Our results indicate that it is possible to meaningfully dissociate irregularity as planned by the motor system and instability of the execution of the motor program. Experiment I revealed that these two factors contribute to the SD of the keystroke intervals as investigated in previous studies. The advantage of our analysis is that we tease apart systematic deviations, which can be rooted in perceptual biases (Penel and Drake, 1998
) or residual expressive timing (Repp, 1999a
), from mere motor execution errors. Another advantage is that the line fit can still be computed even if a few notes are missing or played twice. As a result, our analysis is robust enough to be applied to pianists who play relatively few correct scales, for example because of a movement disorder such as musician’s dystonia (Jabusch et al., 2004
) or experimental design (Maidhof et al., 2009
Note-by-note investigation reveals that instability is greater at the boundaries between the octaves. This is true for two-octave C-major scales and the motorically identical A-minor scales, revealing that it is not related to the C-major musical content but related to motor execution. We interpret these results as revealing that at the octave boundary a transition occurs between subsequent motor program chunks. Previous studies have interpreted the chunking as an aid to learning (Sakai et al., 2004
), which is supported by evidence that in the course of learning, the smaller chunks are merged into larger ones (Rosenbaum et al., 1983
). In our interpretation, this instability is a side-effect of loading the next motor sequence into the motor buffer (Lashley, 1951
). Interestingly, our data stand in contrast to the previous findings of pianists’ tapping, showing reduced variability of taps at sequence boundaries (Loehr and Palmer, 2007
). However, the latter study used much shorter sequences and calculate the variability of the intervals instead of note-by-note variability. These experimental differences may explain the different and robust findings in the present study.
The octave boundary instability is less strong but still present in the F#-major scales. This can readily be explained by the fact that F#-major scales are much less intensively practised because they are less common in the music literature. For example, one participant did not know it is played with a b rather than a b#. In other words, the F#-major scale may be represented more note-by-note in the motor system because it is played less frequently.
Indeed, we searched the ThemeFinder corpus (http://www.themefinder.org
, containing 9792 themes at the time of our search). Of these, 936 themes were composed in C-major. Any theme in A-minor revealed 467 matches. F# major themes were only 139 in number. Indeed, these three counts are not independent: χ2
0.001. In particular, there are between 2.8 and 3.2 (binomial 95% confidence interval) times more C-major themes than A-minor themes. Similarly, there are between 1.2 and 1.4 times (binomial 95% confidence interval) more A-minor than F#-major themes. Of course, some caution is needed in interpreting these corpus search results. They only concern themes and not entire pieces, which may contain modulations. Furthermore, the data is from classical and baroque periods only, and are therefore not necessarily the same as the typical pianists’ repertoire. However, it is likely that the distributions of tonalities are at least comparable. Furthermore, this difference between F#-major and C-major scales cannot be explained by washing out of the instability differences due to higher overall instability in the former case, because the mean instability is the same in both cases (Figure ).
In order to further clarify the processing that occurs at the octave boundary, future investigation could add a weight to the wrist during scale playing, increasing its inertial mass. This means that the preparation for the thumb passage movement would have to be longer (Engel et al., 1997
) and likely accompanied by more variability. Therefore, we predict the appearance of two additional peaks in the instability (at
). However, great caution should be taken in such an endeavor, since the pianist’s muscular system is highly sensitive to changes in the playing environment (Sakai, 2002
) and can easily result in injury. Alternatively, TMS could be applied during the production of the first octave, which would likely interrupt the output that is currently in the motor buffer. However, the second chunk (octave) is at that point not yet in the motor buffer and should therefore not be affected.
The picture that emerges from Experiment I is that the octave boundary instability is mainly a low-level motor sequencing phenomenon. But Experiment III reveals an unexpected parallel in perception: that the detection rate is lower at the boundaries of the two-octaves. Assuming that the two phenomena are causally related, which one is the cause and which the effect?
First we consider the possibility that the lack of auditory resolution at the octave boundary causes the playing to be less precise at those points. Similar hypotheses have been advanced that relate musical production to perception. One is that slowing down at the end is musically appropriate and not perceived as deviant (Repp, 1992b
), and therefore played that way too. On another interpretation the perceptual space is non-veridical, with certain intervals (such as the last intervals of phrases) sounding shorter and therefore played longer: the perceptual hypothesis (Penel and Drake, 1998
). In our case, the problem with both is that they cannot account for the detection impairment at the octave boundary, since we show that there is an increase in playing instability, but no systematic slowing (which would have appeared in the irregularity trace).
The perceptual hypothesis could be amended to include this possibility. Imagine that due to the lack of perceptual resolution at the octave boundary, the interval does not sound systematically shorter, but sometimes shorter and sometimes longer. As a result, the playing would sometimes compensate by playing it longer and sometimes by playing it shorter, yielding increased playing variability but not systematic deviation, in line with our findings. What is not satisfying about this explanation is that it does not account for why perceptual resolution is lower at such locations that do not seem musically meaningful. However, an even more immediate problem is that it would predict the octave boundary instability to be present equally in the F#-major scales, contrary to our findings.
A second explanation is the inverse causality: a lack in playing precision leads to impaired perception. Indeed, participants in Experiment III were musicians and could therefore be heavily influenced by exposure to musical material. A future study could decide this issue by performing the perception experiment on non-musicians. A limitation of such investigation will be that even non-musicians have much been passively exposed to music.
In sum, then, we conclude that the chunks formed in the motor system and in the perceptual system overlap, at least for the materials presently studied. How chunk formation in the two systems is causally related remains yet to be answered.
These questions open the road to further investigation into the relation between music perception and production, which may be more complex than previously accounted for. A future study may use a signal-detection-theoretical framework to tease apart response bias and sensitivity and correlate these to playing irregularity and inconsistency. Our prediction is that the irregularity trace will be mirrored by the detection bias, whereas the instability trace reflects the inverse of the sensitivity.
In sum, our study points to a dissociation between musical phrases and motor programs. Musical phrases have previously been found to be indicated by systematic slowing at the end (i.e., increased irregularity), whereas our finding is that motor sequences are demarcated by increased playing instability. Perhaps the two reflect the previously discovered dissociation between timing processes and item sequencing (Pfordresher, 2003
). This issue could be further clarified by testing whether increased keystroke variability is found at the boundary of learned sequences in a serial reaction time paradigm (Nissen and Bullemer, 1987
), as our interpretation would predict.
One limitation in the current study is that although contrary to previous studies we have included scales of different tonalities, still all our material consisted of two-octave scales. A future study could investigate scales over three octaves, although caution would need to be taken to control for the larger distance the arm needs to cover to reach the three octaves.