Psychological Research

Psychol Res (1989) 51:38-42

© Springer-Verlag 1989

The relationship between variability of intertap intervals and interval duration Michael Peters

Department of Psychology, University of Guelph, Guelph, Ontario, N1G 2WI, Canada

Summary. Subjects tracked intervals in a synchronization paradigm at interval durations of 180, 210, 240, 270, 300, 400, 500, 600, 700, 800, 900, and 1,000 ms. The variability of intertap intervals (ITIs) shows a sudden increase near 300 ms. This increase is interpreted as indicating the transition from automatic to controlled movement. It is suggested that the sudden change in the variability of ITIs does not reflect the operation of different timing mechanisms at short and long intervals, but differences in the way in which attentional processes come to bear on movement initiation for different interval durations. In contrast to previous findings reported in the literature, a U-shaped function between interval duration and variability in the 300-to-l,000-ms range was not observed.

One of the simpler questions to be asked about the timing of behavior is how humans manage to issue regularly spaced responses in synchrony with a pacing source. Hary and Moore (1985, 1987) have found that synchronization depends on the use of internal and external resetting events with more than one independent source of timing error. The present work addresses an additional source of complication in the synchronization paradigm: the role of the duration of an event in conscious perception. When subjects tap quickly and repetitively on a surface, the tapping movements are not individually experienced. When the rate is slowed sufficiently, however, there comes a point when movements are initiated and experienced individually. On the basis of a pilot study in which subjects were asked to identify that point, a rate corresponding to interresponse intervals near 300 ms emerged. Kristofferson (1976) reported that, with a different paradigm, subjects experienced a discontinuity between shorter and longer intervals that emerged near 300 ms as well; subjects felt that at longer intervals preparatory movements preceded the actual response, while at intervals below 300 ms the response was immediate, without such preparations. In a different study, Wing and Kristofferson (1973a) report the variance of ITIs as constant up to 250-ms intervals, with a notable increase for longer intervals. Is it possible that in synchronization paradigms different mechanisms operate at different intervals, with a change from one to the other near 300 ms? Such a possibility would invite further investigation as to whether the mechanisms identified for the timing of repetitive responses (Hary & Moore, 1985, 1987; Wing, 1982) might

operate differently for different interval durations. This study asks the question: can a discontinuity be identified in a region of ITI durations where discontinuities are experienced subjectively?

Method Subjects. Two male and two female right-handed subjects were used. All had experience in tapping tasks, having participated previously in similar experiments that required the repetitive production of equal intervals.

Apparatus. Subjects tapped the lever of a microswitch connected to a microprocessor. The microprocessor also allowed the issue of a pacing beat. The pacing beat was a 600-Hz tone of 80-ms duratinn presented at 68 db, with a rise time of < 3 ms. All switch closures and releases were recorded and the pulses of the pacing tone were recorded as well so that the time difference between the response and the onset of the pulses could be documented. Procedure. Throughout, a synchronization paradigm was used, with the pacing beat present throughout the trial and subjects explicitly instructed to maintain synchronization as well as they could. No other instructions were given. In order to keep the number of trials constant, but avoiding too few values being collected at longer interval durations, the trial durations were lengthened with increasing intervals. The following list of intervals tested gives, in brackets, the average number of taps collected for each of the 80 trials at each interval duration: 180 (50), 210 (41), 240 (35), 270 (32), 300 (29), 400 (22), 500 (36), 600 (29), 700 (24), 800 (21), 900 (29), and 1,000 (26). Subjects A and M performed a minimum of 80 trials for each of the intervals listed above. Subject K did not perform at the fastest interval (180 ms) because performance at this rate was too erratic; and subject S only performed at the intervals from 180 to 400 ms. 1 Each subject performed 20 trials a day, with one interval duration for all 20 trials. Before each daily session subjects performed 3 - 5 practice trials, examI Subjects A and M completed another 100 trials each for the 400-ms interval in order to see if the somewhat smaller number of intervals collected for this series had a marked effect on the SD of the ITI. This turned out not to be the case. For example, for A the SD at 400 ms for the first 80 trials was 11.2 ms, and 10.7 ms for the next 100 trials.

39 ining the quality of performance at the end of each trial (summary data were displayed on computer screen). A trial began with the pacing signal and the subject could join in at any point; the first tap initiated the timing of the trial. The trials were performed in four series. For the first, subjects performed 20 trials daily, beginning with 20 trials at an ITI of 180 ms on the first day, and ascending day by day to the next ITI until the entire series was completed. After a day of rest the second series started, this time descending from the long to the short intervals, followed by another ascending and another descending series until 80 trials were completed at each ITI. All subjects were instructed to tap as synchronously with the pacing signal as possible. The microswitches used produced an audible click when depressed and released.

Table 1. Average standard deviation in ms for the best 10 trials at each interval for each of the four subjects Interval

Subjects A

210 240 270 300 400 500

K

5.9 6.3 6.3 6.3

(58) (62) (62) (62)

M

6.9 7.0 7.9 8.2

S

(63) (64) (72) (75)

4.8 (55) 5.4 (61) 6.0 (68)

10.1 (100)

10.9 (100)

10.1 (100)

11.2(103)

9.1 (103) 10.5(119)

5.5 (60) 6.2 (68) 6.4 (70)

8.8(100)

9.1 (100)* 9.3 (102) -

* Italicized values indicate the interval characterized by a sudden j u m p in variability compared to preceding and following intervals. Values in brackets are SDs expressed as percentages of the value where the jump occurs

Results The variability of interresponse intervals The SD of interresponse intervals for a trial was calculated by measuring the mean interresponse interval and by then expressing the variability of intervals around that mean in terms of the standard deviation. This measure was then averaged across all trials. The SDs obtained in this way and those obtained by calculating the SDs of all intervals around the grand-total mean based on all measured intervals over all trials were similar within less than 1 ms. As might be expected for such a large number of trials, the mean intervals differed by less than 1 ms from the interval created by the pacing pulse, except for the very rapid rates. Figure 1 shows the SD of interresponse intervals for the four subjects and for the intervals tested. It shows the SD of interresponse intervals averaged over trials and subjects and the SD expressed as a percentage of the interval. The error bars refer to the intersubject standard error. (The standard error for each individual subject for a given interval was negligible.) The curves indicate that with increasing intervals from 300 to 1,000 ms the variabilitiy of the interresponse interval declines slowly, but steadily, as a percentage of the overall duration of the interval. There appears to be a sudden change in SD of the ITI in the region between 270 and 300 ms, similar to the region in which a change was observed by Wing and Kristofferson (1973 a). Individual differences obscure the precise occurrence of this change, but Table 1 provides individual data for the

four subjects. On the assumption that the better the performance, the closer the underlying timing processes are reflected, the means are based on the 10 best trials collected at each interval. For each subject, the average SDs for the most regular 10 out of 80 trials was calculated, beginning at 210-ms intervals (the fastest speed of 180 ms was, as Figure 1 shows, too fast for well-controlled performance). For subjects M and S a sudden sharp increase in variability occurs between 270 and 300 ms, while that increase occurs between 300 and 400 ms in the case of subjects A and K. In all cases the important comparison is the change in the SD before the interval designated as "jump" in relation to the change in the SD after that interval. For subjects A and K the comparisons can be made between 300 and 400 and 400 and 500 ms, while for subjects M and S the comparisons have to be made most reasonably between 210 and 300 and 300 and 400 ms. The significance of differences for SDs for adjacent intervals can be evaluated by comparison with the maximum standard error observed for any one value (0.53). By this criterion the mean difference between the point at which the jump occurs and the succeeding interval is less than one standard error in all cases. In contrast, for A and K the difference in the means between the preceding interval (300) and the jump (400) is 7.2 and 5.1 times the standard error. For M and S the change in the difference between means at 240 and 270 amounts to 1.1

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a n d 0.4 times the s t a n d a r d error, while the change between 270 a n d 300 amounts to 5.3 and 5.1 times the s t a n d a r d error. Figure 2 provides a different perspective on the discontinuity. The average values for the first 10 and the last 10 trials are given for one subject, for all intervals. It can be seen that although, as expected, p e r f o r m a n c e is clearly better on the last, c o m p a r e d to the first, 10 trials, the general pattern, with the discontinuity at about 300 ms is preserved.

The variability of the interval between response and pacing signal Figure 3 gives the absolute magnitude o f the discrepancy between pacing tone a n d response in ms, and that value as a percentage of the total interval. It is i m m e d i a t e l y clear that the overall variability of this measure is considerably higher than the variability o f the intertap intervals (Fig. 1). O f particular surprise was the fact that at 180 ms the subjects could not perform well at all. While all could tap faster than 5.6 taps per second, they had trouble p e r f o r m i n g the synchronization at this rate. The graphic printouts for the gap between response and pacing tone at 180ms

yielded a smoothly declining function if the occurrence o f the tap relative to the pacing tone was plotted. This is exactly what would be expected if the two series o f events (taps and pacing pulses) were i n d e p e n d e n t o f each other ( G o t t m a n , 1981, p. 19). Table 2 gives the average magnitude o f the discrepancy between pacing tone and response. It can be seen that at the fastest speeds the response lags b e h i n d the tone, but as the intervals lengthen, the response begins to anticipate the tone, with longer leads as the intervals lengthen. In agreement with H a r y and M o o r e (1985) a n d other researchers (Fraisse & Voillaume, 1971; Kristofferson, 1976), it was f o u n d that the responses t e n d e d to precede the pacing pulse, at least for the longer intervals. H a r y and M o o r e (1987) report an average lead o f 24 ms at 700-ms intervals, r e m a r k a b l y close to the 27 ms observed at 700 ms in this study, even though the p a r a d i g m s differed.

Correlations between adjacent intervals One of the expectations b a s e d on the m o d e l o f a discontinuity in timing m e c h a n i s m over the range of intervals observed was that subjects would have more deliberate control over the onsets o f i n d i v i d u a l responses in the longer range o f intervals a n d would be m o r e likely to adjust interval duration in response to a perceived error in performance. F o r this reason one w o u l d expect correlation coefficients between adjacent intervals to differ for short a n d long intervals. The autocorrelations for a d j a c e n t intervals (lag 1) were calculated for each subject, interval, a n d trial. The resulting averages are shown in Table 3. It can be seen that there is considerable individual variability for the shorter intervals, but that subjects behave m o r e u n i f o r m l y for the longer intervals. A b o o t s t r a p p i n g p r o c e d u r e was used to ascertain the significance o f correlation coefficients. F o r example, trial n u m b e r 72 by subject A, on the 300-ms interval, yielded a correlation coefficient o f - 0 . 1 7 . All o f the intervals for that trial were r a n d o m l y arranged, and a correlation coefficient was c o m p u t e d for the resultant data. This was repeated 500 times so that a distribution could be constructed. In this particular case the distribution of 500 correlation coefficients had a m e a n o f -0.031, with an SD o f 0.055. This permitted the statement that the - 0 . 1 7 correlation coefficient o b t a i n e d for the exp e r i m e n t a l trial was significantly different from zero. The

Table 2. Average discrepancy between pacing signal and response for the various intervals Interval duration (ms)

M SD

180

210

240

270

300

400

500

600

700

800

900

1000

+8 10

+3 16

-10 1"4

-14 16

-18 20

-17 15

-19 16

-18 13

-27 14

-34 17

-29 12

-48 22

M = Mean interval in ms by which the response led ( - ) or followed ( + ) the signal Table 3. Correlations between interval durations of adjacent intervals for subjects for all of the tested intervals

r SD

180

210

240

270

300

400

500

600

700

800

900

1000

0.14 0.17

0.08 0.15

-0.08 0.13

-0.08 0.10

-0.08 0.04

-0.07 0.07

-0.10 0.01

-0.10 0.02

-0.14 0.03

-0.20 0.02

-0.20 0.07

-0.25 0.06

Each correlation coefficient is based on the averaged coefficients computed for each trial, for each subject

41 positive values at the two fastest speeds (180 and 210) are explained by inadequate performance; subjects show systematic drifts between response and pacing pulse at these speeds; this was interpreted as showing independence of the series of pacing pulses from the series of responses (Gottman, 1981, p. 19). Conclusion

With regard to the question of whether there is a sudden change in variability of ITIs near intervals of 300 ms, an affirmative answer can be given. The clearest indication was provided by a sudden increase in the SDs of ITIs near 300 ms, with less clear indications of an equivalent change for the error (gap between response and pacing tone) in relation to interval duration and the lag-1 autocorrelations. The interval duration in the range of 300 ms was remarkably close to the range determined by Kristofferson (1976) with a different paradigm, and to Wing and Kristofferson's (1973 a) study, which used a similar paradigm. Using a continuation, rather than a synchronization, paradigm and separating out timer-delay variance from responsedelay variance, Wing and Kristofferson (1973b) obtained somewhat different results. Timer-delay variance was linearly related to interval duration, while the relationship between response-delay variance and interval duration was variable for different subjects, with at least one of them showing a somewhat linear increase of responsedelay variance with increasing interval duration. Unfortunately, the study did not explore intervals beyond 350 ms; the results from two of our subjects suggest that the sudden change could well occur anywhere between 300 and 400 ms. Wing and Kristofferson suggest that the relative importance of the two sources of variance might vary in relation to the duration of the interval. Does this sudden change in the SD imply the presence of a different set of timing mechanisms at shorter and longer intervals? The answer depends on one's model of timing. One model would see timing attributed to the use of a constant internal "clock" that provides the temporal resolution against which the duration of events is evaluated (e.g., P6ppel & Logothetis, 1986). According to this model, the externally produced event would interact with this clock much as the operator of a stopwatch interacts with the watch by defining the duration of an interval. The existence of such an internal clock has been questioned by Creelman (1962), Treisman (1963), and Michon (1967). A fundamental problem with an internal clock that has a constant clock rate is that the agent or mechanism that "reads" the clock in order to time behavior must itself have some appreciation of time. A more promising model holds that the externally produced interval selects timing circuits in the brain that are matching the duration of that interval. In other words, the event does not instruct the brain to establish a circuit (learning de novo). This model is in keeping with the current emphasis on selective, rather than instructive, processes in sensory-motor processing (Edelman, 1979). The underlying assumption, then, is that there is a very large number of circuits capable of defining intervals within the limits of behaviorally meaningful values. The fact that subjects can adequately repeat a given interval after having experienced it only once supports the selection model of timing. How does this model relate to the performances of subjects who try 1:o synchronize their tapping with a pacing

source? The model assumes that the basic mechanism underlying timed behavior is similar across the interval ranges sampled. So the sudden change in variability of intertap intervals at the shorter end of the range is not due to a change in the basic mechanism, but to other factors. What could these be? First, there is the aspect of strict performance limitations. Wing and Kristofferson (1973b) observed that their subjects had difficulties with the shorter intervals in the 170-ms range, and in our study synchronization was difficult at the 180-ms-interval duration for three subjects, while the fourth had difficulty tapping at this rate altogether. The second factor relates to the mode in which movement is initiated. At the shorter intervals, an automatic mode of responding is probably used, with relatively little freedom to adjust intervals or the ability to analyze discrepancies between pacing source and movement. For instance, the subjects who could tap at 180-ms intervals were not aware of the fact that their movements were badly synchronized with the tapping source. At longer intervals, subjects become aware of discrepancies, and the movements appear to be issued in a more controlled mode, so that individual tapping movements are separately experienced. The increase in the variability of intertap intervals is suggested as occurring when the subject changes from a predominantly automatic mode of tapping to a more controlled mode. With an increase of intervals, attention becomes more and more important in the maintenance of attention; towards 1,000 ms the task has some aspects of a vigilance task. It is suggested here that the relative increase of variability of intervals toward the long intervals that results in the sort of U-shaped function described with considerable agreement in the literature (Bartlett & Bartlett, 1959; Fraisse, 1982; Michon, 1967; Stevens, 1886; Wagner, 1971 ; Woodrow, 1932), is due to attentional factors. These investigators, with the exception of Wagner (1971), agree that somewhere between 300 and 800 ms there is an optimal range below and above which variability shows a relative increase. Wagner's (1971) study on scale playing gives a U-shaped function in a different region, with SDs high in the range below 100-ms intervals, minimal in the range of 100-160-ms intervals, and increasing again as the rate slows towards 500 ms intervals. Wagner's study differs from the other because his subjects did not use the same finger repetitively, but, as is normal in scale playing, a succession of different fingers. How can the discrepancy between this and other studies that look at repetitive movements of a single finger be explained? One possibility lies in the possible difference between synchronization and continuation paradigms. However, according to Michon (1967) there is no discernible difference in performance between the continuation paradigm, where subjects continue to tap at the same pace after the pacing source has been silenced, and the synchronization paradigm, where subjects tap with the pacing source throughout the trial as long as intervals of 1,000 ms and shorter ones are used. Perhaps the larger number of trials in this study is a factor. At longer intervals even the slightest lapse of attention can produce a marked loss in regularity and subject motivation is very important. Note that the very best SDs reached by subjects performing at the longest interval (1,000 ms) were as small as the best values in the 400-ms range; and that subjects were in the position to develop optimal strategies. Two of the subjects

42 who p e r f o r m e d at 1,000 ms, for instance, stayed in the " d o w n " position for half of the duration (almost exactly 500 ms), bisecting the 1,000-ms interval. The third subject stayed in the " d o w n " position for slightly under 100 ms. It is quite likely that this subject m a d e the sort of p r e p a r a t o r y movements described by Kristofferson (1976). In summary, the present study suggests that in the production o f intervals there is a p o i n t at which automatic p r o d u c t i o n gives way to controlled production, and the transition p o i n t that is subjectively experienced can be d o c u m e n t e d quantitatively. Because the transition does not involve a categorical change (such as the shift from rod to cone vision), the sudden increase o f intertap-interval variability at shorter intervals and the p o i n t at which relative increases in variability begin to show at longer intertap intervals are sensitive to practice and attentional effects within and between individuals.

Acknowledgements. This work was supported by a National Sciences and Engineering Research Council of Canada Grant No. A7054. Special thanks to Karin Mertins, Shari Schwartz, and Aldo Tersigni, for supporting the author with the patience required for this study. References Bartlett, N. R., & Bartlett, S. C. (1959). Synchronization of a motor response with an anticipated sensory event. Psychological Review, 66, 203-218. Creelman, C. D. (1962). Human discrimination of auditory duration. Journal of the Acoustical Society of America, 34, 582-593. Edelman, G. M. (1979). Group selection and phasic reentrant signaling: a theory of higher brain function. In G. M. Edelman & V. B. Mountcastle, The mindful brain (pp. 51-100). Cambridge, Mass.: MIT Press. Fraisse, P. (1982). Rhythm and Tempo. In D. Deutsch (Ed.), The psychology of music (pp. 149-180). New York: Academic Press.

Fraisse, P., & Voillaume, C. (1971). Les r6p6res du sujet dans la synchronization et darts la pseudo-synchronization. Annie Psychologique, 71, 359-369. Gottman, J.M. (1981). Time-series analysis. Cambridge: Cambridge University Press. Hary, D., & Moore, G.P. (1985). Temporal tracking and synchronization strategies. Human Neurobiology, 4, 73-77. Hary, D., & Moore, G.P. (1987). Synchronizing human movement with an external clock source. Biological Cybernetics, 56, 305-311. Kristofferson, A. B. (1976). Low-variance stimulus-response latencies: deterministic internal delays? Perception & Psychophysics, 20, 89-100. Michon, J. (1967). Timing in temporal tracking. Soesterberg, Netherlands: Institute for Perception RVO-TNO. P6ppel, E., & Logothetis, N. (1986). Neural oscillations in the human brain. Naturwissenschaften, 73, 267-268. Stevens, L. T. (1886). On the time sense. Mind, 11, 393-404. Treisman, M. (1963). Temporal discrimination and the indifference interval: implications for a model of the internal clock. Psychological Monographs, 77, issue 576. Wagner, C. (1971). The influence of the tempo of playing on the rhythmic structure studied at pianist's playing scales. In J. Vredenbregt & J. Wartenweiler (Eds.), Medicine and Sport, V. 6, Biomechanics II (pp. 129-132). Baltimore: University Park Press, Wing, A. M. (1982). Timing and coordination of repetitive bimanual movements. Quarterly Journal of Experimental Psychology, 34A, 339-348. Wing, A. M., & Kristofferson, A. B. (1973a). The timing of interresponse intervals. Perception & Psychophysics, 13, 455-460. Wing, A. M., & Kristofferson, A. B. (1973b). Response delays and the timing of discrete motor responses. Perception & Psychophysics, 14, 5-12. Woodrow, H. (1932). The effects of rate of sequence upon the accuracy of synchronization. Journal of Experimental Psychology, 15, 357-379.

Received December 8, 1988/January 4, 1989