Reduced timing variability during bimanual coupling: A role for sensory information

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Reduced timing variability during bimanual coupling:A role for sensory informationKnut Drewing a & Gisa Aschersleben aa Max Planck Institute for Psychological Research, Munich, GermanyPublished online: 22 Sep 2010.

To cite this article: Knut Drewing & Gisa Aschersleben (2003) Reduced timing variability during bimanual coupling: A rolefor sensory information, The Quarterly Journal of Experimental Psychology Section A: Human Experimental Psychology,56:2, 329-350

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Reduced timing variability during bimanual

coupling: A role for sensory information

Knut Drewing and Gisa Aschersleben

Max Planck Institute for Psychological Research, Munich, Germany

On a repetitive tapping task, the within-hand variability of intertap intervals is reduced when par-

ticipants tap with two hands as compared to one-hand tapping. Because this bimanual advantage

can be attributed to timer variance (Wing–Kristofferson model, 1973a, b), separate timers have

been proposed for each hand, whose outputs are then averaged (Helmuth & Ivry, 1996). An alter-

native notion is that action timing is based on its sensory reafferences (Aschersleben & Prinz,

1995; Prinz, 1990). The bimanual advantage is then due to increased sensory reafference. We

studied bimanual tapping with the continuation paradigm. Participants first synchronized their

taps with a metronome and then continued without the pacing signal. Experiment 1 replicated the

bimanual advantage. Experiment 2 examined the influence of additional sensory reafferences.

Results showed a reduction of timer variance for both uni- and bimanual tapping when auditory

feedback was added to each tap. Experiment 3 showed that the bimanual advantage decreased

when auditory feedback was removed from taps with the left hand. Results indicate that the

sensory reafferences of both hands are used and integrated into timing. This is consistent with the

assumption that the bimanual advantage is at least partly due to the increase in sensory

reafference. A reformulation of the Wing–Kristofferson model is proposed to explain these

results, in which the timer provides action goals in terms of sensory reafferences.

Many daily activities like driving a car or tying shoelaces require the coordination of different

limbs, thus involving the timing of at least two movements in parallel. One basic finding in

interlimb coordination is that concurrent movements are not executed independently: For

example, bimanual reaching movements with different amplitudes share their starting and

endpoints (Kelso, Southard, & Goodman, 1979). From polyrhythmic finger tapping we know

that performance can break down when participants have to decouple the timing of different

limbs (Deutsch, 1983; Jagacinski, Marshburn, Klapp, & Jones, 1988). Besides temporal

assimilations and interferences during desynchronized bimanual movements, performance

can also be improved when the movements of both hands are synchronized: Helmuth and Ivry

Requests for reprints should be sent to Knut Drewing, Max Planck Institute for Psychological Research,

Amalienstrasse 33, 80799 Munich, Germany. Email: [email protected]

We wish to thank two anonymous reviewers and Patrick Haggard for their helpful criticisms, suggestions, and

comments on an earlier draft, Jonathan Harrow for native-speaker and stylistic advice, and Frank Miedreich for parts

of the programming.

2003 The Experimental Psychology Society

http://www.tandf.co.uk/journals/pp/02724987.html DOI:10.1080/02724980244000396

THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2003, 56A (2), 329–350

Q0198—QJEP(A)12200/Jan 2, 03 (Thu)/ [22 spages – 0 Tables – 5 Figures – 5 Footnotes – 0 Appendices]. .

Centre single caption. Edited from DISK

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(1996) reported an advantage of bimanual simultaneous repetitive finger tapping over

unimanual tapping, the bimanual advantage.

Whereas the phenomenon of strong temporal coupling itself is unquestioned, there is some

controversy about the underlying mechanism: Predominantly, the idea of a coupling of

effector-specific timing structures (e.g., Haken, Kelso, & Bunz, 1985; Helmuth & Ivry, 1996;

Yamanishi, Kawato, & Suzuki, 1980) is contrasted with the proposal of one integrated timing

structure that controls both movements (Vorberg & Wing, 1996; cf., Schmidt, 1980; for an

overview, see Heuer, 1996; Vorberg & Wing, 1996). A less frequently considered but still

important issue is the role of sensory information in temporal coupling (but see Klapp et al.,

1985, on polyrhythmic tapping): Whereas most models implicitly or explicitly assume that

coupling constraints can be described in terms of mere motor processes, the question is crucial

whether, alternatively, processes that control for coordination and timing by taking into

account the sensory reafferences of the movements may be responsible for coupling phenomena.

The present article aims to examine the contribution of sensory information to the bimanual

advantage reported by Helmuth and Ivry (1996).

The bimanual advantage was observed in the standard repetitive tapping task (designed by

Stevens, 1886): On each trial participants first synchronize taps on a response key with a met-

ronome (synchronization phase) and then continue tapping at the target rate without the pac-

ing signal (continuation phase). Performance is assessed by the variability of intervals between

the tap onsets (intertap intervals) in the continuation phase.

For movement control in the continuation phase there is a well-supported and widely used

model by Wing and Kristofferson (1973a, b, see Figure 1). It is assumed that an internal timer

controls tapping at a central level by successively providing intervals of appropriate length (C

in Figure 1) and by triggering motor commands each time an interval has elapsed. Between the

trigger of the motor command and an observable tap, transfer processes require a certain time,

the so-called motor delay. Thus, an observable intertap interval (Ij in Figure 1) results from an

interval provided by a central timekeeper (Cj) that is modified by the following (Mj) and the

previous motor delay (Mj–1):

Ij = Cj + Mj – Mj–1

330 DREWING AND ASCHERSLEBEN

Figure 1. Wing and Kristofferson’s model (1973a, b). C = central timer interval, M = motor delay, I = observable

intertap interval. An observable intertap interval Ij results from a timer interval Cj modified by the following and

previous motor delays Mj and Mj-1.

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Variations in the motor delays and in the timekeeper intervals contribute to the variability

of observable intertap intervals. All processes involved are assumed to be mutually independ-

ent and to function in an open loop. With these assumptions, it is possible to estimate the vari-

ance of both the timekeeper processes and the motor delays (see, e.g., Vorberg & Wing, 1996,

for details). Empirical results, in general, corroborate the corresponding estimates: Timing

processes contribute to the former estimate (here: timer variance) and motor processes to the

latter (here: motor variance; cf., Ivry & Corcos, 1993; Ivry & Hazeltine, 1995).

Originally, the model had been developed for single-handed tapping. More interesting in

this context, it was extended to cover the multi-limb case as well (Vorberg & Hambuch, 1984;

Vorberg & Wing, 1996; Wing, 1982). The multi-limb extensions assume that the timer can

trigger motor commands for different limbs either simultaneously or successively in whatever

order the task requires. Here, temporal coordination between limbs results from a common

open-loop timer.

However, the findings obtained by Helmuth and Ivry (1996) are not consistent with this

view. Using the standard repetitive tapping task, they compared the temporal consistency of

movements made with one effector with that of identical movements performed synchro-

nously with two effectors. Participants tapped target intervals of 400 ms with the left, the

right, or both index fingers synchronously. Total intertap interval variability in the continua-

tion phase for each hand was lower in bimanual than in unimanual tapping. More important,

in an analysis with the Wing–Kristofferson model increased performance during bimanual

tapping was fully attributed to timer variance, whereas motor variance was not affected

(Franz, Ivry, & Helmuth, 1996; Helmuth & Ivry, 1996; Ivry & Hazeltine, 1999). These results

cannot be explained by the multi-limb extensions of the Wing–Kristofferson model, because

for the bimanual case these extensions would simply assume that one timer triggers two motor

commands simultaneously. As the timer remains the same, timer variance would be predicted

to remain the same as well.

Alternatively, Helmuth and Ivry (1996) postulated the existence of effector-specific timers

(i.e., one timer for each of the two hands) that run in parallel. The triggering of the motor com-

mands is limited by a response bottleneck allowing only one timing output in a certain time

period. As a result, the outputs of the two timers have to be integrated before motor commands

are triggered for both effectors. This integration is thought to be a temporal averaging, imple-

mented in a kind of neural threshold model (see Helmuth & Ivry, 1996). It is evident from

statistics that two timers whose outputs are averaged provide more regular intervals than one

timer and can therefore account for the bimanual advantage. Moreover, the two timers are

assumed to be independent of each other, and, hence, the magnitude of the bimanual advan-

tage can be predicted as half the average of the variance of the single timers. Taken together,

Helmuth and Ivry explained the bimanual advantage by constraints in the motor processes,

which result in a coupling of effector-specific timers.

In the present study, we examine an alternative explanation for this coupling phenomenon:

how the sensory reafferences of the movements contribute to the bimanual advantage. In

bimanual tapping not only efferences are enhanced but also tactile and kinaesthetic

reafferences. Possibly, during bimanual tapping timing benefits from the extra hand’s addi-

tional sensory reafferences. A starting point for a corresponding, more specific explanation

may be the usually observed slight asynchrony between taps of the left and right hand: If both

hands are indeed controlled by one common timer, both hands’ sensory reafferences will

TIMING VARIABILITY IN BIMANUAL COUPLING 331

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partly reflect the outcome of this timer, and performance might benefit from integrating the

asynchronous reafferences as compared to using sensory reafferences of one hand only. How-

ever, this is just one specification of our general idea.

Our alternative explanation focuses on the role of sensory information for the bimanual

advantage and draws on the assumptions that the temporal control of repetitive movements is

based on sensory information (Aschersleben & Prinz, 1995; Aschersleben, Stenneken, Cole, &

Prinz, 2002; Prinz, 1990), and that timing becomes more precise the more sensory information

becomes available (Aschersleben, Gehrke, & Prinz, 2001, in press; Mates, Radil, & Poeppel,

1992). The Wing–Kristofferson model is silent on this role, so if our explanation is tenable we

will have to reconsider the model and its empirical support. Indeed, there are studies that

point to some influence of sensory reafferences on continuation tapping: For example, the

availability of feedback tones for taps decreased intertap interval variability as compared to

tapping without tones (Barratt, Patton, Olsson, & Zuker, 1981; Kolers & Brewster, 1985). Also

a single 50 ms-delay of a feedback tone influenced the time point of the following tap (Wing,

1977b).

The present experiments were designed to systematically test the sensory explanation for

the bimanual advantage. In Experiment 1, we replicated the bimanual advantage. Experiment

2 addressed our assumption that the temporal control of repetitive movements is better—that

is, timer variance is smaller—the more sensory information is provided. Experiment 3 tested

whether the sensory reafferences of both hands are taken into account in the temporal control

of repetitive movements and whether the bimanual advantage can be explained by enhanced

sensory information. Experiments 2 and 3 used auditory feedback as a means to vary sensory

information without covariation of movement characteristics.

EXPERIMENT 1

Experiment 1 replicated Helmuth and Ivry’s (1996) first experiment. Participants synchro-

nized finger taps on a key with a metronome-like pacing signal and then continued tapping

without the pacing signal under three conditions: left hand only, right hand only, and both

hands synchronously.

Method

Participants

A total of 12 healthy right-handed participants, mostly students, were tested (mean age 28 years,

range 20–40 years; 9 females). None of them had any musical training or any experience with the tapping

task.

Apparatus

In a sound-absorbing, almost dark room participants sat at a table with their elbows and palms resting

on two wooden response boards, one for each hand, with metal sensory plates fixed to the boards. A PC

recorded responses (1-ms temporal resolution) and controlled auditory stimuli, which were presented

binaurally through headphones (audio-technica ATH-A5) via a D/A converter card (Data Translation

Card DT2821) and an amplifier (Sony TA-F170). A foot key was used to initiate trials. The screen in

front of the participants provided information about the current condition.


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Design and procedure

The design comprised three within-participant variables: coupling (unimanual vs. bimanual), hand

(right vs. left), and phase of experiment (first vs. second vs. third). Corresponding to coupling and hand

there were three experimental conditions: left-handed, right-handed, and synchronous bimanual tap-

ping. The experiment consisted of three phases, each containing blocks of nine trials of each experimen-

tal condition. For a single participant, the order of blocks remained constant in each phase, between

participants it was counterbalanced with a Latin square design. The experiment lasted approximately 1

hour including initial practice trials (one per experimental condition).

Following a 400-ms pause, each trial started with a sequence of 12 pacing tones (1000 Hz, 13-ms

duration, 74 dBA, interstimulus onset intervals 400 ms), with which participants synchronized tapping

with their index finger(s). Participants then continued tapping without the tones, attempting to maintain

the target intertap intervals as accurately as possible, for 45 taps. A tone signalled the end of a trial. White

noise (55 dBA) covered the acoustic effects of the taps.

In single-handed tapping, the inactive finger had to rest on the sensory plate, otherwise the trial was

interrupted. In all conditions trials containing at least one rather long or short intertap interval1(outliers)

were immediately repeated. Outliers were probably due to technical problems with the sensory plate

(switch or finger bouncing, no contact), but might also have indicated a lack of attention to the task.

Trials were treated in the same way when intertap intervals showed a significant linear trend.2

Data analysis

We analysed the intervals between tap onsets as the primary variable starting with the fifth tap in the

continuation phase. For each participant, and trial by trial, we computed means and total variances of the

intertap intervals and timer and motor variances (see Introduction) and averaged them over the last seven

trials of a block. The first two trials of each condition block were excluded from analysis as transfer effects

between conditions were irrelevant for us. Further analyses were based on the averaged individual

scores.

Results

Repetition of trials. Altogether, 21.2% of the trials had to be repeated, partly due to out-

liers (6.8%), but mainly to trends (14.4%). Most trends indicated an acceleration and were

associated with individual participants (four participants accounted for 67% of trends), but

not with conditions (bimanual trials accounted for 31% of trends, matching approximately a

random distribution).

Mean intertap intervals. On valid trials, participants were quite accurate in maintaining

the target intervals (mean 396 ms) with only negligibly small differences between conditions

(range over conditions 390–405 ms). In bimanual tapping the two hands’ taps had a mean


1Starting with the fifth interval in the continuation phase all intervals had to lie within the boundaries given by the

mean intertap interval of the actual trial ± four standard deviations (estimated as 7.5% of the mean intertap interval;

cf., data from Ivry & Hazeltine, 1995; Miedreich, 2000). If intertap intervals have a normal distribution, this criterion

excludes only 0.2% of trials by chance.2Linear trends were defined by a significant (p < .05) correlation between the length of an intertap interval and its

position [1 . . . 40] within the trial. Linear trends lead to an overestimation of local variability and to biases in the

estimates of the Wing–Kristofferson model (1973a, b), because the model assumes stationarity of the expected value

of interval length (Keele, Pokorny, Corcos, & Ivry, 1985).

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asynchrony of –2.3 ms (SD = 8.7 ms between participants, negative value indicating a minus-

cule lead of the left hand) and the asynchronies had a mean within-trial variance of 226 ms2

(SD = 82 ms2). Together these results point to a good coupling of the two hands.

Total variances. An analysis of variance (ANOVA)3

with the variables coupling, hand,

and phase of experiment revealed a main effect of phase, F(2, 22) = 22.7,p < .001, indicating a

decrease in total variance from the first to the last phase (645 ms2vs. 477 ms

2vs. 437 ms

2), and a

marginal interaction Coupling × Hand, F(1, 11)= 3.86,p = .08 (right hand unimanual, 527 ms

vs. bimanual 457 ms2; left hand, 551 ms

2vs. 545 ms

2). There were no other reliable effects (p >

.15).

Autocovariance of intertap intervals. The Wing–Kristofferson model makes clear predic-

tions about the autocovariance structure of the intertap intervals, which provide a test of the

model’s formal assumptions and, thus, also of the validity of its estimates of timer and motor

variance. The most basic prediction—that the autocorrelation between successive intervals

(autocorrelation Lag 1) lies in the range of –.5 to 0—was confirmed by our data for each of the

12 conditions (Coupling × Hand × Phase of experiment) by one-tailed t tests against 0 and –.5

(p < .01). Contrary to the model’s prediction that autocovariances with lags higher than 1 are

zero, autocovariance Lag 2 significantly differed from zero for each of the bimanual (and one

unimanual) conditions (two-tailed t tests; alpha level, .15; high alpha level reduced the proba-

bility of an incorrect failure to reject the prediction); all significant deviations were positive.

Lag 3 autocovariance did not differ from zero in any of our conditions.

Wing (1977a; cf., Wing, 1979) discussed such effects in terms of possible violations of

the model’s assumption of independency between component processes. The empirical

autocovariance function in bimanual conditions here matched rather well (and exclusively)

with predictions for a first-order moving-average process in the motor delays. That is, con-

trary to the basic model, each motor delay partly depends on the previous motor delay—more

precisely, on the magnitude of its random error (for details, see Wing, 1977a). A correspond-

ing dependency might invalidate the basic model’s estimates of timer and motor variance, but

it may be possible to derive more valid estimates for this situation (Wing, 1977a). We chose to

calculate timer and motor variance using both the basic Wing–Kristofferson model (basic

model) and a model that adds a first-order moving-average process in the motor delays (alter-

native model).4The alternative model includes the basic model as a special case and, thus, was

applicable to both bi- and unimanual conditions.

Timer and motor variance. The estimates of timer and motor variance from both models

were entered into ANOVAs with the variables coupling, hand, and phase of experiment. We

start with the results for the basic model. For phase of experiment, only the main effect in

motor variance was significant, F(2, 22) = 20.87, p < .001, indicating a systematic decrease as

the experiment progressed (first, 175 ms2; second, 106 ms

2; third, 79 ms

2), but not that in timer


3If necessary p values were corrected according to Huynh and Feldt (1976).

4We estimated timer and motor variance analytically based on the autocovariances Lag 0 to 2. If equations were

unsolvable, we minimized a least squares measure of goodness of fit.

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variance, F < 1. Interactions of phase of experiment with coupling or hand were not reliable.

Results for coupling and hand averaged across phases are shown in Figure 2. For the timer

variance, only the main effect of the variable coupling attained significance, F(1, 11) = 31.82,

p < .001, indicating a decrease in bimanual as compared to unimanual tapping (229 ms2vs. 345

ms2): that is, the bimanual advantage. For the motor variance, the main effect of Coupling,

F(1, 11) = 8.34, p < .02 (unimanual, 101 ms2; bimanual, 138 ms

2), and the interaction coupling

× Hand, F(1, 11) = 14.67, p <.01 (left unimanual, 101 ms2

vs. bimanual, 161 ms2; right, 101

ms2

vs. 116 ms2) were significant, indicating an increase in the motor variance of the left hand

in bimanual tapping.

A less ambiguous pattern of results emerged with the alternative model. For the timer vari-

ance, again, only coupling was significant, F(1, 11) = 18.56, p < .001, confirming the bimanual

advantage (244 ms2) over unimanual tapping (314 ms

2). For the motor variance, only phase of

experiment was significant, F(2, 22) = 8.98, p < .01, indicating a decrease of motor variance in

the course of the experiment (first, 131 ms2; second, 85 ms

2; third, 77 ms

2).

Discussion

We observed violated predictions of the Wing–Kristofferson model with respect to the

autocovariance functions. Hence, we estimated timer and motor variance using both the basic

model and an alternative one that is able to predict the observed violations. We discuss the

alternative model in detail in the motor variance section. Main results in timer variance were

not affected by estimation procedure.

Timer variance. Experiment 1 replicated the findings from Helmuth and Ivry (1996).

Timer variance was reduced for each hand when tapping together with the other hand in com-

parison with tapping alone. According to the Wing–Kristofferson model, our results support


Figure 2. Mean estimates for timer and motor variance under coupling (uni- vs. bimanual) and hand (left vs. right)

conditions (collapsed across phases of experiment).

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the notion of an improved control of timing when two hands rather than one hand execute

a repetitive tapping movement. The absolute magnitude of the bimanual advantage (basic

model, 116 ms2; alternative model, 71 ms

2) differed only slightly from that in Helmuth and

Ivry (1996, about 77 ms2), but average timer variances were about twice as large in our experi-

ment (basic model, 287 ms2; alternative model, 280 ms

2, compared with their 132 ms

2). This

difference may be due to sample bias, because we studied musically untrained participants

without experience in repetitive tapping. Note that this explanation implies the contribution

of trainable processes to timer variance. More important, these differences were accompanied

by differences in the relative magnitude of the bimanual advantage that violate the predictions

of Helmuth and Ivry (1996). Their model suggests that the bimanual advantage equals half the

average of the variances of the two single timers assumed (see Introduction), and, thus, timer

variance during bimanual tapping is half the average of left and right hand’s timer variances

during unimanual tapping. We computed the corresponding value for each participant and

compared it with the actual estimator of timer variance during bimanual tapping (averaged

across hands): Actual timer variance (basic model, 229 ms2; alternative model, 244 ms

2) was

clearly above the predicted value: basic model, 173 ms2; t(11) = 3.02, p < .02; alternative

model, 157 ms2; t(11) = 5.12, p < .001. Taken together, our results support the notion of

improved timing during bimanual tapping, but fail to confirm Helmuth and Ivry’s (1996)

quantitative predictions about its magnitude.

Motor variance. In both estimation procedures we found effects of practice that were

fully attributable to motor variance. This is in line with general assumptions about the esti-

mates of the Wing–Kristofferson model: It is reasonable that, in the short run, motor pro-

cesses can improve, but timer processes cannot. A benefit from practice is especially plausible

for our untrained participants. In other aspects, the findings from the basic model and the

alternative model diverge. For the basic model we found unexpected effects of coupling,

which vanished in the estimation with the alternative model. Hence, it is plausible to interpret

the coupling effects in terms of artifacts of the first-order moving-average process in motor

delays assumed by the alternative model. The first-order moving-average process means that

the length of each motor delay partly depends on the length of the previous one, or, more pre-

cisely, on its random error (Wing, 1977a). This part can be empirically estimated and reflects

the correlation between successive motor delays: The corresponding parameter was entered in

an additional ANOVA with the variables coupling and hand. Only the main effect of coupling

was (marginally) significant, F(1, 11) = 3.59, p = .09. Bonferroni-adjusted post-hoc t tests

(alpha level, .05) indicated that the parameter differed from zero in bimanual (mean: –.31), but

not in unimanual conditions (–.11). This finding as well as results in the autocovariance func-

tions suggest that the assumed first-order moving-average process is limited to bimanual con-

ditions. One interpretation of this process might relate to the participants’ self-reported

efforts to synchronize their hands: Synchronization efforts are limited to bimanual conditions,

they are likely to operate on motor delays, as the asynchrony between the hands can be

assumed to reflect differences in effector-specific motor processes (Vorberg & Hambuch,

1984), and they are correction processes. The last characteristic matches with the negative sign

of the aforementioned parameter, which indicates that each motor delay comprises a negative

proportion of the previous one.


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EXPERIMENT 2

Experiment 1 replicated the bimanual advantage reported by Helmuth and Ivry (1996).

Experiment 2 aimed at testing our sensory explanation for the bimanual advantage. The

underlying assumptions are that timing is based on sensory information and that temporal

control, as reflected in the timer variance, becomes more precise the more sensory information

is provided. Auditory feedback served to manipulate the amount of sensory information. Con-

ditions in which each tap triggered a feedback tone were compared with conditions without

tones. In the latter conditions, sensory information about the taps was limited to kinaesthetic

and tactile reafferences resulting from the finger movement and the finger tip’s contact with

the sensory plate. Feedback tones are supposed to increase sensory information, as they pro-

vide additional reafference and can be presented and perceived with high temporal precision

(Grondin, 1993). Participants tapped with the right or the left hand, or with both hands

synchronously.

Our sensory explanation predicts timer variance to be highest when participants receive

only tactile–kinaesthetic reafference from one hand, a decrease with additional tactile–kinaes-

thetic reafferences from the other hand (bimanual advantage), but also with additional audi-

tory feedback from the same hand (i.e., within unimanual conditions). Finally, timer variance

should be lowest with tactile–kinaesthetic and auditory reafferences from both hands.

Helmuth and Ivry’s (1996) model also predicts an advantage in bimanual tapping, but no

influence of auditory feedback on timer variance, as it (and the Wing–Kristofferson model)

does not include any role for sensory information in tapping.

Method

Participants

From 26 participants, 2 were dropped because the autocovariance structure of their data showed clear

signs of tapping a rhythm, which interfered with the evaluation of variances. The final 24 participants

were aged between 18 and 37 years (mean 25 years; 14 females). Most of them were students, and all

reported to be right-handed.

Apparatus

The apparatus was the same as that in Experiment 1. In addition, in some conditions feedback tones

(2000 Hz, 15-ms duration, 76 dBA) were used that were clearly discriminable from the pacing tones

(1000 Hz, 13-ms duration, 76 dBA).


The experiment comprised the three within-participant variables hand (left vs. right), coupling

(unimanual vs. bimanual), and feedback (tactile–kinaesthetic vs. tactile-kinaesthetic plus auditory). In

the last condition, tones started at the time-point at which a tap onset was registered, and the tones were

presented monaurally to the ear ipsilateral to the tap. For each of the resulting six experimental condi-

tions there was a block of 12 trials; the order of the blocks was balanced between participants with a Latin

square design.

Motivated by the small intertap interval variability in Experiment 1, we narrowed the boundaries for

outliers (cf., Footnote 1: boundaries based on an estimator for the standard deviation, which was here


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reduced from 7.5% to 5% of the mean intertap interval). The experiment lasted about 1 hour including

initial practice trials (one per experimental condition). In all other aspects the procedure was identical to

that of Experiment 1.

Results

Data were analysed in the same way as that in Experiment 1. A total of 21.5% of the trials were

repetition trials (trends 8.7%, outliers 12.8%5). In valid trials participants maintained the

target interval rather accurately (mean intertap interval 396 ms; range over conditions 393–

400 ms).

Individual total variances were entered into an ANOVA with the variables feedback,

coupling, and hand. The main effect of hand was significant, F(1, 23) = 10.50, p < .01, indicat-

ing that tapping with the right hand (382 ms2) was more consistent than that with the left hand

(455 ms2). There were no other reliable effects (p > .20).

As predicted by the Wing–Kristofferson model for all eight conditions (Feedback × Cou-

pling × Hand), Lag 1 autocorrelations were significantly negative and significantly higher

than -.5 (one-tailed t tests, p < .01). Similar to Experiment 1, there were significantly non-zero

autocovariances Lag 2 (two-tailed t tests, alpha level, .15), indicating both positive (right hand:

each of the bimanual conditions; left hand: unimanual tactile–kinaesthetic) and negative devi-

ations (each of the other unimanual conditions). For Lag 3 we observed positive deviations in

two conditions; these, however, occurred unsystematically and were small in size (< 5 ms2),

and the resulting autocovariance functions did not match the prediction of any of the general-

izations of the Wing–Kristofferson model (Wing, 1977a). Autocovariance functions, once

again, were predicted well by assuming a first-order moving-average process in the motor

delays. As in Experiment 1 we therefore calculated timer and motor variance with both the

basic and the corresponding alternative model.

Estimates of timer and motor variances were entered into ANOVAs with the variables

feedback, coupling, and hand. First, the findings from the basic model (Figure 3): There was a

main effect of hand on motor variance, F(1, 23) = 8.80, p < .01 (left, 124 ms2; right, 89 ms

2), but

not on timer variance, F < 1, indicating that the more consistent tapping of the right hand,

observed in total variances, was fully attributable to motor variance. There was no reliable

interaction with hand. A main effect of coupling on timer variance replicated the bimanual

advantage, F(1, 23) = 79.00, p < .001 (unimanual, 269 ms2; bimanual, 152 ms

2). In addition,

auditory feedback reduced timer variance, F(1, 23) = 13.81, p < .001 (tactile–kinaesthetic plus

auditory, 178 ms2; tactile–kinaesthetic, 244 ms

2). There was no interaction of Coupling ×

Feedback, F < 1, in timer variance. Main effects of coupling, F(1, 23) = 21.04, p < .001, and

feedback, F(1, 23) = 5.78, p < .05, in motor variance indicated an increase by the additional

hand (bimanual, 130 ms2; unimanual, 83 ms

2) as well as by the additional tones (tactile–kinaes-

thetic plus auditory, 119 ms2; tactile–kinaesthetic, 94 ms

2) without any reliable interaction

between the two variables, F(1, 23) = 1.54, p > .20.


5An analysis of intertap interval distributions by means of histograms suggested that the high number of

repetitions due to outliers did not indicate “real” outliers, but rather the setting of too narrow boundaries. However,

an alternative analysis of the data including outlier trials (comprising the first 12 otherwise valid trials per condition)

produced no changes in the basic results and therefore was not considered further.

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Second, the findings of the alternative model revealed almost the same pattern. There was a

decrease in timer variance with bimanual tapping, F(1, 23) = 40.83, p < .001 (unimanual, 219

ms2; bimanual, 152 ms

2), and with auditory feedback, F(1, 23) = 28.39, p <.001 (tactile–kinaes-

thetic plus auditory, 145 ms2; tactile–kinaesthetic, 226 ms

2). Hand had an effect on motor vari-

ance, F(1, 23) = 6.41, p < .02 (left, 125 ms2; right, 95 ms

2), but not on timer variance, F < 1.

Further, motor variance increased with auditory feedback, F(1, 23) = 12.90, p < .01 (tactile–

kinaesthetic plus auditory, 131 ms2; tactile–kinaesthetic, 89 ms

2). However, there was no reli-

able main effect of coupling on motor variance, F < 1, but an interaction of Coupling × Hand,

F(1, 23) = 6.76, p < .02, indicating a decrease of motor variance during bimanual tapping for

the right hand (103 ms2

vs. 86 ms2) and an increase for the left hand (113 ms

2vs. 136 ms

2). In

addition, in timer variance a Coupling × Hand interaction, F(1, 23) = 4.48, p <.05, indicated

an increase for the left compared to the right hand during unimanual tapping, but the effect

was rather small (unimanual: left, 229 ms2vs. right, 209 ms

2; bimanual, 149 ms

2vs. 156 ms

2).

Discussion

Timer variance. Auditory feedback revealed a clear effect on timer variance, which sup-

ports our basic assumption that the timing of repetitive movements is influenced by sensory

information. Moreover, timer variances support our hypothesis that temporal control

becomes more precise the more sensory information is provided: Timer variance is highest for

unimanual tapping with tactile–kinaesthetic reafferences only and lower when more sensory

information is added by tactile–kinaesthetic reafferences from the other hand or through addi-

tional auditory feedback. Also, as expected, timer variance is lowest in the condition contain-

ing the highest degree of sensory information—namely, auditory and tactile–kinaesthetic

feedback from both hands. In other words, timer variance effects of additional sensory infor-

mation provided by feedback tones take the same direction as the effects of the tapping of an


Figure 3. Mean estimates for timer and motor variance under coupling (Unim. = unimanual vs. Bim. = bimanual),

hand (left vs. right), and feedback conditions. Circles refer to conditions with feedback tones (Tk+a); squares, to

conditions without feedback tones (Tk).

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additional hand. In an integrative manner, both effects can be accounted for by a timer based

on and benefiting from sensory information.

However, Helmuth and Ivry’s (1996) model cannot explain the effects of the feedback

tones without making additional assumptions. Like the underlying Wing–Kristofferson

model their hypothesis is silent about the role of sensory information. Moreover, as in Experi-

ment 1, our data contradict quantitative predictions of their model: We compared the empiri-

cal timer variance during bimanual tapping with the value predicted from unimanual

performance: The prediction was smaller, both in conditions without feedback tones, basic

model: difference, 34 ms2, t(23) = 2.76, p < .02; alternative model: difference, 54 ms

2, t(23) =

4.81, p < .001, and in conditions with feedback tones, at least alternative model: difference

31 ms2, t(23) = 2.61, p < .02.

Still, although our assumptions can explain the results in an integrative manner, the con-

clusion that the bimanual advantage is due to augmented sensory information does not neces-

sarily follow from the data: A lack of interaction between feedback and coupling concerning

timer variances fails to demonstrate that the influence of additional feedback tones from two

effectors differs from that of feedback from one effector and, thus, to demonstrate that timing

accounts for sensory reafferences from both hands, as assumed in our explanation. The lack of

interaction is not at odds with the latter idea, but it is also consistent with independent mecha-

nisms that explain the bimanual advantage on one hand and the main effect of auditory feed-

back on the other. Most important, the main effect of auditory feedback could also arise from

nonspecific influence of the mere presence of feedback tones (maybe via salience of the task) or

by a hand-specific influence of feedback only on the “tone-producing” hand’s timer variance.

Experiment 3 examines this issue further.

Motor variance. The basic model revealed unexpected increases of motor variance during

bimanual tapping and during tapping with feedback tones. With the alternative model the

feedback effect was confirmed, but the coupling effect almost disappeared—that is, there was

only a negligibly small Coupling × Hand interaction (right, 17 ms2

decrease during bimanual

tapping; left, 23 ms2increase). Hence, coupling effects in the basic model are likely to be due to

a first-order moving-average process.

As in Experiment 1, the alternative model’s additional parameter was entered into an

ANOVA with the variables coupling and feedback. Both main effects were significant, cou-

pling, F(1, 23) = 17.78, p < .001; feedback, F(1, 23) = 13.15, p < .01, but not the interaction. In

Bonferroni-adjusted t tests (alpha level .05) the parameter differed significantly (bimanual,

tactile–kinaesthetic: mean, –.26) and marginally significantly (unimanual, tactile–kinaes-

thetic plus auditory: mean, .18; alpha, .10) from zero in just two of the four conditions (not in

unimanual, tactile–kinaesthetic: –.13; bimanual, tactile–kinaesthetic plus auditory: –.10) sug-

gesting that the first-order moving-average process was limited to the first two conditions.

However, the lack of interaction in ANOVA rather points to another interpretation in terms of

two independent processes: possibly, one triggered by bimanual tapping and resulting in neg-

ative correlations between motor delays, and a further one due to feedback tones and resulting

in positive correlations. In unimanual, tactile–kinaesthetic, then, none of the processes oper-

ates and in bimanual, tactile–kinaesthetic plus auditory, effects of both processes mask each

other. The former process again can be reasonably identified with synchronization efforts.


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Concerning the latter, positive correlations have been reported elsewhere in connection with

auditory feedback (Wing, 1977a) and could reflect slow, long-term changes in the motor

delays which might be tentatively interpreted in terms of disturbed adjustment processes.

This is consistent with the motor variance increase caused by feedback tones, which also indi-

cates interferences of tones with motor processes.

Finally, we found a less regular tapping of the left than of the right hand, which both basic

model and alternative model clearly attribute to motor variance. Consistent with other studies

that included right- and left-handers (Peters & Durding, 1979; Sergent, Hellige, & Cherry,

1993) this is likely to be related to our participants’ right-handedness. Note that right-handed-

ness seems to be associated with hemispheric asymmetry of motor cortex activation (Ziemann

& Hallett, 2001), which in terms of the Wing–Kristofferson model points to higher-order pro-

cesses reflected in the motor variance than originally assumed. The finding also fits with the

assumption of the model’s multi-limb extensions that motor variance reflects effector-specific

processes.

EXPERIMENT 3

In Experiment 2, we were able to demonstrate a systematic relation between amount of sen-

sory information and timer variance by manipulating auditory feedback, providing indirect

evidence for our sensory explanation of the bimanual advantage. Experiment 3 directly tested

our assumption that the extra hand’s sensory reafferences during bimanual tapping are

responsible for the bimanual advantage by contributing to both hands’ timing control .

In Experiment 3 we varied sensory reafferences for one hand only, again using auditory

feedback: Here, the right hand acted as a “test hand”, and the left hand as the “extra hand”.

For the right hand’s taps we always presented auditory feedback; sensory reafferences from

the left hand were varied in three stages: tactile–kinaesthetic plus auditory, tactile–kinaes-

thetic only, or no sensory reafferences. That is, left hand’s taps either triggered tones or not,

and there was a third unimanual control condition where the left hand rested. Our sensory

explanation of the bimanual advantage predicts, first, a replication of the bimanual advantage

with feedback tones for both hands, and second that the bimanual advantage is smaller when

the extra hand provides no feedback tones—that is, less additional sensory reafference. Thus,

we expect timer variance (for both hands) to systematically decrease with the increase of sen-

sory reafferences from the extra hand.

Helmuth and Ivry’s (1996) explanation predicts no difference between the two bimanual

conditions, in which two movements are timed, and, thus, two timers should be involved. Also

the alternative explanations for the effects of auditory feedback observed in Experiment 2 do

not predict differences between the two bimanual conditions—at least not for the test hand: If

feedback tones influence timer variance in a nonspecific way (e.g., by mere presence) no dif-

ference can be expected, as in both bimanual conditions auditory feedback is provided. And if

the influence of feedback tones is hand specific, the variation of auditory feedback for the extra

hand will have no effect on the test hand. Thus, only our sensory explanation for the bimanual

advantage predicts an influence of sensory reafferences for the extra hand on the timer vari-

ance for the test hand.


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Methods

Participants

A total of 12 right-handed students (mean age 25 years; range 20-35 years; 9 females) took part.

Apparatus

The apparatus was the same as that in Experiments 1 and 2.


The present experiment varied feedback (for left-hand taps) and phase of experiment. Three experi-

mental conditions were created for the variable feedback: unimanual right-handed tapping with auditory

feedback, bimanual tapping with auditory feedback only for the right-hand taps, and bimanual tapping

with auditory feedback for right- and left-hand taps. The experiment was divided into three phases, each

of which entailed eight blocked trials of each of the three experimental conditions. The stimulus onset

interval between the pacing tones (1000 Hz, 13-ms duration, 74 dBA) was set at 600 ms. Feedback tones

(2000 Hz, 15-ms duration, 76 dBA) were always given at the ear ipsilateral to the tap. The experiment

lasted approximately 1 hour. In all other aspects design and procedure were the same as those in Experi-

ment 1.

Results

Data analysis was identical to that in Experiment 1. A total of 22.0% of the trials were repeti-

tion trials (14.6% trends; 7.4% outliers). Mean intertap intervals (right hand) in valid trials

were slightly too short (mean, 585 ms), but comparable between conditions (range, 584–593

ms).

An ANOVA of the total intertap interval variances with the variables feedback and phase of

experiment revealed a main effect of phase, F(2, 22) = 12.13, p < .001, indicating increasing

regularity from the first to the third phase (567 ms2vs. 491 ms

2vs. 456 ms

2). Other effects were

not reliable (p >.2).

Analyses on the autocovariance structure of intertap intervals were performed for both

hands. In all conditions (right hand: Feedback × Phase of experiment; left hand: [bimanual

with auditory feedback for right hand only vs. bimanual with auditory feedback for both

hands] × Phase of experiment), Lag 1 autocorrelations were significantly smaller than zero

and significantly above –.5 (one-tailed t tests, p < .01). In one condition autocovariance Lag 2

was found to be non-zero (two-tailed t tests, p < .15). Because this was only one of 15 compari-

sons, it seems acceptable to ignore this deviation. Thus, the predictions of the Wing–

Kristofferson model concerning autocovariances were fulfilled.

Motor and timer variances of the right hand were entered into ANOVAs with the variables

feedback and phase of experiment. Phase of experiment had a main effect on motor variance,

F(2, 22) = 7.27, p < .02, indicating a decrease as the experiment progressed (first, 137 ms2; sec-

ond, 96 ms2; third, 73 ms

2), but not on timer variance. No reliable interactions of phase of

experiment with feedback were found for timer or motor variance. The variable feedback

showed a clear influence on the timer variance, F(2, 22) = 9.46, p < .01. One-tailed t tests

confirmed the expected differences: Timer variance in unimanual right-handed tapping with

auditory feedback (354 ms2) was significantly higher than in the bimanual condition with


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auditory feedback for the right hand only (305 ms2), t(11) = 2.18, p < .05, which again was

higher than that in the bimanual condition with auditory feedback for both hands (266 ms2),

t(11) = 2.00, p < .05 (Figure 4). An additional ANOVA of the timer variances with the vari-

ables hand (left vs. right) and feedback (the two bimanual conditions only) confirmed the

influence of feedback for both hands, F(1, 11) = 6.87, p < .05 (feedback for right hand only 304

ms2; feedback for both hands 254 ms

2). Between hands timer variance did not differ reliably,

main effect: F < 1, interaction: F(1, 11) = 1.70, p > .20.

Feedback also had a main effect on the right hand’s motor variances, F(2, 22) = 6.90, p <

.01. Two-tailed t tests revealed a significant difference between the two bimanual conditions,

feedback for right hand only, 98 ms2vs. feedback for both hands, 125 ms

2; t(11) = 3.15, p < .01,

but not between the unimanual (82 ms2) and the bimanual condition with feedback for the

right hand only, t(11) = 1.34, p > .20. In an additional ANOVA with the variables hand

and feedback only the interaction Hand × Feedback was significant, F(1, 11) = 12.95,p < .01.

A t test comparing the conditions of feedback for data of the left hand revealed no difference,

t < 1 (feedback for right hand only, 147 ms2; feedback for both hands, 148 ms

2), demonstrating

only the right hand’s motor variance to increase by the left hand’s tones.

Discussion

Timer variance. Results clearly supported our alternative explanation for the bimanual

advantage. The timer variance for both hands decreased systematically with increasing sen-

sory reafferences of the extra (left) hand. Most important, the bimanual advantage decreased

for both hands when auditory feedback for the taps with the extra hand was omitted. This

finding can neither be explained by a nonspecific influence of auditory feedback, because feed-

back tones for the test (right) hand’s taps are presented in all conditions, nor reflect a hand-

specific influence of auditory feedback. Instead, sensory reafferences of one hand affect per-

formance of both hands, demonstrating that sensory reafferences of both hands are integrated


Figure 4. Mean estimates for timer and motor variance under feedback conditions for both hands (collapsed across

phases of experiment). Participants tapped unimanually (right hand) with feedback tones (Unim.-R), bimanually

with feedback for the right hand only (Bim.-R), and bimanually with feedback for both hands (Bim.-RL).

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in the temporal control of repetitive actions. Moreover, reducing one hand’s reafferences leads

to an impairment in timing control. These results demonstrate that the bimanual advantage (at

least in part and during tapping with auditory feedback) is due to enhanced sensory

reafferences.

Motor variance. In the present experiment varying feedback for the left hand influenced

the motor variance of the right hand, only, in contrast to the left hand: Adding auditory feed-

back for left-hand taps increased right-hand motor variance. However, the motor variance

of the left hand seems to be on a high level in both bimanual conditions (about 140 ms2).

Primarily, these feedback effects point to interferences of the tones with motor processes.

Moreover, the fact that feedback tones for left-hand taps affect only right-hand motor variance

points to interferences that are more specific than mere arousal. We assume that motor vari-

ance of one hand increases when additional feedback tones are provided for the other hand’s

taps, an assumption that is also consistent with the high-level motor variance of the left hand,

because in all conditions right hand taps trigger feedback tones. Also, in Experiment 2

additional tones for the extra hand resulted in an increase of motor variance as compared to

unimanual tapping with feedback tones. However, results in motor variance remain puzzling,

and further research is required that includes variations of the right hand’s sensory

reafferences only. In contrast, the practice effects in this experiment were rather clear. They

can be fully attributed to motor variance.

GENERAL DISCUSSION

Timer variance

The present experiments examined the role of sensory information for the phenomenon of

reduced timer variance during bimanual as compared to unimanual tapping. Helmuth and

Ivry (1996) explain this phenomenon by effector-specific timers, the outputs of which are

averaged in bimanual tapping. Alternatively, we suggest that the bimanual advantage is due to

enhanced sensory information given by the reafferences of the extra hand. Our view implies

that timing is better as more sensory information becomes available.

Experiment 1 replicated Helmuth and Ivry’s (1996) finding of a bimanual advantage in

timer variance. Experiment 2 showed that increased sensory information by way of additional

auditory feedback reduced timer variance just as did the extra hand in bimanual tapping.

Moreover, timer variance was smallest in bimanual tapping with auditory feedback. Thus, as

predicted, timer variance systematically depended on the amount of sensory information.

Experiment 3 varied sensory reafferences from the taps of the extra (left) hand only, whereas

the other (right) hand taps consistently provided tactile–kinaesthetic plus auditory feedback.

Again, across all conditions, timer variance for both hands decreased with increasing sensory

information from the extra hand. Importantly, in bimanual tapping timer variance was higher

when the extra hand tapped without than when it tapped with feedback tones. The latter result

demonstrates that the bimanual advantage depends on the extra hand’s sensory reafferences

(at least partly) and tends to indicate a systematic integration of the sensory reafferences of

both hands in timing.


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Taken together, our assumption that the bimanual advantage is due to the increase of sen-

sory reafferences during bimanual tapping receives strong support from the present experi-

ments. In contrast, Helmuth and Ivry’s (1996) model cannot account for the various

influences of sensory information on the timer variance without making additional assump-

tions. Moreover, in part of the present experiments the bimanual advantage was smaller than

that predicted by their model. In addition, their assumption of multiple, independent

effector-specific timers—which is not necessary for our sensory explanation—has been chal-

lenged by other studies concluding that a single temporal representation underlies the control

of both hands (e.g., Semjen & Summers, 2002; Wing, Church, & Gentner, 1989).

Motor variance and processes in motor delays

Alongside the predicted effects on timer variance, there were also some effects on motor vari-

ance. Decreases of motor variance with practice (Experiments 1 and 3) and a smaller motor

variance for the dominant than for the non-dominant hand (Experiment 2) indicate that motor

variance also reflects processes of a higher order than mere transfer. This is in line with notions

of a contribution from motor implementation processes to this estimate (Helmuth & Ivry,

1996; Ivry & Corcos, 1993) and of sources of motor variance in the medial cerebellum (Ivry,

Keele, & Diener, 1988). Further, we found somewhat puzzling effects of auditory feedback

(Experiments 2 and 3) which we discuss later. Most interestingly, motor variance increased

during bimanual as compared to unimanual tapping, but this effect vanished when we re-esti-

mated motor variance under the assumption of a first-order moving-average process in motor

delays (Wing, 1977a). Details matched rather well with an interpretation in terms of the par-

ticipants’ self-reported efforts to synchronize their hands: The process seemed to be limited to

bimanual tapping, operated on motor delays to which between-hand asynchronies are likely to

be due (Vorberg & Hambuch, 1984), and—as can be expected for corrections—indicated that

each motor delay comprises a negative proportion of the previous one. Also the fact that the

process was found only in Experiments 1 and 2 fits well: It is reasonable that especially strong

repetition criteria (Experiment 2) or participants’ missing familiarity with tapping and musi-

cal performance (Experiment 1) particularly draw attention to between-hand asynchronies.

The Wing–Kristofferson model reconsidered

Our findings, particularly those on the systematical relation between sensory information and

timer variance call for further considerations about the Wing–Kristofferson model. Unlike

our hypothesis the model does not include any role for sensory information.

A proximate guess may be that there are immediate correction processes on the basis of sen-

sory reafferences, which affect timer variances. Immediate correction is accompanied by

dependencies between the Wing–Kristofferson model’s component processes and, thus, is

not consistent with the model’s open-loop architecture (Miedreich, 2000), with its predictions

about autocovariances, and with its estimation procedures. However, generally the model’s

predictions are fulfilled as to autocovariance functions and selective variation of either motor

(with effector: Experiment 2; Helmuth & Ivry, 1996; Miedreich, 2000; type of movement:

Wing, 1977a; practice: Experiments 2 and 3) or timer variance (with intertap interval length:

Ivry & Hazeltine, 1995; Miedreich, 2000; Wing & Kristofferson, 1973b). Nonetheless, in our

Experiments 1 and 2 we observed violations of the model’s predictions for autocovariance


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functions. But those could be rather well explained by dependencies within motor processes

(see earlier). Most important, both a re-estimation of the model’s scores under the assumption

of corresponding dependencies and results of Experiment 3 confirmed the systematic relation

between sensory information and timer variance. Thus, immediate correction might have

occurred, but it seemed to affect exclusively motor processes and to be independent from

effects of sensory information on timing and timer variance. Related to this issue is the lack of

effect of core manipulations on total variance, which we, thus, explain by partly opposite but

independent effects on timer and motor processes (e.g., effect of bimanual reafference on

timer and of synchronization efforts on motor processes). This view is supported by recently

reported effects of sensory information on timer and total, but not on motor variance

(Drewing, Hennings, & Aschersleben, 2002).

Taken together, we see no indication that the influence of sensory reafferences on timer

variance should be explained by correction processes or otherwise beyond the general frame-

work of the Wing–Kristofferson model. Alternatively, based on general principles formulated

for action control (cf., Hommel, Müsseler, Aschersleben, & Prinz, in press; Prinz, 1990) we

suggest that the role of sensory reafferences lies in the planning of intervals—that is, we pro-

pose that the timer plans intervals in terms of expected sensory reafferences. This option is

unreasonable within the exact formulation of the Wing–Kristofferson model, where actual

sensory reafferences and end points of timer intervals do not coincide in time (cf., Figure 1).

However, it matches with the notion that the timer controls the endpoints or goals of the tap-

ping movements (i.e., the tap onsets) rather than their starting points (Billon & Semjen, 1995;

Billon, Semjen, & Stelmach, 1996; Miedreich, 2000; Shaffer, 1982). The finding that the

intervals between the endpoints are less variable than those between the starting points sup-

ports this view (Billon & Semjen, 1995; Billon et al., 1996). Moreover, expected sensory

reafferences are a reasonable specification of the so far under-specified goals of the tapping

movements.

Action goal timing: A reformulation of theWing–Kristofferson model

The previous notions of the timer system as providing time points for—behaviourally mean-

ingful—movement goals (“action goals”) and of the planning and communication of these

goals in terms of sensory reafferences imply a reformulation of the Wing–Kristofferson model

(Figure 5).

In the reformulation, timer intervals are not abstract, but rather intervals between antici-

pated sensory reafferences. The timer communicates these to the motor system, which then

controls the movements, so that actual sensory reafferences coincide in time with the antici-

pated ones. Imagine playing a tune on a piano: The timer plans intervals between notes to be

listened to and tells the motor system when the notes are expected. The motor system controls

the finger and arm movements so that the actual notes coincide with the planned notes.

Formally, the reformulation is identical to the original model. An intertap interval results

from the timer interval Cj modified by the motor terms Mj–1 and Mj related to the first and

second taps, respectively (cf., Miedreich, 2000). Timer intervals depend neither on each other


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nor on motor processes as they rely on anticipation (not on actual sensory reafferences). Motor

terms are supposed to usually reflect random errors, which also do not depend on each other.

However, motor terms do no longer reflect delays, but the deviations of the end points of

the trajectories from the action goals—that is, motor errors (cf., Miedreich, 2000). Further, to

terminate a movement at a specific point in time, the motor system has to adapt it flexibly to

the current motor state and predictable variations in the trajectory (Billon et al., 1996;

Miedreich, 2000; Shaffer, 1982). Anticipatory compensation of increased movement speed by

a delayed onset has been observed for accentuated taps and also within non-accentuated taps

(Billon & Semjen, 1995; Billon et al., 1996). Motor errors may emerge at all stages of the motor

process, which is consistent with the earlier notion that high-order processes contribute to

motor variance. They can be expected to be random if anticipatory compensation is well

trained—as for tactile–kinaesthetic action goals. Unfamiliarity of auditory action goals may

explain the presence of effects of feedback tones: Increased motor variance and positive corre-

lation of motor terms may be due to limited persistence of systematic anticipation errors.

Furthermore, a timer that plans and communicates intervals in terms of anticipated sen-

sory reafferences can be expected to do this such that the anticipated intervals will be per-

ceived as being correct, for example, by means of a simulation process. Similar notions have

been made for synchronization tapping (Stenneken, Aschersleben, Cole, & Prinz, 2002) and

with the so-called forward models (Blakemore, Wolpert, & Frith, 1999). In line with this, the

cerebellum seems to play a role in the forward models and to be a source of timer variance (Ivry

et al., 1988). Additionally, timer intervals seem to be subject to the same constraints as the per-

ception of intervals between sensory stimuli (Ivry & Hazeltine, 1995). In the present study, the

reduction of timer variance by feedback tones matches with the observed excellent perceptual

discrimination of auditorily marked intervals (Grondin, 1993). On the other hand, it can be

expected that the number of anticipated sensory reafferences corresponds to the number of

simulation processes, and that different simulation processes compensate for their respective


Figure 5. Raw sketch of a reformulation of the Wing–Kristofferson model. The timer system provides the time

points for the goals of the action instead of those for triggering motor commands. The motor system plans trajectories

in accordance with the prescribed action goals. Action goals are communicated in terms of sensory reafferences. An

intertap interval Ij results from a timer interval Cj and the previous and the following errors of the motor system, Mj-1

and Mj.

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errors. Hence, we primarily explain the bimanual advantage and other systematic influences

of additional feedback observed here by the number of anticipated sensory reafferences—that

is, by the number of averaged simulation processes. The idea of averaged control signals

resembles that of Helmuth and Ivry (1996), but our emphasis on anticipated sensory

reafferences as action goals further explains the influence of sensory information on timer

variance. Taken together, our conclusion from the present experiments is that sensory

reafferences contribute to the coupling phenomenon “bimanual advantage” and that they do

this in terms of a commonly determined timing goal.

REFERENCES

Aschersleben, G., Gehrke, J., & Prinz, W. (2001). Tapping with peripheral nerve block: A role for tactile feedback in

the timing of movements. Experimental Brain Research, 136, 331–339.

Aschersleben, G., Gehrke, J., & Prinz, W. (in press). A psychophysical approach to action timing. In C. Kaernbach, E.

Schröger, & H. Müller (Eds.), Psychophysics beyond sensation: Laws and invariants in human cognition. Hillsdale,

NJ: Lawrence Erlbaum Associates, Inc.

Aschersleben, G., & Prinz, W. (1995). Synchronizing actions with events: The role of sensory information. Perception

& Psychophysics, 57, 305–317.

Aschersleben, G., Stenneken, P., Cole, J., & Prinz, W. (2002). Timing mechanisms in sensorimotor synchronization:

Intersensory integration of action effects. In W. Prinz & B. Hommel (Eds.), Attention and performance XIX.

Common mechanisms in perception and action (pp. 227–244). Oxford: Oxford University Press.

Barratt, E.S., Patton, J., Olsson, N.G., & Zuker, G. (1981). Impulsivity and paced tapping. Journal of Motor Behavior,

13(4), 286–300.

Billon, M., & Semjen, A. (1995). The timing effects of accent production in synchronization and continuation tasks

performed by musicians and nonmusicians. Psychological Research, 58(3), 206–217.

Billon, M., Semjen, A., & Stelmach, G.E. (1996). The timing effects of accent production in periodic finger-tapping

sequences. Journal of Motor Behavior, 28(3), 198–210.

Blakemore, S.-J., Wolpert, M., & Frith, C.D. (1999). The cerebellum contributes to somatosensory cortical activity

during self-produced tactile stimulation. NeuroImage, 10, 448–459.

Deutsch, D. (1983). The generation of two isochronous sequences in parallel. Perception & Psychophysics, 34(4), 331–

337.

Drewing, K., Hennings, M., & Aschersleben, G. (2002). The contribution of tactile reafference to temporal regularity

during bimanual finger tapping. Psychological Research, 66(1), 60–70.

Franz, E.A., Ivry, R.B., & Helmuth, L.L. (1996). Reduced timing variability in patients with unilateral cerebellar

lesions during bimanual movements. Journal of Cognitive Neuroscience, 8(2), 107–118.

Grondin, S. (1993). Duration discrimination of empty and filled intervals marked by auditory and visual signals.

Perception & Psychophysics, 54(3), 383–394.

Haken, H., Kelso, J.A., & Bunz, H. (1985). A theoretical model of phase transitions in human hand movements.

Biological Cybernetics, 51, 347–356.

Helmuth, L.L., & Ivry, R.B. (1996). When two hands are better than one: Reduced timing variability during bimanual

movements. Journal of Experimental Psychology: Human Perception and Performance, 22(2), 278–293.

Heuer, H. (1996). Coordination. In H. Heuer & S.W. Keele (Eds.), Handbook of perception and action, Vol. 2: Motor

skills (pp. 121–180). London: Academic Press.

Hommel, B., Müsseler, J., Aschersleben, G., & Prinz, W. (in press). The theory of event coding (TEC). A framework

for perception and action planning. Behavioural and Brain Sciences.

Huynh, H., & Feldt, L.S. (1976). Estimation of the box correction for degrees of freedom from sample data in

randomized block and splitplot designs. Journal of Education Statistics, 1, 69–82.


Dow

nloa

ded

by [

Uni

vers

ity O

f Pi

ttsbu

rgh]

at 1

0:10

30

June

201

4

Ivry, R.B., & Corcos, D.M. (1993). Slicing the variability pie: Component analysis of coordination and motor

dysfunction. In K.M. Newell & D.M. Corcos (Eds.), Variability and motor control (pp. 415–448). Champaign, IL:

Human Kinetics Publishers.

Ivry, R.B., & Hazeltine, R.E. (1995). Perception and production of temporal intervals across a range of durations:

Evidence for a common timing mechanism. Journal of Experimental Psychology: Human Perception and

Performance, 21(1), 3–18.

Ivry, R.B., & Hazeltine, R.E. (1999). Subcortical locus of temporal coupling in the bimanual movements of a

callosotomy patient. Human Movement Science, 18(2–3), 345–375.

Ivry, R.B., Keele, S.W., & Diener, H.C. (1988). Dissociation of the lateral and medial cerebellum in movement timing

and movement execution. Experimental Brain Research, 73, 167–180.

Jagacinski, R.J., Marshburn, E., Klapp, S.T., & Jones, M.R. (1988). Tests of parallel versus integrated structure in

polyrhythmic tapping. Journal of Motor Behavior, 20(4), 416–442.

Keele, S.W., Pokorny, R.A., Corcos, D.M., & Ivry, R. (1985). Do perception and motor production share common

timing mechanisms: A correlational analysis. Acta Psychologica, 60(2–3), 173–191.

Kelso, J.S., Southard, D.L., & Goodman, D. (1979). On the coordination of two-handed movements. Journal of

Experimental Psychology: Human Perception and Performance, 5(2), 229–238.

Klapp, S.T., Hill, M.D., Tyler, J.G., Martin, Z.E., Jagacinski, R.J., & Jones, M.R. (1985). On marching to two differ-

ent drummers: Perceptual aspects of the difficulties. Journal of Experimental Psychology, 11(6), 814–827.

Kolers, P.A., & Brewster, J.M. (1985). Rhythms and responses. Journal of Experimental Psychology: Human Percep-

tion and Performance, 11(2), 150–167.

Mates, J., Radil, T., & Poeppel, E. (1992). Cooperative tapping: Time control under different feedback conditions.

Perception & Psychophysics, 52(6), 691–704.

Miedreich, F. (2000). Zeitliche Steuerung von Handlungen: Empirischer Test des Wing–Kristofferson Modells. Aachen:

Shaker.

Peters, M., & Durding, B. (1979). Left-handers and right-handers compared on a motor task. Journal of Motor Behav-

ior, 11(2), 103–111.

Prinz, W. (1990). A common-coding approach to perception and action. In O. Neumann & W. Prinz (Eds.), Relation-

ships between perception and action (pp. 167–201). Berlin: Springer-Verlag.

Schmidt, R.A. (1980). On the theoretical status of time in motor-program representations. In G.E. Stelmach & J.

Requin (Eds.), Tutorials in motor behavior (pp. 145–165). Amsterdam: North-Holland.

Semjen, A., & Summers, J.J. (2002). Timing goals in bimanual coordination. Quarterly Journal of Experimental

Psychology: Human Experimental Psychology, 55A(1), 155–171.

Sergent, V., Hellige, J.B., & Cherry, B. (1993). Effects of responding hand and concurrent verbal processing on time-

keeping and motor-implementation processes. Brain and Cognition, 23, 243–262.

Shaffer, L.H. (1982). Rhythm and timing in skill. Psychological Review, 89(2), 109–122.

Stenneken, P., Aschersleben, G., Cole, J., & Prinz, W. (2002). Self-induced versus reactive triggering of synchronous

movements in a deafferented patient and control subjects. Psychological Research, 66(1), 40–49.

Stevens, L.T. (1886). On the time sense. Mind, 11, 393–404.

Vorberg, D., & Hambuch, R. (1984). Timing of two-handed rhythmic performance. In J. Gibbon & L. Allan (Eds.),

Annals of the New York Academy of Sciences: Timing and time perception Vol. 423 (pp. 390–406). New York: New

York Academy of Sciences.

Vorberg, D., & Wing, A. (1996). Modeling variability and dependence in timing. In H. Heuer & S.W. Keele (Eds.),

Handbook of perception and action: (Vol. 3): Motor skills. London: Academic Press.

Wing, A.M. (1977a). Effects of type of movement on the temporal precision of response sequences. British Journal of

Mathematical and Statistical Psychology, 30(1), 60–72.

Wing, A.M. (1977b). Perturbations of auditory feedback delay and the timing of movement. Journal of Experimental

Psychology: Human Perception and Performance, 3(2), 175–186.

Wing, A.M. (1979). A note on estimation of the autocovariance function in the analysis of timing of repetitive

responses. British Journal of Mathematical and Statistical Psychology, 32(1), 143–145.

Wing, A.M. (1982). Timing and co-ordination of repetitive bimanual movements. Quarterly Journal of Experimental

Psychology: Human Experimental Psychology, 34A(3), 339–348.


Dow

nloa

ded

by [

Uni

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ity O

f Pi

ttsbu

rgh]

at 1

0:10

30

June

201

4

Wing, A.M., Church, R.M., & Gentner, D.R. (1989). Variability in the timing of responses during repetitive tapping

with alternate hands. Psychological Research, 51(1), 28–37.

Wing, A.M., & Kristofferson, A.B. (1973a). Response delays and the timing of discrete motor responses. Perception &

Psychophysics, 14(1), 5–12.

Wing, A.M., & Kristofferson, A.B. (1973b). The timing of interresponse intervals. Perception & Psychophysics, 13(3),

455–460.

Yamanishi, J., Kawato, M., & Suzuki, R. (1980). Two coupled oscillators as a model for the coordinated finger

tapping by both hands. Biological Cybernetics, 37, 219–229.

Ziemann, U., & Hallett, M. (2001). Hemispheric asymmetry of ipsilateral motor cortex activation during unimanual

motor tasks: Further evidence for motor dominance. Clinical Neurophysiology, 112, 107–113.

Original manuscript received 15 December 2000

Accepted revision received 20 January 2002


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Reduced timing variability during bimanual coupling: A role for sensory information