338 Motor Control
two different types of task, the one involving sequences of
movements with different effectors and the other discrete
movements, mostly of short duration. By and large there
seem to be no striking discrepancies between the conclusions
based on the two types of experimental paradigm, although
the precise relation between them is not fully clear. For ex-
ample, one cannot exclude that certain constraints may
evolve gradually so that they are effective for sequences of
movements, but not for brief discrete ones.
A highly consistent finding is that periodic oscillations of
the upper limbs are more stable when they are performed
symmetrically than when they are performed asymmetrically.
The same kind of observation has also been made for bi-
manual circle drawing (e.g., Carson, Thomas, Summers,
Walkers, & Semjen, 1997). However, the symmetry con-
straint, which favors the concurrent activation of homologous
muscle groups, is not universal; in addition, there is a bias to-
ward identical movement directions (e.g., Serrien, Bogaerts,
Suy, & Swinnen, 1999). This is particularly obvious for peri-
odic movements with nonsymmetric effectors. For example,
Baldissera, Cavallari, and Civaschi (1982) and Baldissera,
Cavallari, Marini, and Tassone (1991) found that concurrent
up-and-down movements of foot and hand in identical direc-
tions are more precisely coordinated than concurrent move-
ments in opposite directions. Thus, although essentially there
is always a preferred phase relation for periodic movements
of different effectors, which phase relation this is depends on
the particular effectors chosen and their plane of motion.
A second highly consistent finding is related to the timing
of bimanual response sequences. Such sequences are simple
when they have the same frequency, and they are also fairly
accurately produced when the frequencies are harmonically
related, that is, by integer ratios. However, for polyrhythms
performance deteriorates (e.g., Klapp, 1979). For this it is not
essential that the polyrhythms are produced by the two hands,
but poor or even chance performance can also be observed
in vocal-manual tasks (Klapp, 1981). There seems to be a
general rule that the variability of the temporal errors of indi-
vidual responses increases as the product mn for m:n
rhythms increases (Deutsch, 1983); for example, variability
is higher with a 2:5 (mn=20) than with a 2:3 (mn=6)
rhythm. When the overall rate of polyrhythms is increased,
not only does performance become poorer, but in addition
complex rhythms may switch to less complex ones, like 2 : 5
to 1 : 2 (e.g., Peper, 1995).
The observations on polyrhythms have been taken to sug-
gest the existence of a unitary timing-control mechanism for
movements of the two hands (Deutsch, 1983). In fact, formal
analyses of polyrhythm production in terms of timer models
(cf. Vorberg & Wing, 1996) generally reveal integrated
control, in which the timing of a response with the one
hand can be relative to a preceding response with the other
hand (Jagacinski, Marshburn, Klapp, & Jones, 1988; Klapp
et al., 1985; Summers, Rosenbaum, Burns, & Ford, 1993).
The difficulty in the production of polyrhythms is then basi-
cally related to the complexity of the integrated timing
control structure. Only recently evidence has been reported
according to which professional pianists can exhibit parallel
timing control for the two hands when they produce
polyrhythms at rapid rates (Krampe, Kliegl, Mayr, Engbert,
& Vorberg, 2000). Except for such a select population, how-
ever, temporal coupling appears to be so tight that tasks that
apparently require decoupling are performed in a way that
maintains a unitary timing control.
Relatively little research effort has been invested in the
study of sequences of bimanual movements with different
amplitudes. Franz, Zelaznik, and McCabe (1991) studied the
concurrent production of periodic lines and circles with the
two hands. Drawing circles with one hand requires periodic
oscillations with the same amplitudes along both axes of the
plane, while drawing lines with the other hand requires a pe-
riodic oscillation along only one axis; however, for the other
axis, one can think of a periodic oscillation with zero ampli-
tude. Franz et al. found that both the lines and the circles be-
came elliptical (Figure 12.15). Thus, the different amplitudes
of the oscillations became more similar in the bimanual task:
The larger amplitude oscillations in drawing circles were re-
duced in amplitude, and the zero-amplitude oscillations in
drawing lines were enhanced in amplitude. More straightfor-
wardly, such an amplitude assimilation for periodic move-
ments was shown by Spijkers and Heuer (1995) and by Franz
(1997), both for lines (that is, one-dimensional oscillations)
and for circles (that is, two-dimensional oscillations). In ad-
dition, Spijkers and Heuer (1995) found that the amplitude
assimilation became stronger as the frequency of oscillations
was increased.
Kelso, Tuller, and Harris (1983) had their subjects oscil-
late a finger and concurrently repeat the syllable stock. When
every second syllable had to be stressed, there was an invol-
untary increase of the amplitude of the accompanying finger
movement; similarly, voluntarily increased finger amplitudes
were accompanied by involuntary stresses of the syllable.
These findings, which have been confirmed by Chang and
Hammond (1987), suggest that, in addition to amplitude
assimilation, changes of amplitude might overflow to other
effectors.
For a more systematic exploration of the contralateral ef-
fects of large-to-small or small-to-large amplitude changes,