally with tempo?

Summary Evidence is presented that expressive timing in music is not relationally invariant with global tempo. Our results stem from an analysis of repeated performances of Beethoven's variations on a Paisiello theme. Recordings were made of two pianists playing the pieces at three tempi. In contrast with the relational-invariance hypothesis (see Repp, 1994), between-tempo correlations were in general lower than within-tempo correlations. Analyses of variance of log-transformed inter-onset intervals (IOIs) showed significant interactions between tempo and IOI, i. e., evidence against a proportional relation between timing and tempo. Complex, but consistent, nonproportional patterns were shown in the analyses of the timing of the grace notes in the piece. The analysis suggests that timing aspects of music are closely linked to the musical structure and can be studied and manipulated only respecting this relation — not as a global timing pattern or tempo curve. Finally, it is shown that methodological issues of data collection and analysis had a significant influence on the results.     

Error monitoring in speech production: a computational test of the perceptual loop theory

A theory of speech monitoring, proposed by Levelt (1983), assumes that the quality of one's speech is checked by the speech comprehension system. This system inspects one's own overt speech but would also inspect an inner speech plan ("the inner loop"). We have elaborated and tested this theory by way of formalizing it as a computational model. This model includes a new proposal concerning the timing relation between planning the interruption and the repair: the proposal that these two processes are performed in parallel. We attempted to simulate empirical data about the distribution of error-to-cutoff and cutoff-to-repair intervals and the effect of speech rate on these intervals (these intervals are shorter with faster speech). The main questions were (1) Is an inner monitor that utilizes the speech perception system fast enough to simulate the timing data? (2) Can the model account for the effects of speech rate on these intervals? We conclude that including an inner loop through the speech comprehension system generates predictions that fit the empirical data. The effects of speed can be accounted for, given our proposal about the time course of planning interruption and repair. A novel prediction is that the error-to-cutoff interval decreases with increasing position in the phrase.     

Dynamics of time discrimination: II. The effects of multiple impulses.

According to a diffusion generalization model, time discrimination is determined by the frequency and recency of preceding intervals of time. A procedure for studying rapid timing was used to investigate whether pigeons' wait-time responses were sensitive to these factors. In Experiment 1 the number (two or eight) and spacing (consecutive or far apart) of 5-s interfood intervals (called impulses) intercalated in a series of 15-s interfood intervals (nonimpulses) were studied. Experiment 2 was identical to the first but the interfood intervals were increased by a factor of three. Overall, impulses shortened wait times in the next interfood interval. However, several impulses occurring in succession extended the localized effect of an impulse: Wait times following a set of eight-close impulses were slow to recover to preimpulse levels. The results show that linear waiting is only an approximation to the dynamic process, and a process that is sensitive to events in an animal's remote past, such as the diffusion generalization model, provides a better account of rapid timing effects.     

Sensorimotor synchronization: motor responses to regular auditory patterns.

Subjects (N = 32) were asked to synchronize a motor response with tones in auditory patterns. These patterns were created from six tones and six intertone intervals of equal duration. The pitch of the first tone differed from the others. It was found that subjects used three types of timing in their motor response: (1) the first intertone interval was prolonged and the second interval was shortened, (2) the second intertone interval was prolonged and the first interval was shortened, and/or (3) the first interval and the second interval were of approximately the same length. The prolongation of the fifth interval was observed during all three types of timing. The results are explained using the concept of suprasegmental control of timing, which explains a prolongation of intervals at critical control point of the patterns. The occurrence of three different strategies of timing is discussed in connection with similar principles in musical performance.     

Sensorimotor synchronization: Motor responses to regular auditory patterns

Subjects (N = 32) were asked to synchronize a motor response with tones in auditory patterns. These patterns were created from six tones and six intertone intervals of equal duration. The pitch of the first tone differed from the others. It was found that subjects used three types of timing in their motor response: (1) the first intertone interval was prolonged and the second interval was shortened, (2) the second intertone interval was prolonged and the first interval was shortened, and/or (3) the first interval and the second interval were of approximately the same length. The prolongation of the fifth interval was observed during all three types of timing. The results are explained using the concept of suprasegmental control of timing, which explains a prolongation of intervals at critical control point of the patterns. The occurrence of three different strategies of timing is discussed in connection with similar principles in musical performance.