Psychot Res (1995) 58:206 217

© Springer-Verlag 1995

M. Billon • A. Semjen

The timing effects of accent production in synchronization and continuation tasks performed by musicians and nonmusicians

Received: 25 November 1994/Accepted: 6 June 1995

Abstract Two groups of subjects differing in their musical expertise produced periodic finger-tapping sequences involving a pattern of accentuation. In some situations, the taps were synchronized with the clicks of a metronome. We recorded the trajectory of the subjects' finger displacement in the vertical plane, and the force and the moment of occurrence of the taps on the response key. Musicians tended to equalize the durations of the downstrokes at all positions in the sequence. Nonmusicians moved their finger quickly to produce the accent, and more slowly to produce the subsequent tap. These variations in the movement-execution time were partly compensated by opposite variations in the onsets of the movements, e.g., the short-duration movements were delayed. Despite these differences in their movement strategies, musicians and nonmusicians generated very similar tap-timing profiles. The intertap interval after the accent was lengthened regardless of the subjects' musical expertise and the metronome conditions (metronome present or absent). The lengthening did not depend on whether the interval before the accent was shortened (without the metronome) or not (with the metronome). It is suggested that an internal timekeeper may generate temporal goal points at which the keytaps should occur. The lengthening of the interval after the accent is attributed to transient changes in the working of the internal clock.

Introduction When subjects produce a sequence of periodic finger taps at a moderate rate, the accentuating of one of the M, Billon (1~) CNRS-LNC-31, Chemin Joseph Aiguier, F-13402 Marseille Cedex 20, France; E-mail: [email protected] A. Semjen Centre National de la Recherche Scientifique, Laboratoire de Neurosciences Cognitives, Marseille, France

taps disrupts the temporal regularity of the sequence: the intertap interval before the forceful tap is usually shortened and the following interval is lengthened. This kind of temporal distortion of the timing, due to accent production, has been described several times in the literature (Billon, Semjen, & Stelmach, in press; Fraisse, 1956; Fraisse & O16ron, 1954; Keele, Ivry, & Pokorny, 1987; Semjen & Garcia Colera, 1986) and has been explained in terms of either peripheral or central factors. One explanation of the former kind is based on the idea that accent production may induce changes in the movement dynamics, resulting in the mistiming of the taps. Let us assume, for instance, that the tapping movements are initiated at equal intervals by an internal timekeeper (Wing & Kristofferson, 1973), but that the forceful movement is actually executed more quickly than the other movements: if this is so, the interval before the accent will be shortened and the next interval lengthened. A more centralist view might be that the speed of the internal timekeeper undergoes some transient modulation while the subject is preparing to switch the movement force from low to high level or vice versa: here the timing pattern of the taps could be said to reflect the working of an altered internal clock. To settle the issue, Billon, Semjen, and Stelmach (in press) recorded subjects' hand trajectories in the vertical plane during the production of tapping sequences including an accentuated component. These authors observed that the downstroke during accent production had a higher velocity, and was completed in less time, than the other movements. Analysis of the movement trajectories also showed, however, that the fast downstroke was initiated with a sizeable delay, while the following downstroke, which was initiated quite shortly after the previous one, was executed much more slowly than the other downstrokes. Billon, Semjen, and Stelmach (in press) concluded that the distortion of the intertap intervals reflected the combined effects of peripheral perturbations induced by the production of a forceful tap and central compensations serving to

207

attenuate the effects of these perturbations on the timing of the finger-taps. The short-long pattern of the intertap intervals before and after the accent indicated, however, that the subjects' compensatory strategy was not sufficient to ensure regular timing of the taps. In the present study, we addressed the question as to why the compensation was less than perfect. One possibility is that the subjects may have lacked information about their timing performances. Alternatively, their motor- and/or timing-control capacity may not have been up to the requirements of the task. To test the former possibility, the subjects in the present experiments produced tapping sequences either synchronized with a metronome, or without a metronome. It was reasoned that the presence of an external temporal reference might improve the accuracy of the tap timing by reinforcing the internal representation of the interval to be produced. In addition, by the monitoring of their synchronization error, the subjects could develop more efficient motor strategies for producing equal tap intervals despite the dynamic perturbations introduced by the production of an accent. The role of possible control-capacity problems was tested by the comparison of two groups of subjects, nonmusicians and musicians. The use of a musicians' group was motivated by previous studies, showing that musicians achieved better performances than did nonmusicians in both motor-timing and time-judgment tasks. For instance, musicians produced less variable interta p intervals when tapping without a metronome (e.g., Keele, Pokorny, Corcos, & Ivry, 1985); they made smaller synchronization errors when tapping in synchrony with a metronome (Aschersleben, 1994); they judged and reproduced short tones and pauses more accurately (Keele et al., 1985; Franek et al., 1991a, 1991b). We were interested in determining whether they also used more efficient strategies that permitted them to wholly overcome the timing effects of dynamic accent production. Under the hypothesis that the short-long pattern of intertap intervals reflected incomplete compensation for the peripheral perturbations occasioned by the production of an accent, we expected in short that the presence of the metronome signal and the musical expertise of the subjects would both contribute to some degree to improving the timing of the taps when accentuation was required. If the results did not fit this prediction, they would indicate that the speed of the internal timekeeper is inherently modified when the tapping force is suddenly increased or decreased, as occurs when an accentuated tap is produced. The notion that a compensatory strategy might be used whereby short-lasting down-strokes could be initiated later, and long-lasting downstrokes earlier, in order to equalize the time intervals between the successive taps, is contrary to the view that the internal timekeeper may trigger the successive movements in the sequence (e.g., Wing & Kristofferson, 1973). It calls

rather for a model of an internal timekeeper that provides temporal goal points, at each of which the movements must produce behaviorally meaningful events (Shaffer, 1982). An "endpoint timing" model of this kind (e.g., Billon et al., in press; Jordan, 1981) predicts that the finger taps are temporally more accurate (less variable) than the onsets of the tapping movements, whereas trigger models of timing predict that the inverse relationship will apply because motor execution adds greater delay and variability to the taps. One of the aims of the present study was to determine which of these alternative views is true. Method Subjects. Two groups of six subjects participated in the experiment. The subjects in the musicians' group (mean age: 22) had received at least seven years of formal musical training and played their instrument almost every day. They were all pianists except for one (a clarinettist). The mean age of the subjects in the nonmusicians' group was 25.

Apparatus. The response key and the manipulandum were mounted on a wooden support fixed to a table. The manipulandum (Figure 1) consisted of a moulded forearm support 6 cm in height and a metal finger bar that could be pivoted in the vertical plane. The finger bar was adjustable in length; it was parallel with the forearm and fitted at its distal end with a cylinder to which the index finger could be inserted. The axis of rotation of the finger bar about the support was directly beneath the wrist, whereas the response key (a circular metal plate 2 cm in diameter) was just beneath the distal end of the finger bar. Any rotation of the finger bar (i.e., downward or upward movements of the hand about the wrist) that occurred during tapping with the index finger was recorded with a potentiometer. The subject was seated with his or her forearm lying on the moulded support, with the elbow flexed at 90 °. Being attached to the finger bar did not perturb the subjects' tapping responses on the key, since it had been ascertained in a previous study that the timing of the key taps was identical whether the finger bar was removed or mounted on the apparatus (Billon, Semjen, & Stelmach, in press).

Task and procedure. The subjects produced sequences of 65 taps under four different conditions that resulted from orthogonal combinations between the metronome factor (metronome present or absent) and the accentuation requirements (accent required or not required). In one condition, the subjects had to synchronize their taps with the clicks of a metronome without producing any voluntary accents. In another condition, the synchronization task had to be performed while also every fifth tap was accentuated (i.e., tapped more strongly). In the other two conditions ("without the metronome"), the metronome delivered a periodic signal until the subject executed the first tap. Upon detection of the first tap, the metronome was switched offand the subject continued to tap at the speed set by the metronome. These tapping sequences were again executed either without any accentuation or with an accent on every fifth tap. Three different metronome frequencies were used, corresponding to interclick intervals of 900, 600, and 300 ms. The two slower frequencies were in the range of the tapping rates at which the addition of an accentuation has been found to induce the shortening-lengthening phenomenon. At fast tapping rates (intervals of 300 ms or less), the accentuation is known to induce a lengthening of the interval both before and after the accentuated tap (Semjen & Garcia-Colera, 1986; Piek, Glencross, Barrett, & Love, 1993). The use of the 300-ms rate provided a qualitatively different situation with which to continue our investigations on the effects of providing a metronome signal as well as the effects of musical expertise.

208

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Fig. 1 Diagram of the apparatus and definition of the dependent variables. The impact of the finger on the response key generated a force signal (1) and a contact signal. Contact duration (2) was measured between the onset and offset of the contact. Intertap intervals (3) were measured between successive contact onsets. Contact duration was a constituent part of the intertap interval. Rotation of the finger bar generated an output voltage (displacement signal). The onset of the downstrokes was identified from instantaneous velocity values derived from the displacement data. Velocity

zero crossing was taken to indicate the onset of the downstroke. Downward movement time (4) was measured between the onset of the downstroke and the onset of the contact with the response key. Onset intervals (5) were measured between the onset of the successive downstrokes. When accentuation was required, an accentuated tap occurred every five taps. In these trials, all the dependent variables were analyzed by their serial position being taken into account with respect to the (recurrent) accent. In this and subsequent figures, the accent position is indicated by a vertical arrow

A trial was initiated with metronome clicks being presented via loudspeakers. The clicks were generated by equally paced rectangular electric pulses with a duration of 5 ms. The subjects were instructed to listen to several clicks before starting to tap. Each subject participated in a single experimental session consisting of two parts. During the first part, the subjects performed the sequences in which no accentuation was required, whereas during the second part, they performed the sequences with voluntary accents. Within each part of the session, the tapping rates were tested in decreasing order of speed (with intervals of 300, 600, and 900 ms) with half of the subjects, and in increasing order (900, 600, and 300 ms) with the other half. At each tapping rate, the subjects performed six sequences, three with the metronome and three without it; these conditions were presented to the subjects in an alternating order. Any tapping sequences produced with at least one intertap interval twice as large or twice as small as the required value were discarded and immediately replaced by a new sequence. Any sequences with incorrect accent position(s) were treated in the same way. At the beginning of the first part of the session, the subjects performed two training sequences, one with the metronome and one without. In these sequences, the interclick interval was set at 500 ms. During the second part of the session, the subjects performed one further training sequence with the metronome and an accentuated tapping pattern before each new tapping rate was run.

(Figure 1 (1)) was measured in arbitrary units as the peak output voltage of the piezoelectric crystal. Contact duration (Figure 1 (2)) was defined as the time elapsing from contact onset to offset. Intertap intervals (Figure 1 (3)) were measured between successive contact onsets. The output of the potentiometer was sampied and digitized at a frequency of 250 Hz. The duration of the downward movement, i.e., downward movement time (Figure 1 (4)) was measured between the beginning of the downstroke and the contact between the index finger and the response key. Onset intervals (Figure 1 (5)) were measured between the beginning of successive downstrokes. The beginning of the downstrokes was identified from instantaneous velocity data calculated from the displacement values. The velocity profile was smoothed by the application of a moving average of 5 points, and the time of occurrence of the velocity zero crossing was taken to be the onset of the downward movement.

Measurements. All the experimental events and measurements were controlled with an Olivetti PC (M 290). The definitions and methods of measuring the dependent variables are given in Figure 1. Tapping on the response key activated a piezoelectric crystal. Tapping force

Data analysis. The dependent variables (i.e.~ tap force, contact duration, intertap interval, downward-movement time, and onset interval) were analyzed on the basis of the recurrent accentuated taps. To this end, each trial sequence (65 taps) was subdivided into 13 subsequences of 5 taps with one accentuated tap in each. The sequences without voluntary accent were treated in the same way. Descriptive statistics were computed after sequential indexing (1 to 5) of the dependent variables. The computations were carried out on each subject, trial by trial. Mixed-design analyses of variance (ANOVAs) based on the individual mean scores averaged over trials were carried out in order to test the effects of Experimental Group or Expertise (musicians/nonmusicians); Metronome (present/absent); Accentuation (present/absent); and Serial position (1 to 5) within the subsequence.

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NoAc Tap positions Fig. 2 M e a n c o n t a c t d u r a t i o n in sequences w i t h o u t v o l u n t a r y accent (NoAc) a n d in sequences with an accent occurring every fifth tap. T h e a c c e n t u a t e d tap is s h o w n in position 1 (arrow). D a t a were collapsed across g r o u p s a n d m e t r o n o m e conditions

Results

Tap force and contact duration The accentuated taps were more forceful than the nonaccentuated taps, as was to be expected. The tap force did not show any systematic variation across the experimental groups and conditions. Accentuated taps involved longer contact durations with the response key than did nonaccentuated taps. This difference can be seen in Figure 2, which shows the mean contact durations averaged over metronome conditions. Individual mean contact durations were subjected to (Groupx Metronome × Accentuation x Tap position) ANOVAs (one per tapping rate). Tap position was the only significant main effect consistently found to occur in all three ANOVAs, F(4, 4 0 ) = 6.02, 7.68 and 20.27, at rates of 900, 600, and 300 ms respectively, all ps < .001.

Intertap intervals When accentuation was not required, the intervals did not vary depending on the serial position. In Figure 3, these intertap intervals are shown averaged over sequential positions (Figure 3, NoAc). When the subjects accentuated every fifth tap, the duration of the intervals depended on their position with respect to the accentuated tap (Figure 3, positions 1 to 5). The most systematic effect was a lengthening of the interval following the accentuated tap (position 5). Other intervals underwent more complex variations depending on the experimental conditions. The effects of Experimental Groups, Accentuation, Metronome, and Interval position were tested by 2 x 2 x 2 × 5 ANOVAs run separately at each tapping rate. No significant main effect of Group or Metronome was observed in any of the three analyses. At the 900-ms rate, significant effects were found for Accentuation, F(1,10)= 9.25, p < .05, and Interval

position, F ( 4 , 4 0 ) = 13.57, p < .001. Significant interactions were found for Position x Accentuation, F(4,40) = 15.88; Position x Metronome, F(4, 40) = 6.82; and Position x Accentuation x Metronome, F(4, 40) = 4.33, all ps < .001. The three-way interaction indicates that the pattern of timing induced by the accentuation constraint was modified during synchronization with the metronome. One difference noted in the timing patterns, depending on whether the metronome was present or absent, concerned the interval just before the accentuated tap (position 4). This interval was shortened in the no-metronome condition, considerably so in the nonmusicians and less so in the musicians. During synchronization with the metronome this effect no longer existed. At the 600-ms rate, the main effect of Accentuation was not significant. The effects of Interval position were significant, F(4, 40) = 19.76, as were the following interactions: Position x Accentuation, F(4,40) = 15.88; Position x Metronome, F(4, 40) = 7.45; and Position x Accentuation × Metronome, F(4, 40) = 4.20, all ps < .01. Note that at the 600-ms rate, the interval just before the accentuated tap was shortened under the no-metronome condition only by the nonmusicians. This difference between the groups presumably contributed to the four-way interaction being significant, F(4, 40) = 3.22, p < .025. At the 300-ms pace, the ANOVA yielded significant effects for Interval position, F(4, 40) = 5.94, p < .001, and for the interactions between Position and Accentuation, F(4,40) = 4.76, p < .01, and between Position, Accentuation, and Metronome conditions, F ( 4 , 4 0 ) = 2.63, p < .05. Figure 3 shows that at this relatively fast pace, the interval just before the accentuated tap was lengthened and that the lengthening occurred both with and without the metronome. This effect contrasts with the shortening of this interval observed at the slower rate under the no-metronome condition. Was the lengthening of the intertap interval just after the accentuated tap due to the lengthening of the contact duration at that tap? (Remember that contact duration is a constituent part of the intertap interval (Figure 1), and that the accentuated taps involved longer contact durations than the other taps). In order to answer this question, the correlation was calculated between the contact duration of the accentuated tap and the interval that occurred after that tap. The correlations ranged from - .46 to .70; they were systematically positive with some subjects and systematically negative with others. The mean of the correlation coefficients (averaged over subjects and metronome conditions) was 0.11, 0.11, and 0.16, at the rate of 900, 600, and 300 ms, respectively. The means of the coefficients of determination (r 2) were .08, .08, and. 10. Given these weak values, it is unlikely that the lengthening of the intertap interval after the accent may simply have reflected the increase in the duration of the contact at the accentuated tap.

210 Fig. 3 Mean intertap interval in sequences without any voluntary accent (NoAc) and in sequences with an accent occurring every fifth tap. The interval just before the accent (arrow) is shown in position 4; the interval just after the accent, in position 5. Metronome conditions are indicated by symbols (see insert)

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Downward movement time

We have taken downward movement time to mean the interval between the onset of the top-down finger displacement and the moment of contact with the response key (see Figure 1). The mean downward-movement times are given in Figure 4. At the rates of 900 ms and 600 ms, the movement times showed striking differences between musicians and nonmusicians. The musicians completed their downstrokes in less time than the nonmusicians did. In addition, when a voluntary accent was required, their movement times barely varied, whatever the sequential position of the movements, whereas for nonmusicians, the movement that produced the accent had a shorter duration than the other movements, and the subsequent downward movement tended to have a longer duration than the other movements. At the 300-ms rate, these variations disappeared; musicians and nonmusicians all showed quite similar patterns of movement times.

Interval position

The individual movement times computed for each tapping rate were subjected to 2 x 2 x 2 x 5 (Group x Accentuation x Metronome x Tap position) ANOVAs. The main effect of Group was not significant at the rate of 300 ms; it was significant at the rate of 600 ms, F(1, 10) = 9,21, p < .025; and fell short of significance at the rate of 900 ms, F(1, 10)= 4.58, p > .05. The main effect of Accentuation was not significant in any of the three ANOVAs. The main effect of Metronome and Tap position reached significance level only at the rate of 900ms, F(1,10)= 13.27, p < . 0 1 (Metronome) and F(4,40) = 3.38, p < .05 (Position). The differentiating effects of Accentuation observed between musicians and nonmusicians at the rates of 900 ms and 600 ms were confirmed by significant Group x Position interactions, F(4, 40) = 4.24 and 5.42; and by significant Group x Accentuation x Position interactions, F(4,40)= 5.40 and 4.69, all ps < .01. At the rate of 300 ms, none of these interactions was statistically significant. How was it that, at the slow tapping rates, the musician subjects maintained roughly equal movement

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times whether the taps were accentuated or not, while the nonmusicians produced the accentuated movement times with much shorter duration than the nonaccentuated movement times? We examined the angular displacement of the finger bar from downstroke onset to tap contact. Accentuated taps started from a higher position than nonaccentuated taps in both groups. With the accentuated and nonaccentuated taps the mean displacement was 26.9 ° and 13.1 ° respectively in the case of musicians; and 32.3 ° and 23.3 ° in that of nonmusicians. The displacement was on the average smaller in musicians than in nonmusicians and, most importantly, the increase in the accentuated movement amplitude compared with the nonaccentuated movement amplitude was greater in musicians than in nonmusicians. This difference may at least partly explain why the musicians produced both accentuated and nonaccentuated downward movements with roughly the same movement time.

When no accentuation was required, the time intervals between successive movement onsets did not vary systematically as a function of the interval's serial position, metronome conditions, or groups; but when accentuation was required, the duration of the intervals from one movement onset to the next varied as a function of their position with respect to the accentuated tap. At the rates of 900 ms and 600 ms, the variation of the onset intervals according to serial position differed between nonmusicians and musicians. In the nonmusicians' group, the onset interval before the accentuated tap was lengthened and the subsequent interval shortened, whereas in the musicians' group, the onset interval before the accent was shortened and the next interval lengthened. Individual mean onset intervals were subjected to 2 x 2 x 2 x 5 (Group x Accentuation x Metronome x Interval position) ANOVAs. The main effects were not statistically significant. However, confirming the difference in the timing profiles observed between musicians and nonmusicians, a significant three-way interaction (Group x Accentuation x Interval position) was found to have occurred at both the 900ms rate, F(4,40) = 3.29, p < .025, and the 600-ms rate, F(4, 40) = 6.04, p < .001. Figure 5 shows the timing pattern of the interresponse intervals at the onset of the downstrokes (i.e., onset intervals) and at the completion of the downstrokes (i.e., intertap intervals) in musicians and nonmusicians. The data were collapsed across metronome conditions. In the nonmusicians' group, the onset intervals showed the reverse pattern to that of the intertap intervals. That is, in this group of subjects, the long-short pattern of onset intervals before and after the accent (see black arrows) changed to short-long pattern as the result of systematic variations in the downward-movement times. In the group of musician subjects, no such reversal of the pattern of intervals before or after the accentuated tap could be observed. At the rate of 300 ms, the main effect of Interval position was significant, F(4,40)=7.05, p < . 0 0 1 . However, the interactions between this factor and other factors were all statistically nonsignificant. In other words, the onset intervals had a quite similar pattern both in musicians and nonmusicians; it was characterized by a lengthening of the intervals that occurred both before and after the accentuated tap.

Timing variability As we have just seen, when initiating the accent, the nonmusicians delayed the downward movement (which had a short duration), i.e., they lengthened the onset interval; and conversely, when initiating the next, much slower, downward movement, they shortened the

212 Fig. 5 M e a n onset intervals and contact intervals, depending on their position with respect to the accentuated tap. The interval just before the accent (arrow) is shown in position 4; the interval just after the accent, in position 5. D a t a were collapsed across m e t r o n o m e conditions

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onset interval. This modulation of the timing of the movement onsets suggests that the subjects' timing goal was the moments of contact with the response key, and that they flexibly adapted the timing of movement onsets to that goal, taking into account the dynamic characteristics of their movements (e.g., movements with shorter durations were initiated later than those with longer durations). On the hypothesis that finger taps, rather than downstroke onsets, were mainly controlled in time, one might expect the intertap intervals to be less variable than the intervals measured between successive downstroke onsets. Although musicians adopted a motor strategy that attempted to equalize their movement times, which differed from that of the nonmusicians, the prediction that the endpoint timing was likely to be less variable than the movement initiation timing seemed liable to hold in the case of both groups of subjects. The mean variability (in terms of the variance) of the onset intervals and intertap intervals is given in Figure 6. ANOVAs were carried out on individual

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mean-variance scores in order to test the effects of Type of interval (onset or intertap), Accentuation, Metronome, and Group. Intertap intervals were found to be less variable than onset intervals at the rate of 900 ms, F(1, 10) = 41.13, p < .001, and at the rate of 600 ms, F(1, 10) = 19.26, p < .01, whereas at the rate of 300 ms, the difference fell short of significance, F(1, 10) = 4.82, p > .05. The effects of Group and Accentuation were significant only at the 900-ms pace, F(1, 10)= 7.97, (Group) and F(1, 10) = 8.37 (Accent), ps < .05. The fact that the variability of the intertap intervals was lower than that of the onset intervals may reflect a trade-off between the time of onset of the downstroke and the duration of the movement down to the key. For example, late initiation of the downstroke may have been compensated for by the speeding up of the performance of the movement, or early initiation of the downstroke may have been compensated for by the slowing down of the performance of the movement. In order to test this hypothesis, we carried out the following analysis. The interresponse intervals were split into

213 Fig. 6 Mean variance of onset intervals and intertap intervals when accentuation was not required (NoAc) or was required (Ac). Tapping rates are indicated by symbols (see insert). Data were collapsed across metronome conditions

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downward movement time (MT) and complement time (CT). The CT is the interval between the contact with the response key and the onset of the next downstroke (see Figure 7, insert). Both variables are indexed variables (MTi, CTi). The sum of an MT and a CT sharing the same index constitutes an onset interval ( M T i ¢- C T i ) , whereas the sum of a CT and the next MT constitutes an intertap interval (CT~ + MTi÷ ~). The existence of a trade-off between the time of initiation of the downstroke and its duration would show up as a negative covariance (correlation) between these terms (CTi, MT~+I). Note that the endpoint-timing hypothesis does not predict any correlation between the constituents of onset intervals (i.e., MTi, CTi). We calculated the correlation between the constituents of the intertap intervals (CTi, MTi+I), and of the onset intervals (MTi, CTi) separately in each subject, experimental condition, and trial, taking into account the sequential position of the intervals. Figure 7 shows the distributions of the correlations pooled over conditions, sequential positions, and subjects (n = 360 per distribution). At the two slower tapping rates, the pattern of distributions was very similar with both musicians and nonmusicians. Highly negative correlations were obtained between the constituents of the intertap intervals (CTi, MTi-- 1). This finding supports the existence of a trade-off between the time of initiation of the downstroke and its duration. The distributions of the correlations between the constituents of the onset interval (MT~, CTi) were centered on only slightly negative values, however. At the rate of 300 ms, the correlations calculated in the case of the musicians still showed the patterns previously described. With the nonmusicians, however, both distributions overlapped. They were centered on slightly negative values.

Discussion

In this study, musician and nonmusician subjects were asked to execute a series of periodic finger taps at

Onset

Intertap

Onset

Intertap

Interval

a predetermined rate, either in synchrony with the clicks of a metronome or without the help of a metronome. The tapping sequences were performed either without any voluntary accent or with an accent placed on every fifth tap. Results showed that with the musicians, the timing of the taps was less variable overall, and less dependent on the metronome conditions (i.e., metronome present or absent) than with the nonmusicians. At the rates of 900 and 600 ms, major differences between the two groups were observed in the duration of the downstrokes as well as in the timing of the downstroke onsets. Nonmusicians completed the accentuated downstroke in less time, and the following downstroke in more time, than the other downward movements. On the other hand, they initiated the quick downstrokes later, and the slow downstrokes earlier, than the other downstrokes. The musicians used a completely different movement-control strategy, designed to equalize the downward-movement times at any position in the sequence. Despite these differences between the two groups' motor strategies, there were remarkable similarities between the timing performances of the musicians and the nonmusicians. First, the temporal variability of the keytaps was less conspicuous in both groups than the variability of the downstroke onsets. Secondly, the effects of accent production on the timing of the taps were quite similar with both musicians and nonmusicians. One such effect was the lengthening of the intertap interval before the accent when tapping was performed at the fast rate (300 ms). Previous studies have shown that the lengthening of the interval before the accent occurs in relatively fast sequences, presumably because the preparation of the accent force cannot be wholly completed within a normal tapping period (Semjen & Garcia-Colera, 1986; Piek et al., 1993). With tapping rates of 600 and 900 ms, the interval before the accentuated tap was shortened rather than lengthened. This effect was most obvious in the nonmusicians' group when they were tapping without the metronome. The shortening of the interval before the accent can be taken to reflect partial failure of the

214

Fig. 7 Absolute-frequencyplots of the correlation coefficients estimated between the componentsof the onset intervals (open symbol)and those of the intertap intervals (black symbol) in nonmusiciansand in musicians at each of the tapping rates. The composition of the intervals is shown in the insert. Data were pooled across metronome conditions, accent conditions, and serial positions with respect to the accent

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~, 100-]

75 50. 25

25. -.9 -.7 -,5 -.3 -.I .1 .3 .5 ,7 .9

Correlations(classmidpoints)

strategies compensating for the dynamic perturbations introduced by a forceful tap, since the provision of the subjects with a periodic metronome signal either attenuated or abolished the shortening of the interval. In both groups, the most prominent effect of the production of an accentuated tap was the lengthening of the intertap interval that followed the accent. Unlike the shortening of the interval before the accent, this effect could not be eliminated or attenuated by the subjects being provided with periodic metronome signals. Thus it emerges that the lengthening of the interval after the accent did not depend on whether or not the previous interval had been shortened. Nor did it

-.9 -.7 -.5 -3 -.1 .1 .3 .5 .7 .9 Correlations (class midpoints)

depend on specific motor-control strategies or on the subjects' musical expertise. It therefore seems inappropriate to attempt to account for this lengthening effect in terms of insufficient compensation between the movement-onset and movement-execution times. Taken as a whole, these findings relate to two major issues, namely, the function of the internal timekeeper in the time control of movement sequences, and the origin of the interaction between time control (cadence) and force control (accent).

The timekeeper's function in the control of repetitive taps. The internal-timekeeper hypothesis is usually said to be justified by the fact that the same movement

215

sequence can be executed at will at different rates or at the rate indicated by an external timekeeper. It is generally assumed that this is achieved by the internal timekeeper being set at the desired rate to pace the successive movements in the sequence (see for reviews Semjen, 1992; Summers & Burns, 1990). The actual mechanism involved in the timekeeper is not known as yet. It has been suggested that time keeping may be based on some integration of the pulses of a number of neural oscillators, or on activities propagated in a delay-line network (Miall, 1992; Moore, 1992). Whatever the internal structure of the timing unit may be, the results of the present experiment are relevant to the question of how the timekeeper participates in motor execution. One type of model assumes that the timekeeper's output triggers the successive movements as if they were discrete events (e.g., MacKay, 1985; Wing, 1980; Wing & Kristofferson, 1973). Another type of model suggests that the internal timekeeper provides temporal goal points at which the movements must produce behaviorally meaningful events (e.g., taps on the key). According to this conception, movement initiation and movement trajectory are coordinated with a view to timing goals (Shaffer, 1982). The data obtained in the present study support the second hypothesis because of (a) the nonmusicians' compensatory behavior (for instance, delayed onset of the fast accentuated downstroke); (b) the lower timing variability of the keytaps as compared with the tapping movement onsets; and (c) the negative covariance between the time of initiation and the duration of the downstrokes. Results consistent with (b) have been previously reported by Jordan (1981), who requested musically trained subjects to tap with their index finger on a response key in synchrony with a metronome; to move quickly after the tap to a home position some distance from the response key; to keep their finger in the home position until it was time to make the next tap; and then to move smoothly from the home position to the response key and effect the next tap. The interresponse intervals between successive starts from the home position proved to be more variable than the interresponse intervals between successive movement ends, that it, between successive taps. A more recent study by Bootsma and Wieringen (1990) indicated that the principle of endpoint or goal timing applies far beyond the limited activity of periodic tapping. These authors analyzed the timing of an attacking forehand drive in top-level tabletennis players. Consistently with (b), the moment of ball-bat contact was found to be less variable than the moment of drive initiation. Consistently with (c), a negative correlation was found to exist between the time of initiation of the drive and its mean velocity and acceleration: early initiation was associated with a slower swing and late initiation with a faster swing. The organizing principles of movement timing thus appear to be quite similar in both the table-tennis task and ours, regardless of how the timing-goal point was

actually specified, namely, by a perceptual cue (the relative rate of dilatation of the optical contour of the approaching ball, i.e., tau; see Bootsma & Wieringen, 1990) or by the internal timekeeper. The notion that internal time keeping consists of specifying temporal goals is also compatible with findings on interlimb synchronization. Bimanual movements aimed, for instance, at performing a cooperative action (e.g., opening a spring-loaded drawer with one hand and taking a piece of food out of the drawer with the other hand) were found to be synchronized at the moment of goal achievement, despite large spatial and temporal variabilities occurring in the initiation and execution of the component movements (Kazennikov et al., in press). Another example is provided by selfinitiated finger-foot synchronization. In this task, the activity of the foot always shortly precedes the activity of the finger. As Paillard (1948) pointed out, this order of movement initiation permits the movement-generated afferent signals to reach the central nervous system almost simultaneously, given the difference in length between the afferent conduction pathways. If the finger and foot motor systems received a common timing signal initiating the movements, as is suggested by the trigger models of timing, the finger would be activated before the foot, given the difference in length between the efferent conduction pathways (Paillard, 1948; Bard et al., 1992). How the anticipated timing goal may constrain the initiation and execution of the movement is an unsolved question as yet. The working principles of the neural mechanisms that underlie this achievement may not be very different, however, from those responsible, for instance, for the shaping and timing of the speech motor system, depending on anticipated sequences of phonemic goals. Further work is now necessary to model these mechanisms. One may conjecture at least that the subtle compensatory effects that occur between movement initiation and movement duration with a view to reaching a specific timing goal may rely upon kinesthetic, and perhaps tactile, sensory information. Evidence for this hypothesis was obtained in a study on a patient suffering from large-fiber sensory neuropathy (Billon, Semjen, Cole, & Gauthier, submitted). Interaction between time control and force control. In the present experiment, each accentuated (strong) tap was preceded and followed by a nonaccentuated (weak) tap. Previous studies have shown that if a tapping sequence contains several strong taps in succession, the durations of the intervals bounded by strong taps do not differ from those bounded by weak taps. Interval lengthening occurs only when a strong tap (i.e., a single accentuated tap, or the last tap in a sequence of strong taps) is followed by a weak tap (Fraisse, 1956; Fraisse & Ol&on, 1954; Semjen, unpublished manuscript). The production of a forceful tap may possibly induce some

216

refractory state in the motor-executive systems, and this relative refractoriness may impede the organization and/or execution of the next low-force tap. Since relaxation from a refractory state is likely to have a progressive time course, the impeding effects of the strong tap on the weak tap should be greater when the intertap interval is shorter. Our present findings did not show the existence of any trend of this kind, and so refractoriness cannot be taken to account satisfactorily for the lengthening of the interval. A more central type of explanation may be that the production of recurrent accents parses the whole sequence of taps in smaller subunits, between which the lengthened interval acts as a boundary marker or pause. Pausing at subunit boundaries is known to occur in many serial skills, ranging from finger tapping (e.g., Restle, 1970; Povel & Collard, 1982) to speech (e.g., Cooper, Paccia, & Lapointe, 1978). It has been variously interpreted as an effect of muscular relaxation, or of programming the next subunit, or even as a tool for expressive communication (see for a review Semjen, 1992). The evidence shows, however, that our lengthening phenomenon cannot be equated with pausing. For instance, the effect is not dependent on the actual recurrence of the accents, since it occurs also when a single strong tap is inserted into a short 5-tap sequence (Semjen & Garcia-Colera, 1986; Billon et al., in press). Further, Fraisse (1956) compared the timing profiles generated by alternating strong and weak taps when the subunits were conceived of as either trochees (strong weak) or iambs (weak strong). The interval following the strong tap was longer in both cases than the interval following the weak tap. The lengthening was greater, however, in the iambic structure. As Fraisse (1956) pointed out, in the iambic structure the effects of accentuation and pausing between subunits are summed up, whereas in the trochaic structure, these effects partially compensate for each other, the effect of accentuation per se being somewhat predominant. Because refractoriness and pausing do not seem to constitute valid explanations for the lengthening phenomenon, the question arises as to whether under certain conditions, the processes involved in the control of movement force may interact centrally with the functioning of the internal timekeeper that controls the cadence of the taps. The internal timekeeper is often modeled as a relatively encapsulated unit that may subserve both perceptual and motor-timing functions without being influenced by nontiming aspects of motor implementation such as the control of overall force (Ivry & Keele, 1989; Ivry, Keele, & Diener, 1988; Keele, Nicoletti, Ivry, & Pokorny, 1989; Wing, 1980; Wing & Kristofferson, 1973). Recent research has shown, however, that the driving frequency of the timing unit can be affected by the presentation of periodic click stimuli at a rate that differs very slightly from the driving frequency (Treisman et al., 1990; Treisman, Faulkner, & Naish, 1992). This finding suggests that

the timing unit may be not completely insulated from all sensory influences. Likewise, the timing unit may be open to some degree to influences from processes involved in the motor implementation of the intended movements. We have observed that during periodic tapping, the intertap interval is lengthened when it is bounded by taps with unequal intensities, i.e., when a strong tap is followed by a weak one. The step-like switching from high-level to low-level force involved in accent production may require inhibition to develop in order to prevent the high-level force from being carried over to the next tap. If the inhibition spread over the timing unit, the driving frequency of the unit can be transiently slowed down. Alternatively, the inhibitory signal may reset the accumulator that integrates the sum of the frequency pulses (Allan, 1992). In either case, the next beat of the timekeeper would be delayed and hence the interval following the accentuated tap would be lengthened. The notion that inhibitory processes (e.g., withholding a response) may cause the subjective beat to be somewhat delayed has been supported by the results of experiments on beat subdivision (Sternberg, Knoll, & Zukofsky, 1982). Although our account of the lengthening phenomenon is highly speculative, it suggests some possible lines on which future neurophysiological and psychophysiological investigations might be carried out. Acknowledgements Preparation of this article was partly supported by a CNES research grant (No 94 CNES/0274) to the second author. A short account of the experiment was presented at the Fifth Workshop on Rhythm Production and Perception held at Sheffield, 8-11 Sept, 1994. We acknowledge the helpful comments of Herbert Heuer, Steven Keele, and an anonymous reviewer on an earlier version of the MS.

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