faster than 100 bpm, the tendency is same and a stronger
coordination is observed. On 120 bpm the right hip is
weakly desynchronised, but the phenomenon may be due
to the fact that the body could not be kept up with the
fast tempo. 120bpm tempo, for example, requires 3 Hz
oscillation.
We face a contradiction here. The performances were
musically best for both subjects when they played on
100 bpm, but strengths of synchronisation among joints
were worst synchronised on the tempo. On the faster or
slower tempo, stronger synchronisation phenomena were
seen, but their performances were not musically better.
We did not feel a groove or swing in their performances
played on tempos other than 100 bpm though they pro-
duced correct rhythms with proper accents. Both sub-
jects reported that 120 bpm was too fast for them to
play the rhythm. How can we solve this puzzle?
We need to extend our conception of coordination and
differentiation to accommodate the case for samba. The
desynchronised movement around his hip is thought to
be the source of the swinging rhythm and acquired for
better musical expressions through practices. The fre-
quency distribution of the left hip exhibits two peaks.
This feature indicates that the phase difference is fixed
in this subject. The direction of desynchronisation is not
regular and the fluctuation of rhythm may be generated.
It should be noted that the desynchronisation is found
within coordinated movement where other parts are syn-
chronised. Also, desynchronised part did not break co-
ordination of the whole body. We thus conclude that
a hierarchical order is found, too, as is the case with
kneading.
The same goes for the other subject, Y (Figure 9). We
found additionally a hysteresis phenomenon for his case.
We asked him to play for five trials on different tempos:
90, 100, 110, 120 and 100 bpm in this order. We found
his hip desynchronised only on 100 bpm (left column in
the figure) as is the case with the subject, X. His hip is
synchronised to other parts of his body on faster tempos,
110 and 120 bpm.
Especially, for this sub ject, Y, only at 100 bpm, the
result of spectrum analysis by FFT shows a broad hump
for his right hip and all other joints exhibit sharp peaks.
(The graph is not shown for space limit.) We therefore
conclude that his hip is not synchronised to his knee and
torso.
Also interestingly, his hip remained to be synchronised
when he played the shaker again on 100 bpm (right col-
umn in the figure) in the last trial. The phenomenon can
be explained as the result of his fatigue as he reported
to us. A physical interpretation is that he lost the en-
ergy after performing four trials and it might become
difficult to maintain the body balance only by his right
leg. It is important to note that to make differentiation
at the one side of the hip requires a redundant DOF.
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100 bpm. Right: 90 bpm.
Figure 8: distributions of relative phase of subject X. Left:
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Figure 9: distributions of relative phase of subject Y. Left:
first 100 bpm. Right: second 100 bpm (after 120 bpm trial).
Only after this coordination of one leg and the torso is
established and balance is maintained, the other leg can
make a differentiation.
All the results above point to the hierarchal structure,
“differentiation within coordination”. The hierarchical
organisation of coordinative structure is different from
Bernstein’s “freezing and freeing” (Bernstein, 1967),
where only flat structures are considered.
5 Concluding remarks
We have suggested through our experiments and analysis
of kneading and shaking that there are two stages in
the development of coordinative structure. In the first
stage, the novice learns to synchronise his various joint
movements to form a rough trajectory necessary for the
task. The synchronisation is achieved by decreasing the
degree of freedom innate with our body. In the second
stage, the person learns to differentiate the synchronised
movement into several sections, executing each section
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