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
.--I
7
W
6
-I.L
0
5
~
4
W
3
30
zo
10
0
re"
W
z
2
Z
LL
I.u
I.-.
,",
,..,
tn
,'-i
t~
w
u~
I
I
I
200
300
400
I
I
I
I
I
1
500
600
700
800
900
1000
o
1. The variability
of the duration of the
measure expressed as
(decreasing function).
in function at 300 ms
-
I ' ~ FIRST TEN TRIALS I
I - X - LAST TEN TRIALS I
•
Z
ILl
~
z
ILl
~
Ln
INTERVAL (MSEC)
Fig.
5
of the interresponse interval as a function
interval (increasing function) and the same
percentage of the duration of the interval
Bars indicate standard errors. Note break
X ~ x ~ X ~
\x~X~x
I
I
180 210
I
240
I.t/ I
270 300
I
400
I
500
I
600
I
700
I
800
I
900
I
1000
INTERVAL (MSEC)
Fig. 2. Example of the variability of intertap intervals in relation
to interval duration for the first and last 10 trials for subject M
40
lO
so
h,
~E
&O
Z
o
a
cl
ix
2
--
20
z
3,
1
o
I
I
3oo
I
4oo
I
soo
I
6oo
INTERVAL
I
7o0
I
8oo
I
9oo
I
mo
-
lO
{ MSECI
Fig. 3. The variability of the absolute error in ms between the occurrence of the response and the presentation of the pacing signal,
as a function of interval duration (increasing function). The same
measure expressed as % of interval duration is seen in the decreasing function. Large standard errors indicate considerable intersubject variability. Note break in function at 300 ms
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