The Coordinative Structure of Polyrhythmic Performance and Korte’S Third Law

The Coordinative Structure of Polyrhythmic Performance and Korte’s Third Law

THESIS

Presented in Partial Fulfillment of the Requirements for the Degree Master of Arts in the Graduate School of The Ohio State University

Emanuele Rizzi

Graduate Program in Psychology

The Ohio State University

2015

Master's Examination Committee:

Dr. Richard Jagacinski, Advisor

Dr. Alex Petrov

Dr. Steven Lavender

Copyrighted by

Emanuele Rizzi

2015

Abstract

Previous research examining the performance of bimanual polyrhythmic tapping has utilized temporal covariance analysis to determine the interdependence of limbs being coordinated. The prevailing finding is that the perceptual-motor system couples the actions of the left and right hand into a dependent or integrated unit, with one notable exception in a study by Krampe et al. (2000). This study found that concert level pianists performing a 4:3 bimanual polyrhythm could exhibit relatively independent (i.e. parallel) performance between the two hands. In other coordination experiments parallel performance between the upper and lower body was achieved fairly regularly in the timing structure of moderately skilled golfers during their swing (Jagacinski et al., 2011).

Combining aspects of these previous works, we tested the effects of speed on the coordinative structure of skilled drummers’ hands and right foot while performing a 4:3:2 polyrhythm. All participants showed parallel performance between one or more limb pairs in both 3-limb polyrhythmic conditions and bimanual polyrhythmic conditions. Given that participants were coordinating both of their hands and their foot, they exhibited coordinative structures that mixed both integration and parallelism between limb pairs.

Faster performance speed resulted in more parallel performance as well as more variable performance. Parallel organization between one of the hands and the foot was more prevalent than between the two hands. We interpret these results by expanding a gestalt

principle known as Korte’s Third Law to encompass perceptual-motor behavior (Klapp &

Jagacinski, 2011).

iii

Acknowledgments

I would like to thank my advisor, Dr. Richard Jagacinski for his patience and guidance in the duration of this project. I would also like to thank Dr. Steven Lavender and Dr. Alex Petrov for their comments and advice on my work. I finally would like to thank my colleague and friend Lassiter Speller for his advice and assistance in the early stages of this study.

Vita

May 2006 ...... Miami Beach Senior High

2010...... B.S. Psychology, Florida State University

2010...... B.S. Statistics, Florida State University

2012 to present ...... Graduate Associate, Department of

Psychology, The Ohio State University

Fields of Study

Major Field: Psychology

Table of Contents

Abstract ...... ii

Acknowledgments...... iv

Vita ...... v

Fields of Study ...... v

Table of Contents ...... vi

List of Tables ...... ix

List of Figures ...... x

Introduction ...... 1

Integrated Timing in Bimanual Polyrhythmic Performance ...... 1

Promoting Relatively Independent Timing in Polyrhythmic Performance ...... 3

Perceptual Phenomena Affecting Coordinative Structures...... 5

Timing Structures in Other Domains ...... 9

Heart Rate Variability as a Covariate ...... 15

Hypotheses ...... 19

Methods...... 21 vi

Participants ...... 21

Apparatus ...... 21

Stimuli ...... 22

Procedure ...... 22

Experimental Conditions ...... 23

Heart Rate Variability ...... 25

Results ...... 26

Participant...... 26

Pattern Recognition ...... 27

Main Hypotheses ...... 28

Event Rate Effects on Parallelism ...... 33

Stricter criteria for parallelism ...... 35

Pattern effects on parallelism ...... 36

Height and heart rate variability as predictors of parallelism ...... 36

Coordinative Structures ...... 38

Measures of Performance: Distortion and Variability ...... 40

Covariates on measures of performance ...... 47

Pattern effects on parallel performance ...... 53

Variability of performance ...... 59

vii

Covariates of individual differences ...... 63

Biomechanical effects on parallelism ...... 67

Variability effects on parallelism ...... 72

References ...... 76

viii

List of Tables

Table 1: Beat Patterns Assigned to Each Limb and Resulting Events per Second ...... 25

Table 2: Within-Subjects One-Tailed t-test Results Under Stricter Criteria for Parallelism

...... ………35

Table 3: Correlations of Parallelism and Absolute Distortion ...... 48

Table 4: Correlations of Parallelism and Coefficient of Variation ...... 49

List of Figures

Figure 1: Temporal Correlation Diagrams ...... 29

Figure 2: Limb and Speed Effects on Parallel Performance in 3-Limb Conditions ...... 31

Figure 3: Parallel Performance of Hand-Hand Pairs in Bimanual and 3-Limb Conditions

...... ……..32

Figure 4: Percentage of Parallelism Across Event Rates ...... 34

Figure 5: Relationship Between Height and Parallel Performance in Bimanual

Polyrhythms ...... 37

Figure 6: Geometric Representation of the Three Limbs a Subject Coordinates ...... 39

Figure 7: Results From Four ANOVAs Testing Mean Absolute Distortion and

Coefficient of Variation in Bimanual and 3-limb Conditions ...... 42

Figure 8: Results from Four ANOVAs Testing the Effects of Speed and Pattern Type on

Measures of Performance ...... 44

Figure 9: ANOVAs Showing the Limb by Pattern Interaction on Measures of

Performance ...... 46

Figure 10: Diaram Illustrating the Relationships among Parallelism, Heart Rate

Variability, and Performance Measures ...... 67

Figure 11: Rhythmic Distortion Diagram ...... 71

Introduction

The present study investigates the underlying organization of the perceptual- motor system during a skilled tapping task. We will examine how the lower and upper limbs are coordinated while tapping a difficult polyrhythmic pattern composed of three different rhythms occurring simultaneously. By examining the temporal correlation between the limbs, we seek to determine conditions under which individual movements of different limbs behave relatively independently of one another and conditions when they are organized into a cohesive integrated structure.

Integrated Timing in Bimanual Polyrhythmic Performance

Early studies strongly suggest that our motor system combines coordinative actions into a single unit – a particularly prominent finding in studies of rhythmic synchronization. One such study compared models of integrated and parallel timing in bimanual coordination (Jagacinski, Marshburn, Klapp, & Jones, 1988). Musically trained subjects were asked to tap two different isochronous rhythmic patterns with each hand

(i.e. a polyrhythm). Jagacinski et al. compared the covariances in the natural temporal variability for the left and right hand’s rhythmic performance of a 3:2 polyrhythm. They found that the covariance patterns strongly supported an integrated timing organization of the two hands rather than a relatively independent timing of the two hands. These

findings were consistent with variants of this study by other researchers (Klapp et al.,

1985; Klapp, Nelson, & Jagacinski, 1998; Krampe, Kliegl, Mayr, Engbert, & Vorberg,

2000; Summers, Ford, & Todd, 1993; Summers, Todd, & Kim, 1993).

Polyrhythmic performance has provided an effective context in which to examine interlimb dependency due to the difficulty these patterns present to the perceptual-motor system. In fact, when asked to tap simple rhythmic patterns (e.g. 2:1 or 3:1), one study found subjects are fairly adept at being able to coordinate the two hands in doing so, but inferior performance can be observed from the same group of subjects when asked to tap a polyrhythm, e.g., 3 vs. 2, 4 vs. 3, etc. (Deutsch, 1983). For the most part these same relative difficulties in performance have been observed in trained musicians attempting a polyrhythm (Deutsch, 1983; Jagacinski et al., 1988; Summers, Ford, et al., 1993). The role of experience and training was examined in a study by Summers, Todd, and Kim

(1993) of forty-eight right handed subjects, half of which had at least six years of musical experience. Both experienced and novice subjects were tested on their ability to tap in synchrony to a simultaneous or shifted 3:2 polyrhythm. The covariance analysis of their performance aligned with previous findings that the timing variations of the two hands were more consistent with an integrated organization. Furthermore, musical experience did not seem to have an effect on how likely subjects were to use an integrated strategy in either the training or performance of the polyrhythms, though some articles have suggested otherwise (see below).

Another study by Klapp et al. (1998) examined whether parallel organization could be encouraged through specific training approaches. Thirty-two right-handed

participants were divided between two training groups: a whole-task training group that encouraged integrated timing and a part-task training group that encouraged parallel timing. In the whole-task group participants were presented with the full 3:2 polyrhythm, practicing both their right and left hand’s patterns together. In the part-task group, the two rhythmic patterns for each hand were trained separately from one another; this approach was intended to have participants think of their two hands independently when they had to combine them to form the polyrhythm. The study found “integrated training was effective; separate training was not” (Klapp et al., 1998). The part-task group was not able to reproduce the polyrhythm, while the whole-task group could; even when given more training time, the part-task group failed to perform accurately, if at all. The study also tested how the whole-task group would perform when asked to reproduce a single- hand’s pattern in the polyrhythm they had learned. Whole-task subjects were told to drop out one of the component parts of the 3:2 polyrhythm, and performance declined when doing a single-hand pattern, even though it was part of the polyrhythm they had just learned. Overall, these findings support that integration between the hands occurs when learning a polyrhythm. Independent manual training does not lead to accurate performance of a polyrhythm. An integrated motor representation does not constitute an independent coding of the coordinative components involved (Klapp et al., 1998).

Promoting Relatively Independent Timing in Polyrhythmic Performance

Although most studies suggest that integrated coupling between the hands is typical within our motor system, there have been some notable exceptions. Krampe,

Kliegl, Mayr, Engbert, and Vorberg (2000) proposed that our motor system utilizes either integrated or relatively independent timing depending on the speed constraints of coordinative performance. Their experiment examined fifteen expert pianists who were asked to tap a syncopated rhythm and a 4:3 polyrhythm over a wide range of tempos, including some very rapid ones. They were initially trained on the tasks, provided ample feedback, and then tested in their ability to perform them. Of the fifteen pianists, six were able to provide good performance at all the tempos. Temporal covariance patterns for the tasks at slower tempos (.75 – 4 events/sec) supported the integrated timing model (a result that agreed with many previous findings), but data for the faster tempos (5 – 10 events/sec) “found that the pianists used parallel timing for the hands, thereby permitting partial hand independence” (Krampe et al., 2000). The study suggests that for very rapid performance highly trained individuals switch to relatively independent timing.

Krampe et al’s study was not the first to find this particular independence in performance. While their approach focused on speed as a factor in performance ability, they also addressed their concern that participants in previous polyrhythmic studies were not adequately skilled performers for the level of difficultly these rhythms present.

Shaffer (1981) was one of the first to address the complexity of skilled performance by analyzing the hand movements of highly trained professional pianists performing pieces from Chopin, Bach, and Bartok. In a very thorough review of the data, Shaffer argues how the hand movements of the performers provide evidence that they were able to decouple the two hands performing these rather complex pieces. A strong example of this was observed when a pianist specializing in Chopin committed two errors during her

performance. In her first error, the pianist mistakenly hit the wrong note with her left hand and corrected this by hitting the appropriate note in sequence only 66 ms later; while doing so, the timing in the pianist’s right hand remained unaffected. In her second mistake, the pianist accidentally hit 9 notes in an 8 note sequence on her left hand. The pianist corrected for this error by speeding up subsequent left-hand notes by about 20 ms, while maintaining the timing in the right hand consistent. Shaffer suggests that perhaps this phenomenon of interlimb independence emerges in highly trained performance.

This same result was found in a study of professional percussionists performing a

4:3 polyrhythm either alone, with a performer as reference, or along with a tone sequence

(Pressing, Summers, & Magill, 1996). They utilized a similar covariance analysis procedure to those found in Jagacinski et al. (1988) and Krampe et al. (2000), and concluded that subjects showed flexibility in performance, being able to utilize relatively independent timing in their polyrhythmic production. It is important to note that many of the subjects in this study had highly specialized musical backgrounds in jazz and West

African percussion ensembles. This study further supports evidence that independent coordination is a highly specialized function that our motor system is capable of doing with specific training.

Perceptual Phenomena Affecting Coordinative Structures

The results found by Krampe et al.’s (2000) study are analogous to results found in experiments on auditory perception. Particularly, the occurrence of perceptual streaming could have implications for the coordinative timing structure of polyrhythmic

tapping. Bregman (1990) explains that when a sequence of two tones that are distant in pitch space are alternating rapidly, we perceive these tones as two simultaneous

“streams” of sound, an effect called auditory streaming. In contrast, rapidly alternating tones that are close in pitch space are grouped together, making us perceive the tones as a melodic sequence that is “jumping” up and down (Bregman, 1990, p. 49). Bregman suggests the grouping results from people forming “perceptual units” from tones that are relatively close pitch space (Bregman, 1990, pp. 51 – 52).

These perceptual units are also affected by the temporal separation of tones (i.e., speed or tempo). A study by Van Noorden (1976) altered the pitch separation and the temporal separation of the tones being presented to subjects in order to test the boundary at which two separate streams were perceived as one (“fission boundary”), as well as the boundary in which a single perceptual stream split into two separate streams (“temporal coherence boundary”). Sequences of tones that were very close in pitch space perceptually formed a single melodic stream until the onset between tones was about

60ms. At that very fast presentation rate perception of tones crossed the temporal coherence boundary. However, when tones were further apart in pitch space the temporal coherence boundary could be achieved at relatively larger temporal separations of about

150 ms between tone onsets (Van Noorden, 1976). Essentially “it becomes increasingly harder to hear one coherent stream at high speeds”, a point that may have implications for perceptual-motor organization (Bregman, 1990, p. 60).

In 1985, Klapp, Hill, Tyler, Martin, Jagacinski, and Jones found a striking relationship between auditory streaming and polyrhythmic performance. In Experiment 3

of their study, they had participants tap a 3:2 polyrhythm while varying the pitch difference between the tones representing the polyrhythmic pattern. They believed that the difficulty in polyrhythmic performance has a perceptual component affecting it; therefore, by varying the perception of the polyrhythm, they could affect the timing structure of their tapping response. Participants were placed in either a “streamed” condition, in which the two tones used for the polyrhythm were very different in pitch

(300 Hz and 3500 Hz), or an “integrated” condition, in which the tone frequencies were much closer (300 Hz and 350 Hz). Participants in the “streamed” condition actually performed considerably worse than those in the “integrated” condition, a result that was surprising because “enhancing the distinctiveness of discrete stimuli…should, in turn, enhance the division of labor in tasks involving both hands” (Klapp et al., 1985).

Klapp et al.’s (1985) findings were further supported in Jagacinski et al.’s (1988) follow-up study. They utilized the same pitch difference procedure with different tones

(262 Hz, 349 Hz, and 2,794 Hz). They found that participants in the “streamed” tones condition had more “variable” performance, and were unable to utilize the streamed tones to induce more parallel limb coordination. Jagacinski et al. suggest that this evidence points to a stimulus-response compatibility issue. All subjects relied on integrated timing during polyrhythmic tapping, and Jagacinski et al. suggest that because subjects fared worse in the streamed condition “the temporal pattern structure of perception can influence the temporal pattern structure of motor performance” (Jagacinski et al., 1988).

Klapp and Jagacinski (2011) discuss how gestalt principles may be able to describe the phenomena previously addressed. Korte’s Third Law is a major gestalt

principle that was initially used to describe how apparent motion is achieved based on the relationship between two successive stimuli’s perceived distance and onset time. This principle has been shown to apply to perceptual grouping in auditory streaming as well

(Bregman, 1990). Korte’s Third Law defines a velocity threshold, V*, at which perception switches from a single perceptual unit to two separate, simultaneously occurring streams:

V* = d / Δt

Here the d is the perceived distance between stimuli, which can be represented as perceived spatial distance or pitch separation, and Δt is the timing interval between successive stimuli. When applying this equation to audition, we are able to explain the results found in Van Noorden’s (1976) study. When tones are presented “fast enough” then it is difficult to hear a single coherent stream because the stimuli have “crossed” a velocity threshold at which point we perceive two streaming tones. It is also important to emphasize that it is perceived pitch distance that is responsible in defining the velocity threshold in Korte’s Law (Klapp & Jagacinski, 2011, p. 13).

Korte’s Law can potentially be extended to the organization of temporal motor sequences. When reexamining the results from polyrhythmic tapping studies, we could argue that if we perceive the hands as having some distance d between them, then we could find a Δt interval small enough to reach a velocity threshold beyond which we can observe relative independence between the tapping hands (Klapp & Jagacinski, 2011, p.

13). This may explain why most studies have found integrated timing in polyrhythmic

tapping, but Krampe et al.’s (2000) study was able to produce relatively independent timing when having subjects perform much faster (the Δt is smaller in Korte’s equation).

Timing Structures in Other Domains

One could argue that all these previous studies are looking at a highly constrained domain of rhythmic organization that would not apply outside of musical performance.

However Schmidt, Heur, Ghodsian, and Young (1998) provide evidence for coordinative timing structures beyond tapping tasks. Five subjects were trained to use two handheld levers to produce a three-part flexion-extension-flexion movement with their right arm while simultaneously producing a two-part flexion-extension movement with their left arm, i.e., a 3:2 pattern (Heuer, Schmidt, & Ghodsian, 1995; R. A. Schmidt, Heuer,

Ghodsian, & Young, 1998). A temporal covariance analysis was conducted on the time intervals between the acceleration peaks. The study concluded that the two arms shared an integrated timing structure, which was described as a “generalized motor program”.

This motor program possesses a “single rate parameter” that defines the movement times

(i.e., performance speeds) for the motor components involved (R. A. Schmidt et al., 1998, p. 352).

The single rate parameter implies an important constraint on the perceptual-motor structure responsible for temporal coordination. It suggests that temporal aspects of motor components sharing an integrated unit cannot change independently (if one part of the unit speeds up, all parts speed up). Schmidt et al. (1998) tested this implication by

instructing participants to slow down the left arm’s movement pattern without changing the right arm’s speed; participants found this task extremely difficult and almost always slowed down both arms together. When participants were instructed to speed up both arms together, participants adopted this change fairly easily and the between-arm temporal covariance increased. This indicated that the two arms’ movements were coupled more tightly when performing faster. These results support the idea that perceptual-motor coordination between arms may consist of integrated temporal units.

Schmidt et al.’s finding that temporal correlations between the arms increased with performance speed is surprising. This contrasts Krampe et al.’s (2000) observations relatively independent performance is achieved as performance speed increase during polyrhythmic tapping. Schmidt et al.’s participants were able to produce the target arm movements in about 400ms (equivalent to 11 events/sec), which is faster than the speed at which Krampe et al.’s subjects switched over to relatively independent timing (5 – 10 events/sec). From this result one might infer that there is something inherently different between the coordination tasks in these two studies. Though the results of their study are puzzling, they do extend the nature of coordinative coupling beyond that of bimanual tapping and present the idea that coordination could behave different among limbs sharing different “limb-spaces”. How our limb’s perceptual-distances are defined in our perceptual-motor system is not yet known, but some studies have begun to explore this.

In a study by Jagacinski, Kim, and Lavender (2009) golfer’s upper and lower torso movement patterns during short golf shots were observed. They examined the relationship between the weight shift timing that occurred in the lower torso and the

timing of the force applied to the clubhead throughout the swing. A golf swing is often said to have “a rhythm” (Nicklaus, 1974), and Jagacinski et al. found that the full swing of the body was similar to a 3:2 polyrhythmic pattern between the upper and lower body.

The clubhead exhibited a three-peaked force pattern corresponding to the backswing, downswing, and follow-through (i.e., a 3-part rhythmic pattern), while the legs exerted a two-peaked weight shift to the back leg and then to the front leg (i.e., 2-part rhythmic pattern). The subjects were 10 male golfers between the ages of 18 and 25. The timing intervals between the three force peaks of the clubhead remained “approximately invariant” regardless of the demands of the specific shot they were attempting, though weight shift timing intervals decreased when the shot aimed for a further target

(Jagacinski, Kim, & Lavender, 2009). This observation was evidence that the coordination of the swing and weight shift followed a relatively independent timing structure rather than integrated timing (contrary to the results found for bimanual tapping). One could interpret this result as indicative that in certain actions that require upper and lower torso coordination, an independent strategy between the parts is more common than a dependent one. Perhaps the perceptual-distance between the arms and legs is greater in our perceptual system, and therefore relatively independent timing can be achieved more readily.

In a follow up study by Kim, Jagacinski, and Lavender (2011), they found age- related differences in the use of relatively independent or integrated timing during the golf swing. The subjects included 20 young golfers (ages 18 – 25) and 20 older golfers

(ages 60 – 69) matched for handicaps. While younger golfers still exhibited strong

evidence for relatively independent timing structures between their upper-body swings and weight shifts, about half of the older golfers used an integrated timing structure. The overall tempo of the golf swing (i.e. time it took to complete the swing) surprisingly did not differ significantly between younger and older golfers, and did not differ significantly between shorter or longer shot distances (40 and 80 yards). Similar to bimanual tapping, there may be strategic or conditional circumstances in which our perceptual-motor system may adopt either an integrated or relatively independent timing structure to compensate for some difficulty in coordination (Kim, Jagacinski, & Lavender, 2011).

Limb Independence in Tracking

The complex nature of perceptual-motor coordination is further revealed in a different paradigm of bimanual coordination studies. Rosenbaum, Dawson, and Challis

(2006) performed a series of experiments in which participants used their arms to follow a moving target being manipulated by an experimenter. In one particular setup, blindfolded participants were told to track a magnetic disc on a vertical plane with each arm. Participants had to lightly touch the disc (as a greater force would cause the magnetic discs to decouple from the wall) while the disc moved around in some predetermined path. The two discs were “driven” by two different experimenters, with one of them creating a circular path and the other creating a square path for the disc.

Participants were able to generate these complex bimanual movement patterns very easily with little tracking error. This is a surprising finding because having participants

simultaneously generate a circle and square pattern on their own with each arm is a considerably harder task to accomplish.

Rosenbaum et al. additionally tested participants’ abilities to track two separate circles whose frequency ratio was 4:3 (i.e., 4 circular cycles of one arm for every 3 circular cycles of the other). The movements were polyrhythmic and the study challenged a “robust phenomena in … bimanual performance – the tendency of the two hands to veer toward simple frequency ratios when both hands generate cyclic movements”

(Rosenbaum, Dawson, & Challis, 2006, p. 1271). Similar to the square and circle condition, participants were able to generate these independent motions easily with the tracking paradigm. The conclusion that Rosenbaum et al. reach is that their “experiments indicate that people are physically capable of moving their two hands independently”

(Rosenbaum et al., 2006, p. 1273). This suggests that the difficulties reproducing limb independence does not occur at the execution level of movements, but perhaps at the planning level.

This finding from Rosenbaum et al.’s paper was supported by Klapp, Nelson, and

Jagacinski’s (1988) experiment on subjects learning a 3:2 polyrhythmic pattern. Subjects either learned the pattern by separately training the 3-pattern and the 2 pattern alone or by training how to do the 3:2 pattern together as a whole. The group that learned the pattern separately was easily able to do the 3- and 2-patterns when there were on their own, and only struggled to put those two pattern together. Even within a bimanual tapping paradigm, the challenges to perceptual-motor coordination are not motoric but rather lie within the action-planning of the limbs.

Stronger evidence for this could be drawn from a different tracking study done by

Kovacs, Buchanon, and Shea (2010). In their experiment participants sat on a table with their arms on two levers. The levers could be moved by flexion-extension motions from the subjects’ arms. Subjects were instructed to move their arms in a 5:3 polyrhythm (i.e. five flexion-extension motions on the right arm for every three on the left arm). While performing this pattern, a display in front of them represented their movements in a

Lissajous plot which displayed right arm motions as horizontal motions of a dot on the screen, while left arm motions corresponded to vertical motions of the same dot. Subjects used this information to match a template path on the display that corresponded to the 5:3 polyrhythmic movement. Similar to the Rosenbaum et al. (2006) results, subjects quickly and easily were able execute the required arm motions after some initial practice.

Furthermore, having understood how to utilize the Lissajous plot to analyze their performance they were able to do a transfer task in which they attempted to match a

Lissajous template that corresponded to a 4:3 polyrhythm. Subjects were able to immediately perform in this transfer task even though they had not previously practiced the 4:3 arm pattern.

Kovacs and Shea (2011) then followed up the results from this experiment by testing if reducing the amount of feedback subjects received from the Lissajous plot could result in an internal representation of the pattern their arms were generating. To test this they placed subjects in one of three groups that received either 100%, 50%, or 0% performance feedback. Each group was asked to performance flexion-extension motion with their left and right arms which represented a relative phase of 90⁰ between the two

arms. As expected subjects in the 50% feedback group showed the most accurate performance of the required arm motions when feedback was removed, while the 100% and 0% groups could not perform the required actions. From this result we observe that even difficult coordinative patterns can be generated when an appropriate feedback (i.e. perceptual-representation) is attended. It could be argued that the task of keeping a consistent relative 90⁰ phase between the two hands is not as demanding a coordinative task as polyrhythmic performance. However, subjects in the 0% and 100% groups could barely perform the task at all. Their study showed that when feedback is systematically removed it becomes possible for people to adopt the appropriate feedback from the environment that can result in them guiding the required coordination patterns internally.

Heart Rate Variability as a Covariate

Though the core of our research is focused on investigating the timing structure of perceptual-motor performance, we are also interested in seeing how these structures relate to physiological measurements. Heart rate variability in particular has gotten a lot of attention in recent years. In a review of heart rate variability research, Thayer and Lane

(2009) discuss various sources of evidence for heart rate variability’s role in cognitive regulation. One example they cite is an experiment by Hansen, Johnsen, and Thayer

(2003) which examined the relationship between subjects’ heart rate variability and their performance on a working memory task requiring detection of a number from 1 to 9 repeated in a continuous flow of digits. The heart rates’ of 53 male sailors (ages 18 – 34) were measured prior to the administration of the test. Heart rate variability was then

assessed by doing a spectral analysis of the heart rate and extracting a high-frequency

(0.15 - 0.4 Hz) component (Hansen, Johnsen, Sollers, Stenvik, & Thayer, 2004). The results of their study showed that the higher heart rate variability group had more positive detections and fewer false positive responses than a subject with lower heart rate variability (Hansen, Johnsen, & Thayer, 2003). People with higher resting high frequency heart rate variability may be “better able to perform tasks involving executive function”

(Thayer & Lane, 2009, p. 86).

This link between executive function and heart rate variability suggests this system may be responsible for adaptivity in highly cognitive tasks. Perceptual-motor coordination in many areas has been shown to be highly skilled; polyrhythms are challenging even to trained musicians and many golfers take years to develop a proficient swing. It is possible that if executive function is important to attaining skilled perceptual- motor performance, then heart rate variability may be an interesting covariate in analyzing the performance consistency in tasks such as polyrhythmic tapping. Heart rate variability may potentially share some relationship with the use of relatively independent timing structures in perceptual-motor coordination.

Experimental Design

Considering the contrasting findings in bimanual coordination and golf

(predominantly integrated coordinative timing in one domain, while predominantly relatively-independent timing in the other, respectively), we conducted an experiment that explored the effects of performance speed on different limbs in a polyrhythmic

tapping task. In this experiment, we want to test the specific parameters affecting the use of parallel and integrated timing of the limbs performing a complex polyrhythm. Similar to previous studies, participants will be expected to tap a polyrhythmic pattern. In our study the polyrhythm will be composed of isochronous 4-, 3-, and 2-beat patterns; all three patterns will start together and thus synchronize on the first beat of the polyrhythm.

By requiring participants to use both hands and one foot, we will be able to test if there is a systematic coordinative separation between the upper and lower torso such as that found in Jagacinski et al.’s 2009 golf study.

We expand on previous works by having participants produce a more coordinatively demanding polyrhythm. Due to the high degree of difficulty this task will present, we expect that extensive experience may be important in the production of these particular polyrhythms (Krampe et al., 2000; Pressing et al., 1996). We only tested trained percussionists with at least six years of drumming experience in order to provide a stronger test of our hypotheses.

Because the participants required three limbs to perform our polyrhythm, we were able to investigate the effects of varying which component beat pattern in the polyrhythm

(4-, 3-, or 2-beat) each of the three limbs received, i.e. the limb assignment. This manipulation tested whether there was a rhythmic effect on the coordinative structure between limbs. For comparison, we also tested three polyrhythms without the foot (4:3,

3:2, and 4:2).

To test the findings from Krampe et al. (2000) that suggest that faster performance speeds promote parallel coordinative timing of the limbs, we varied the

performance speed of the polyrhythms, 30 and 50 cycles per minute. To compare our assessment of speed effects to that of Krampe et al.’s study we used a global measure of speed-of-performance called average event rate. This measure is the number of separate taps per second occurring among all the limbs. In previous studies integrated timing patterns had events rates ranging from 2 to 4 events per second, and Krampe et al.’s study found parallel timing occurring at about 5 to 10 events per second. The rate of performance in our present study resulted in event rates ranging from 2 to 5 events per second.

Event rate served as an index of speed effects representing the average coordinative load our subjects experience organizing the limbs involved in a particular polyrhythmic performance. This allowed us to compare different polyrhythmic patterns occurring at different speeds. For example, a 2-beat pattern at 30 cycles per minute produces an event rate of 1 tap/sec (60 beats / 60 sec); a 3 beat pattern at the same cycle speed produces a higher event rate of 1.5 taps/sec (90 beats/ 60sec). In a cognitive sense, the coordinative timing system is behaving faster in the production of the 3-beat pattern.

It is important to note that nearly simultaneous taps of multiple limbs are counted as one event. The reason for this is because we are interested in the timing structure and correlation of the intervals in-between taps. Therefore, multiple taps occurring nearly simultaneously have been temporally coordinated at the same instant; thus we assume the system would then signal all these taps concurrently.

Inherent within our study design, we present the potential for a mixed timing structure to occur, in which coordination between two limbs (e.g., the hands) is

integrated, and act relatively independently of a third limb (e.g., the foot). One can imagine such behavior as being analogous to a task such as driving where arguably the two hands on the steering wheel share a high degree of movement correlation, but they act relatively independently of the foot’s pressing actions against the accelerator and brake.

Hypotheses

We present four hypotheses in this study for the conditions under which we would expect to see relatively independent timing:

(1) Based on the findings of Krampe et al.’s (2000) piano study, we would expect that parallel timing will be more prevalent at faster pattern speeds. This is because faster performance would contribute a smaller Δt in the Korte’s Third Law equation, which would result in a perceptual velocity large enough for performance of the limbs to cross the velocity threshold, V*, into parallelism.

(2) From the aforementioned golf studies, we predict that we will observe more independent coordination between the upper and lower torso than we would between the two hands (Jagacinski et al., 2009; Kim et al., 2011). The foot should more frequently maintain parallel performance from the hands during a polyrhythm because the d between the hand-foot pairing would be larger than the d between the hand-hand pairing in

Korte’s equation.

(3) Given hypotheses 1 and 2, under the appropriate conditions we expect to observe integrated timing between the hands while simultaneously having relatively

independent (i.e., parallel) timing between the hands and foot, i.e., “mixed timing”.

Korte’s Law will govern the performance structure of the limb pairings within the 3-limb context allowing more complicated coordinative structures to emerge.

In addition to the previous hypotheses:

(4a) Based on previous studies (Jagacinski, Peper, & Beek, 2000; Summers,

Rosenbaum, Burns, & Ford, 1993), we expect that with more polyrhythmic complexity, there will be more variability in the performance of the hands (variability of 4:3 > variability of 3:2 > variability of 4:2).

(4b) We expect that variability in hand-hand polyrhythmic performance will be greater when subjects are coordinating the foot then when the two hands are performing alone. Yet, because we believe speed will factor into this relationship, variability in the hand-hand component of 3-limb polyrhythmic conditions should be less affected at the faster performance speed because the foot tapping is expected to be relatively independent of hand tapping.

(5) Finally, we expect that high frequency heart rate variability will serve as a good predictor of individual differences in polyrhythmic performance ability (Thayer &

Lane, 2009).

Methods

Participants

Twenty-two right-handed male participants with at least 6 years of drumming experience were tested. Most subjects were college students completing a psychology participation experience while some were college music students or local drummers who were paid $15 per hour for their involvement. Participants’ heights (mean = 177.32 cm, sd = 6.5 cm) were recorded to serve as a potential covariate in the analysis process.

Apparatus

Participants sat on a Dixon drummer’s stool and tapped on a Formica desk table top with their hands and on the floor with their right foot. Sony computer speakers

(Model SRS-PC91) were used to present the rhythmic tonal patterns. A Vernier differential voltage probe was used to record the electrical signal being sent to the speakers.

Participants wore golf gloves and aquatic shoes with Vernier three-dimensional 5 g accelerometers attached to them. The vertical output of the accelerometers was sampled at 100 Hz in order to detect peaks in the force pattern when the subjects struck the table or floor. A Vernier sound level meter was used to detect the initial tone onset to trigger data recording. A Vernier exercise heart rate monitor will also be worn by the drummers at specific parts of the study. All Vernier components were connected to LabQuest Pro2 interfaces that fed the data to Logger Pro 3.8 data collection software via USB cables.

Stimuli

Subjects heard a polyrhythm comprised of three distinct auditory tones. The tones for this study were generated using a program called Bounce Metronome. Using the software’s built in grand piano midi sound, 3 tones were generated: a 262 Hz (C4, i.e., the musical note C in the fourth octave), 1,397 Hz (F6,), and 2,093 Hz (C7). The tones were edited on Audacity, a freely available online audio editing software, to build Mp3 files of each polyrhythmic condition for this experiment.

Procedure

Participants attended four sessions of approximately 1.5 – 2 hours each across four days. Their primary task was to tap a polyrhythm composed of 4-, 3-, and 2-beat rhythmic patterns. Days 1 and 2 served as practice days for the participants to learn the polyrhythm; only data from Days 3 and 4 were used for analysis.

The polyrhythms were represented by the three distinct tones described above.

To tap these three-part rhythms, participants were required to use their two hands and their right foot. Each limb was assigned to a specific tone in the polyrhythm. The lowest pitched tone (C4) corresponded to the participants’ right-foot rhythm, while the highest pitched tone (C7) corresponded to their right-hand’s rhythm; both of these tones were projected from the right-side speaker. The middle tone (F6) represented the participant’s left hand rhythm and was projected out of the left-side speaker.

At the beginning of a trial participants heard a click indicating that the tones were about to start. They were instructed to only listen to the first 4 cycles of the 4:3:2

polyrhythm presented. After this listening period, participants were then asked to tap in synchrony to the polyrhythm for the next 4 cycles. Following these 4 cycles, two of the tones dropped out and only the middle F6 tone remained at the beginning of each cycle to serve as a metronome to set the pace of their tapping. They continued tapping the same

4:3:2 pattern for another 16 cycles until the metronome stopped, at which point they were given a 10-second rest period. A single trial therefore consisted of 4 cycles of listening to the polyrhythm, 4 cycles of playing along with the polyrhythm, and 16 cycles of playing along to a metronome for a total of 24 cycles per trial. Following the rest period, another click signaled that the next trial’s start. This process was repeated six times to form a block of 6 trials. After a block was completed participants were given about a half-a- minute break before the next 6-trial block was presented, so not to fatigue them.

Experimental Conditions

Across experimental conditions we varied which limb performed which beat pattern in the polyrhythm, i.e. the limb assignment. Six different limb assignments were used in the course of the experiment. The 4-, 3-, and 2-beat patterns were each in turn assigned to the foot in different conditions. The remaining component rhythms (3:2, 4:2, and 4:3) were then assigned to the hands with the right hand always performing the faster rhythmic pattern between the two. Assigning the faster beat to the right hand was done to be consistent with previous research that showed more consistent performance when the dominant hand performed the faster beat (e.g., Byblow & Goodman, 1994). In addition to these three limb assignments, the bimanual 4:3, 3:2, and 4:2 patterns were also performed

without any tapping by the foot. These bimanual conditions served as comparison conditions.

In addition to the limb assignments, the patterns were also presented at two speeds, slow and fast (30 and 50 cycles per minute). A particular limb assignment at one speed was always followed by that same limb assignment at its other speed. The speed and limb assignment remained the same throughout each 6-trial block. Therefore our experiment contained 12 conditions (6 limb assignments x 2 speeds). A Latin square design was used to order the six limb assignments. Each limb assignment was used for 2 successive blocks at the two different speeds. Within a day’s session, for a given subject, the order of the two speeds remained constant (slow-then-fast or fast-then-slow). The order of speeds was counterbalanced across participants and across days. The full list of conditions can be seen in Table 1.

Table 1 Beat Patterns Assigned to Each Limb and Resulting Events per Second Distinct** Right Hand Left Hand Right Foot Events/Sec Slow (30 Cycles/Min) 3 2 4 3 3 2 - 2 4 2 3 3 4 2 - 2 4 3 2 3 4 3 - 3 Fast (50 Cycles/Min) 3 2 4 5 3 2 - 3.33 4 2 3 5 4 2 - 3.33 4 3 2 5 4 3 - 5 ** Two or three beats occurring at the same time were counted as one event

Heart Rate Variability

On Day 1 participants’ heart rate variability was measured using a specialized chest band worn directly on their skin. Prior to the start of the experiment participants were told to sit, stand, and sit for 5 minutes each. This is a common procedure to assess a baseline of the participant’s heart rate variability (Thayer, 2009).

On Day 4, after the polyrhythmic tapping portion of the experiment was completed, the participants’ heart rate variability was measured again while they tapped continuously for 4 minutes. They were asked to perform only the bimanual conditions at the slow speed (i.e. not incorporating the foot). The ordering of the limb assignments was

counterbalanced with each participant receiving one of the six possible orderings of the three bimanual conditions. This resulted in a total of 3 back-to-back trials of tapping for 4 minutes each. Participants tapped the faster rhythmic pattern with their right hand.

Similar to the core experiment, the trials began with a click indicating the tones were about to start. Following this, participants listened to the polyrhythm for 4 cycles and then began tapping along with the polyrhythm for the next 4 cycles. After these 8 cycles one toned dropped out, and the F6 tone served as a metronome which they used to tap along for 120 cycles (4 minutes) to provide an accurate assessment of their overall heart rate variability. Only the 30 cycle per minute speed was used in this portion of the experiment.

Results

Participant

Of the 22 participants, that data for 10 were excluded from the final analysis due to not meeting minimum performance criteria. Participant performance was assessed on

Days 2, 3, and 4 of the study. On Day 2 the minimum criterion for continuance was that participants perform 75% intact cycles (see below) for each the six rhythmic patterns at either the slow or fast speed. On Days 3 and 4 the criterion for continuation was that participants perform 75% intact cycles for each combination of rhythmic pattern and speed. These criteria ensured that each participant had a sufficient number of cycles for statistical analysis.

Pattern Recognition

Participants’ performance was assessed by analyzing the accelerometer time history for each limb. The time history was normalized by subtracting the mean and then taking the absolute value. This rectified dataset was analyzed through a Matlab algorithm to find the peak forces corresponding to the participants’ taps against the table top. The taps were identified as the maxima in a successive set of non-overlapping temporal windows whose widths were ½, ⅓, and ¼ of the cycle duration for the 2-, 3-, or 4-beats per cycle patterns, respectively. The starting point of each window series was adjusted so that the taps were relatively centered.

Once the taps’ were identified, intact cycles were determined. A cycle was considered “intact” if the participants performed the required number of taps for each limb within a temporal window specified in our analysis algorithm. Cycles with a tap missing or on a window boundary for any limb were discarded. Any cycles that showed an extra tap within a window were also discarded. Ideal performance produced 192 intact cycles (2 days x 6 trials/block x 16 cycles/trial) per combination of rhythm and speed.

Further analysis was restricted to intact cycles (mean = 191.51, n = 12).

Intertap intervals were estimated by subtracting the onset times of consecutive taps for each limb within a cycle (one interval for the 2-beat pattern, two intervals for the

3-beat pattern, and three intervals for the 4-beat pattern; see Figure 1). For each rhythmic pattern correlations were calculated between pairs of time intervals in different limbs that did not share the initial metronome at the beginning of each cycle.

Main Hypotheses

To test our hypotheses we calculated the mean absolute temporal correlation for each of the limb pairings in a polyrhythm (one limb pairing for bimanual performance and three for 3-limb). For the 192 cycles used to create these interlimb correlations, the criterion for the statistical significance of any single correlation was |r| ≥ 0.15, two-tailed.

This criterion provided at least 80% power for detecting correlations of |r| = 0.2 or greater. The means of the absolute correlations shown in Figure 1 that were less than 0.15 identified parallel performance between two-limb pairings. The number of parallel pairs was then determined for each subject for each polyrhythm and speed, and served as our dependent measure. The mean of the mean absolute correlations for limb pairs across subjects for the 3-limb and bimanual polyrhythms were 0.196 and 0.211, respectively.

The mean number of parallel pairs of limbs per subject for the 3-limb and bimanual polyrhythms were 6.17 out of a possible 18 (34%; 3 limb pairs x 3 rhythmic patterns x

2 speeds) and 2.00 of out a possible 6 (33%; 1 limb pair x 3 rhythmic patterns x 2 speeds), respectively.

Our first main hypothesis that more parallel limb performance would occur at the faster speed was supported. For 3-limb polyrhythmic conditions, a one-tailed t-test showed greater prevalence of parallel performance in the fast conditions than in the slow ones ( t(11) = 2.80, p < 0.01, ¯x fast = 3.92 [44%], ¯x slow = 2.25 [25%] ). In bimanual conditions there was also greater prevalence of parallel performance at faster speeds

( t(11) = 3.92, p < 0.01, ¯x fast = 1.58 [53%], ¯x slow =0.42 [14%] ).

(A) Interbeat intervals present in each beat pattern contained within the polyrhythm

(B) 3:2 Pattern correlation

Figure 1: Temporal correlation diagrams. (A) Shows the three idealized beat patterns present in the study and their respective interbeat intervals contained within each cycle. (B), (C), and (D) show the pairs of intervals for which the correlations of time intervals across cycle were calculated. (Continued)

Figure 1: Continued. (D) 4:3 pattern correlation

Our second main hypothesis was that the more distant limbs in perceptual space were likely to be coordinated independently. To test this hypothesis we examined the 3- limb conditions and compared the number of parallel hand-to-hand limb pairings with the number of parallel hand-to-foot pairings divided by two. The division by two was done to control for the fact that each 3-limb condition possessed two possible hand-foot pairs (left hand to right foot & right hand to right foot) and only one single bimanual pairing. The one-tailed t-test revealed relatively more frequent parallel performance between the hands and foot than between the two hands ( t(11) = 4.22, p < 0.01, ¯x (HF)/2 = 2.5 [42%],

¯x HH = 1.17 [20%] ). These simple t-tests did not address a possible interaction occurring between the limb effect and the speed effect in 3-limb conditions. Plotting the data

(Figure 2) clearly demonstrated that only main effects were present. Both hand-to-hand and hand-to-foot limb pairings behaved similarly. A 2 (speeds) x 2 (limb pairings: hand- hand, [hand-foot] / 2) within subjects ANOVA resulted in only a main effect of speed

( F(1, 11) = 8.41, p < 0.02, ¯x slow = 0.65 [21%], ¯x fast = 1.19 [40%] ) and a main effect of

limb pair ( F(1, 11) = 17.82, p = 0.01, ¯x HH = 0.58 [19%], ¯x (HF)/2 = 1.25 [42%] ). The interaction between these variables was not significant ( F(1, 11) = 0.50, p = 0.83 ).

Limb and Speed Effects on Parallel Performance

in 3-Limb Conditions 70%

60%

50% H-F

40%

30% H-H 20%

10%

0% 30 50

Percentage ofLimb Pairs Performing in Parallel Speed (Cycles per Minute)

Figure 2: This graph shows the main effects of limb pairings and performance speed in 3-limb polyrhythmic conditions on parallel limb performance. N = 12 for each point.

The results from the limb effect t-test led us to compare the number of parallel pairings in bimanual conditions to the number of parallel pairings in 3-limb conditions divided by three (to equate the two groups for the fact 3-limb conditions possess 3 pairings that can decouple). This test revealed that the 3-limb polyrhythms were no more likely to exhibit parallel performance than the bimanual polyrhythms ( t(11) = 0.15, p = 0.44, ¯x 3-limb/3 = 2.06 [34%], ¯x bimanual = 2.00 [33%] ). This is surprising because we expected that coordinating more distant limbs in the 3-limb polyrhythmic conditions would result in more decoupled limb pairs overall than in the bimanual polyrhythms. 31

We further compared bimanual and 3-limb conditions by testing whether the hand-hand limb pairings in the 3-limb context exhibited different performance structure from the simply bimanual conditions (Figure 3). A 2 (speeds) by 2 (conditions: bimanual limb pair vs. 3-limb hand-hand limb pair) within subjects ANOVA was conducted on the number of parallel pairs. This analysis found a main effect of speed ( F(1, 11) = 19.64, p < 0.01, ¯x slow = 0.38 [13%], ¯x fast = 1.21 [40%] ) and condition ( F(1, 11) = 7.86, p < 0.02, ¯x bimanual = 1 [33%], ¯x 3-limb(HH) = 0.58 [19%] ). Though Figure 3 might suggest otherwise, the interaction between condition type and speed was not significant

( F(1, 11) = 2.59, p = 0.14 ). It was surprising to find that the two hands exhibited more parallelism by themselves than when performing in a 3-limb context.

Parallel Performance of Hand-Hand Pairs in Bimanual and 3-Limb Conditions 80% 70% 60% Bimanual HH

50% 40% 30% Parallel 3-Limb HH 20% 10% 0% 30 50

Percentage ofLimb Pairs Performing in Speed (Cycles per Minute)

Figure 3: Graph comparing how the proportion of bimanual limb pairs performing in parallel compares to the proportion of 3-limb hand-hand limb pairs.

Event Rate Effects on Parallelism

We compared the four polyrhythmic conditions that possessed equal event rate.

These four polyrhythms were the 4:3 bimanual condition and three 3-limb conditions, which respectively had event rates of 3 and 5 events per second at the slow and fast speeds. A 2 (event rate) x 4 (polyrhythmic pattern) ANOVA was run to examine whether the 4:3 bimanual pattern had similar parallel/integrated performance as the 3-limb patterns when they were both in the same event rate context. To equate the 3-limb polyrhythm’s number of possible parallel pairings to those of the bimanual condition, they were divided by 3. The results from the ANOVA only showed a significant main effect of event rate ( F(1, 11) = 19.29, p < 0.01, ¯x 3 events/sec = 0.23 [23%],

¯x 5 events/sec = 0.45 [45%] ).

We addressed the possibility that the 4:3 polyrhythm’s distribution of parallel pairings might violate the ANOVA assumption of homogeneity of variance and normality by running a Friedman’s ANOVA, which is a common rank-based nonparametric alternative to typical ANOVAs. The test comparing the four polyrhythmic patterns was non-significant ( χ2(3) = .124, p = 0.99 ), and the test comparing the two event rates showed a significant difference ( χ2(1) = 10, p < 0.01 ). The Friedman test demonstrated that under nonparametric assumptions our results showed the same pattern of statistical significance. The results from the parametric and nonparametric ANOVA imply that the 4:3 bimanual polyrhythm does not result in more parallelism than the

3-limb polyrhythms, and that any changes in performance are mainly due to performance speed.

We were curious how the full range of event rates in our study affected mean number of decoupled limb pairings per subject. We could not fairly test this since certain event rates (2 and 3.33) only contained bimanual conditions which would be compared unevenly against the other two event rate groups which contained both a bimanual and 3- limb conditions. Therefore, we plotted the mean proportion of limbs performing in parallel for each event rate in Figure 4. It suggests a relationship between parallelism and event rate regardless of pattern being performed.

Percentage of Parallelism Across Event Rates 60%

50%

40%

30% Parallel 20%

10%

Percentage ofLimb Pairs Performing in 2 3 3.33 5 Event Rate

Figure 4: This plot shows how the proportion of limbs performing in parallel increases with event rate. N = 12 at each data point. Circles represent bimanual mean percentages. Squares represent 3-limb mean percentages.

Stricter criteria for parallelism

One of the challenges of our analysis is how we define limb pairs performing in

parallel when some pairs possess more than one interval of interest. By taking the mean

absolute correlations as we did in the aforementioned approach, we try to define an

overall coordinative structure from the multiple intervals being compared in each pattern

combination. A more conservative approach was also applied to our data to confirm the

findings from the previous approach. We denote a limb pairing as performing in parallel

if all pairs of intervals of interest in Figure 1 have |r| ≤ 0.15.

Under the stricter criterion the same pattern of t-tests for the major hypotheses

was obtained as for the previous definition of parallelism. For a summary of resulting test

values see Table 2.

Table 2 Within-Subjects One-Tailed t-test Results Under Stricter Criteria for Parallelism Number of limb-pairs p-value t-value df performing in parallel

Fast vs. slow in

3-limb conditions < 0.02 2.65 11 ¯x fast = 2.08 [35%] ¯x slow = 0.92 [15%]

Fast vs. slow in

bimanual conditions < 0.01 5.00 11 ¯x fast = 1.00 [33%] ¯x slow = 0.17 [6%]

(Hand-foot)/2 vs. hand-hand in 3-limb

conditions < 0.05 1.91 11 ¯x HF/2 = 1.21 [40%] ¯x HH = 0.58 [20%]

3-limb/3 vs. bimanual

decoupling 0.70 -0.54 11 ¯x 3-limb/3 = 1.00 [33%] ¯x bimanual = 1.17 [39%]

Pattern effects on parallelism

Given that parallelism between limb pairings did occur, we investigated whether particular pattern couplings were more or less likely to demonstrate it. To test this a

2 (speeds) x 3 (pattern couplings: 4:3, 4:2, or 3:2) within subjects ANOVA was done on the number of parallel pairs for both 3-limb and bimanual conditions. Both the 3-limb

( F(1, 11) = 7.86, p < 0.02, ¯x slow = 0.75 [25%], ¯x fast = 1.31 [44%] ) and bimanual

( F(1, 11) = 15.40, p < 0.01, ¯x slow = 0.14 [5%], ¯x fast = 0.53 [18%] ) ANOVA showed only a main effect of speed. Neither pattern nor the interaction between pattern and speed was significant. This implies that no particular pattern, not even the simple 4:2, was more likely to be integrated than the other two patterns.

Height and heart rate variability as predictors of parallelism

A Pearson product-moment correlation was computed to examine if there was a positive correlation between participants’ height and amount of parallel performance.

Parallelism was assessed by counting the total number of parallel limb pairings that participants exhibited in the bimanual conditions and 3-limb conditions, and in the slow and fast conditions. Only height’s correlation with bimanual parallelism was significant

( r = 0.65, p = 0.02, n = 12, one-tailed ). Taller subjects were more likely to show more instances of parallel performance in bimanual conditions (see Figure 5). Given the limited power in this study the remaining three correlations tested did not reach statistical significance ( r ≥ 0.497 ).

Relationship Between Height and Parallel Performance

in Bimanual Polyrhythms 120.0%

100.0%

80.0%

60.0%

40.0%

20.0%

0.0%

160 165 170 175 180 185 190 195 200 Percentage ofLimbs Performing in Parallel Height (cm)

Figure 5: Scatterplot demonstrating the relationship between subject height and overall percentage of limb pairs performing in parallel during bimanual conditions

We also computed a Pearson product-moment correlation to examine if there was a correlation between participants’ high frequency measures of heart rate variability and amount of parallel performance in the bimanual and 3-limb conditions, as well as the slow and fast conditions. Fourier spectra were calculated for two baseline heart rate measurements taken on Days 1 and 4, and for each 4-minute trial of bimanual tapping taken on just Day 4, and the high-frequency power (0.15 - 0.4 Hz) was calculated. The high frequency powers for the 4-minute trials were averaged together to accuracy of the estimate of participants’ heart rate variability during these recording periods.

The only significant correlations found were between bimanual parallelism and

Day 4 baseline heart rate variability ( r = 0.578, p = 0.05, n = 12 ), and parallelism during

30 cycles per minute performances and Day 1 baseline ( r = .587, p = 0.05, n = 12 ).

Baseline heart rate variability was very similar on Days 1 and 4, having a correlation of

0.835 ( p < 0.01, n = 12 ), but different enough that we could find significant correlations with one baseline reading and not the other. If we had more power in this study we would expect that both baseline readings would have been significant, as well as seeing the other moderately high correlations we found reach statistical significance ( r ≥ 0.576, n = 12 ).

Coordinative Structures

When parallelism occurred in a 3-limb polyrhythmic condition, the organization of the three limbs could take on 8 possible coordinative structures. Coordinative structures were defined by how each limb was integrated to or performed in parallel to one or both of the other limbs. Full integration was defined as all three limb pairings of the left hand, right hand, and right foot showing correlation values |r| > 0.15 during a polyrhythmic performance, while full parallelism was defined when all possible pairings of the limbs had |r| < 0.15 (criterion for parallelism, i.e. decoupling). Given that correlations are not transitive it is possible for just one decoupling to occur and give rise to a coordinative organization with two integrated couplings. In this structure the correlation for a single pairing of limbs in a polyrhythmic pattern exhibited parallelism, but the remaining two pairings did not. This could occur with the foot decoupled from either the left hand or right hand (not both), or with the hands decoupling from each other, but remaining integrated to the foot. A coordinative structure called a mixed timing

structure was also observed in participants in which one limb pairing remained integrated and the remaining limb decoupled from both limbs in the integrated pair.

(A)

LH RH

(B) Number of Decouplings in 3-Limb Rhythm ZERO ONE TWO THREE

Frequency 26 14 10 2 8 1 3 8 Figure 6: (A) A geometric representation of the three limbs a subject coordinates in our polyrhythmic task. The dots represent the limbs in space: Right Hand (RH), Left Hand (LH), and Right Foot (RF). (B) This table visually depicts the 8 possible coordinative structures a participant may demonstrate during a 3-limb polyrhythmic performance. The lines between dots represent whether that limb is integrated with another limb. Absence of a line indicates those two lines are performing in parallel. The highlighted coordinative structures denote structures we expected to observe more frequently due to our limb’s perceptual-space hypothesis. Each coordinative structure is characterized by whether 0, 1, 2, or all 3 limbs decoupled from the rest (performed in parallel). The frequency of each coordinative structure is shown beneath each the image.

The frequency distribution of these coordinative structures can be seen in Figure

6. Note that each subject contributed six data points to the coordinative structures’ frequency count since they performed six 3-limb polyrhythmic conditions. Therefore, it was possible for a single subject to exhibit various coordinative structures based on the 39

polyrhythm and speed he was performing. Figure 6 demonstrates the relatively high frequency of parallel performance of limb pairs that possessed a foot decoupling. In the single decoupling coordinative structure 24 of out 26 instances involved the foot decoupling from one of the hands, and in the mixed timing coordinative structure

(i.e., two decouplings) 8 out of 12 instances involved the foot fully decoupling from the hands.

Measures of Performance: Distortion and Variability

The mean duration of the 4-, 3-, and 2-beat intervals within each limb were subtracted from the ideal durations of those intervals. The absolute values of these differences were divided by the ideal duration to calculate the absolute distortion of each interval. Mean absolute distortion was calculated for each rhythmic component (2-, 3-, or

4-beat) in the polyrhythmic pattern and then averaged across components to arrive at an overall value for that pattern. The coefficient of variation, i.e., the standard deviation divided by the mean, was also calculated for each interval and an average for each polyrhythmic pattern was calculated in the same manner as for distortion. This provided a measure of variability (e.g. Wing, 1980). ANOVAs were performed on these values.

Prior to each ANOVA, boxplots were generated from the data being analyzed and potential outliers were identified. If a subject contributed any outlier that deviated from the mean of the remaining subjects by more than 4σ, they were excluded from that particular analysis.

A 3 (pattern type) x 2 (speed) within-subjects ANOVA was conducted for both

3-limb and bimanual polyrhythms. In the test of mean absolute distortion in the 3-limb case subject 11 contributed an outlier that met our criteria for outlier classification and thus had to be removed from the final analysis. After his removal the ANOVA showed only a significant main effect of speed ( F(1, 10) = 14.669, p < 0.01, ¯x slow = 0.012,

¯x fast = 0.020 ) and no significant interaction contrary to our expectations

( F(1, 11) = 0.53, p = 0.60 ). For the bimanual case, boxplots of the data revealed the presence of 3 outlier values again from Subject 11. The ANOVA for bimanual mean distortion without Subject 11’s contributions revealed a significant main effect of pattern

( F(2, 20) = 29.38, p < 0.01, ¯x 3:2 = 0.008, ¯x 4:2 = 0.005, ¯x 4:3 = .017 ) and a marginally significant main effect of speed ( F(1, 10) = 4.92, p = 0.051, ¯x slow = 0.009,

¯x fast = 0.011 ), with no significant interactions. These two result can be seen in Figure 7A

& 7B, respectively.

3 (pattern type) x 2 (speed) within subjects ANOVA’s were also conducted on the coefficient of variation. After reviewing the boxplot for these ANOVAs, Subject 11 was excluded from both the 3-limb and bimanual tests, along with Subject 15 who was excluded from just the bimanual test. The resulting ANOVA after removing Subject 11 from the coefficient of variation test in the 3-limb context showed a significant effect for speed ( F(1, 10) = 45.70, p < 0.01, ¯x slow = 0.031, ¯x fast = 0.041 ) and a marginally significant effect of pattern type ( F(2, 20) = 3.40, p = 0.054, ¯x 4:3:2 = 0.034,

¯x 4:2:3 = 0.037, ¯x 3:2:4 = 0.037 ), with no significant interactions (Figure 7C). In the bimanual case, after removing Subjects 11 and 15, the ANOVA revealed a main effect of

speed ( F(1, 9) = 19.78, p < 0.01, ¯x slow = 0.028, ¯x fast = 0.033 ) and pattern type

( F(2, 18) = 17.73, p < 0.01, ¯x 3:2 = 0.029, ¯x 4:2 = 0.028, ¯x 4:3 = 0.034 ) with no other meaningful results (Figure 7D).

(A)

Mean Absolute Distortion in 3-limb Conditions

0.03 0.025 0.02 4:3:2 0.015 3:2:4 0.01 4:2:3

0.005 AbsoluteDistortion 0 30 50 Speed (Cycles per Minute)

(B)

Mean Absolute Distortion in Bimanual Conditions

0.03

0.025 0.02 4:3 0.015 0.01 3:2

0.005 4:2 AbsoluteDistortion 0 30 50 Speed (Cycles per Minute) Figure 7: Results from the 4 ANOVAs testing mean absolute distortion and coefficient of variation in bimanual and 3-limb conditions. Note in (A) the lines for 4:3:2 and 4:2:3 lie directly on top of each other. Similarly, in (C) the lines for 3:2:4 and 4:2:3 lie directly on top of each other. No significant interactions were found. (Continued)

Figure 7: Continued. (C)

Coefficient of Variation in 3-limb Conditions

0.05 0.045 3:2:4 0.04 4:3:2 0.035 0.03 4:2:3 0.025

30 50 Coefficient Coefficient ofVariation Speed (Cycles per Minute)

(D)

Coefficient of Variation in Bimanual Conditions

0.045

0.04 4:3 0.035 4:2 0.03 3:2 0.025 30 50 Coefficient Coefficient ofVariation Speed (Cycles per Minute)

The hand performance component of the 3-limb polyrhythmic conditions (i.e., hand-hand limb pairs in the presence of the foot) was compared to the performance of bimanual polyrhythmic conditions (i.e., hand-hand limb pairs without the foot). A

3(pattern: 4:3, 4:2, 3:2) x 2(speed) x 2(context: 3-limb vs. bimanual) ANOVA was conducted on mean distortion and the coefficient of variation. The ANOVA for mean distortion excluded Subject 11 once again due to four outlier contributions. The test without Subject 11 showed a significant main effect of context ( F(1, 10) = 38.47, 43

p < 0.01, ¯x 3-limb( H-H) = 0.016, ¯x bimanual = 0.010 ), speed ( F(1, 10) = 13.83, p < 0.01,

¯x slow = 0.010, ¯x fast = 0.016 ), pattern ( F(2, 20) = 20.67, p < 0.01, ¯x 3:2 = 0.011,

¯x 4:2 = 0.008, ¯x 4:3 = 0.019 ), an interaction between context and speed

( F(1, 10) = 13.37, p < 0.01 ) and an interaction between context and pattern

( F(2, 20) = 7.03, p < 0.01 ). The 3-limb results can be can be seen in Figure 8. The

ANOVA on the coefficient of variation also excluded Subject 11, as well as Subject 15 once again. The test revealed the similar findings as the ANOVA on absolute distortion: a main effect of context ( F(1, 9) = 7.23, p < 0.03, ¯x 3-limb (H-H) = 0.034, ¯x bimanual = 0.031 ), a main effect of speed ( F(1, 9) = 33.75, p < 0.01, ¯x slow = 0.029, ¯x fast = 0.035 ), a main effect of pattern ( F(2, 18) = 15.71, p < 0.01, ¯x 3:2 = 0.030, ¯x 4:2 = 0.031, ¯x 4:3 = 0.035 ), an interaction between context and speed ( F(1, 9) = 7.55, p < 0.03 ), and an interaction between context and pattern ( F(2, 18) = 9.02, p < 0.01 ) which can be seen in Figure 8.

(A)

Mean Absolute Distortion of 3-Limb Hand- Hand Pairs Against Strictly Bimanual Conditions

0.03

0.02 3-Limb H-H

0.01 Bimanual H-H

0 AbsoluteDistortion 30 50 Speed (Cycles per Minute)

Figure 8: Result from 4 ANOVAs testing the effect of speed and pattern type on hand-hand absolute distortion and coefficient of variation in either 3-limb or bimanual polyrhythmic conditions. (Continued)

Figure 8: Continued. (B)

Mean Absolute Distortion for Hand Component Patterns Given Polyrhythmic Context

0.03

0.02 4:3 3:2 0.01 4:2

0 AbsoluteDistortion Bimanual 3-limb Polyrhythmic Condition

(C)

Coefficient of Variation for 3-Limb Hand-Hand

Pairs Against Strictly Bimanual Conditions

0.04 3-Limb H-H 0.035 Bimanual H-H 0.03

0.025

30 50 Coefficient Coefficient ofVariation Speed (Cycles per Minute)

(D)

Coefficient of Variation for Hand Component Patterns Given Polyrhythmic Context

0.04 4:3 0.035 4:2 3:2 0.03

0.025

Bimanual 3-limb Coefficient Coefficient ofVariation Polyrhythmic Condition

The final ANOVA we conducted was a 2(speed) x 3(limb: right hand, left hand, or right foot) x 3(pattern: 3:2:4, 4:2:3, 4:3:2) on absolute distortion and coefficient of variation to test whether there were differences in performance between the limbs, particularly the hands versus the right foot. The ANOVA on distortion revealed Subject

11 again as an outlier. The test resulted in a main effect of speed ( F(1, 9) = 12.45, p < 0.01, ¯x slow = 0.012, ¯x fast = 0.020 ) and an interaction between limb and pattern type

( F(1, 9) = 8.52, p < 0.01; Figure 9 ). The ANOVA on coefficient of variation had to exclude both Subject 11 and Subject 15. After exclusion, this ANOVA revealed a main effect of speed ( F(1, 9) = 40.65, p < 0.01, ¯x slow = 0.031, ¯x fast = 0.040 ), a limb effect

( F(2, 18) = 12.77, p < 0.01, ¯x right hand = 0.036, ¯x left hand = 0.031, ¯x right foot = 0.038 ), a pattern effect ( F(2, 18) = 4.59, p < 0.03, ¯x 3:2:4 = 0.036, ¯x 4:2:3 = 0.036, ¯x 4:3:2 = 0.033 ), and an interaction between limb and pattern type ( F(4, 36) = 35.30, p < 0.01; Figure 9 ).

(A)

Limb Absolute Distortions By Polyrhythmic Pattern

0.04

0.03 Left Hand 3 4 3 0.02 Right Hand 3 4 4 0.01 Right Foot

2 2 2 AbsoluteDistortion 0 3:2:4 4:2:3 4:3:2 Polyrhythmic Pattern

Figure 9: ANOVAs showing the limb by pattern interaction for absolute distortion and coefficient of variation values. The numbers next to each point represent the beat pattern that limb was performing during that polyrhythm. (Continued) 46

Figure 9: Continued. (B)

Limb Coefficient of Variation By Polyrhythmic Pattern

0.054 0.049 4 0.044 3 0.039 4 3 Left Hand 0.034 3 4 Right Hand 0.029 2 2 2 Right Foot

Coefficient Coefficient ofVariation 0.024 3:2:4 4:2:3 4:3:2 Polyrhythmic Pattern

Covariates on measures of performance

A Pearson product-moment correlation was computed to test if there was a negative relationship between high frequency heart rate variability and absolute mean distortion and the coefficient of variation. We found a marginally significant moderate negative correlation of Day 1 heart rate variability with 3-limb distortion (r = -0.496, p = 0.051, n = 12, one-tailed). There were other moderate correlations, including 3-limb distortion with Day 4 baseline heart rate variability (r = -0.426, p = 0.08, n = 12, one-tailed), but given our small sample size, these correlations did not reach the statistical significance (r ≥ 0.497).

A Pearson product-moment correlation was also computed between measures of performance and instances of parallelism. This resulted in two 5 x 5 correlation matrices

(one matrix for parallelism vs. absolute distortion, and one matrix for parallelism vs. coefficient of variation). None of the correlations for distortion were significant and most

were below r = 0.3; however, we found that all the correlations in the 5 x 5 matrix were

negative. When examining values for coefficient of variation, all the correlations were

positive, eleven were significant (r ≥ 0.576, n =12), and two were marginally significant.

However, given the limited power of our study we are hesitant draw conclusions from

these results. All the correlations and corresponding p-values can be seen in Table 3 and

Table 4.

Table 3 Correlations of Parallelism and Absolute Distortion

Distortion Instances of Slow Fast Parallelism 3-Limb Bimanual Overall Conditions Conditions -0.216 -0.214 -0.225 -0.344 -0.178 Overall (0.501) (0.505) (0.482) (0.274) (0.579) -0.185 -0.215 -0.210 -0.315 -0.168 Slow Conditions (0.564) (0.502) (0.513) (0.318) (0.603) -0.221 -0.178 -0.210 -0.327 -0.165 Fast Conditions (0.490) (0.580) (0.513) (0.300) (0.609) -0.313 -0.227 -0.284 -0.313 -0.253 Bimanual Conditions (0.322) (0.477) (0.371) (0.322) (0.428) -0.149 -0.187 -0.176 -0.326 -0.126 3-Limb Conditions (0.645) (0.560) (0.585) (0.301) (0.696) Numbers in parentheses are statistical significance levels

Table 4 Correlations of Parallelism and Coefficient of Variation

Coefficient of Variation Instances of Slow Fast Parallelism 3-Limb Bimanual Overall Conditions Conditions 0.781** 0.372 0.616** 0.515 0.661** Overall (0.003) (0.233) (0.033) (0.086) (0.019) 0.758** 0.371 0.603** 0.556 0.615** Slow Conditions (0.004) (0.235) (0.038) (0.061) (0.033) 0.687** 0.315 0.535 0.381 0.617** Fast Conditions (0.014) (0.319) (0.073) (0.222) (0.033) 0.572* 0.176 0.399 0.302 0.449 Bimanual Conditions (0.052) (0.585) (0.198) (0.341) (0.143) 0.808** 0.432 0.662** 0.570* 0.701** 3-Limb Conditions (0.001) (0.161) (0.019) (0.053) (0.011) Numbers in parentheses are statistical significance levels * p ≈ 0.05, ** p < 0.05

Discussion

Most previous work on bimanual tasks found that the limbs could not perform

independently of one another (e.g. Klapp et al., 1985; Jagacinski et al., 1988; Summers,

Ford, & Todd, 1993). However, our study was able to constructively replicate Krampe et

al.’s (2000) findings that highly skilled individuals can demonstrate parallel limb

coordination when performing polyrhythmic tapping. All subjects in our experiment

exhibited some form of parallelism when performing the 3-limb polyrhythm, while most

subjects even showed parallelism during the bimanual patterns. We hypothesized that

these results were being driven by two potential factors. One factor was similar to

Krampe et al.’s (2000) study which showed that increasing performance speed resulted in

more parallel limb performance. In our experiment the 50 cycles per minute condition 49

(our fast condition) exhibited more instances of parallelism between limb pairings from participants in both bimanual and 3-limb polyrhythmic conditions than at 30 cycles per minute. The second factor was based on previous work by Jagacinski, Kim, and Lavender

(2009) that suggested when performing these polyrhythms, limbs further away from each other in perceptual-space would be more likely to be performing in parallel than limbs perceived as closer together. This hypothesis was supported when examining the 3-limb polyrhythmic conditions that utilized the use of the left hand, right hand, and right foot.

The data revealed that there was a higher prevalence of parallel performance between the hands and foot (42% decoupling) than between the two hands (19% decoupling).

The main results from our study can be predicted in terms of Korte’s Law. The breadth of this principle’s application in our perceptional system is illustrated by the fact it was originally used to describe the factors affecting how apparent motion occurred in vision and was then later shown to extend to auditory streaming phenomena as well

(Bregman, 1990). Following this trend we contend that Korte’s Law may be an organizational principle present in the perceptual-motor system as well (Klapp &

Jagacinski, 2011). Korte’s Law demonstrated that speed of stimulus presentation and stimulus distance (defined within the context of the perceptual domain being considered) predicts when stimuli will likely be separated into multiple perceptual units. A classic auditory streaming example involves three high tones and three low tones whose presentation alternates high-low. As tone presentation speed increases the single melodic perceptual stream will break apart, and the tones will form two separate perceptual groups with the high tones sequenced together and the low tones sequenced together

(Bregman, 1990). Our experiment is analogous to this in the perceptual-motor domain.

As participants perform the patterns faster, their performance’s speed passes a Korte velocity threshold at which the coordinative organization of the limbs doing the polyrhythm switch from a single integrated group to two or more independent groups.

This grouping mimics that of the high-low tone experiment, which suggests that Korte’s

Law may underlie both of these results.

When this threshold was reached during a 3-limb polyrhythm, coordination of the multiple limbs could take on various possible structures. The most basic structure observed was full integration, in which all limb pairings of the hands and right foot remained coupled to each other. The opposite of this structure was full parallelism in which the perceptual-motor system broke into three independent limbs (as if the three limbs were being controlled by three different motor sources/programs). Many participants performed coordinative structures that were somewhere in between these two extremes.

To better understand how various coordinative structures arise, consider the results of Summers et al. (1993). They argued that when performing bimanual patterns a likely strategy for subjects would be to subordinate control of one hand to the other hand.

In this manner subjects could simplify the task of error-correcting their performance by only needing to monitor the behavior of their dominant hand. This process is described by Pressing et al. (1996) as a figure-ground relationship between the limbs, which allows for the ground limb to perform more consistently than the figure limb. Corrections made to the dominant limb’s performance are reflected in the figure limb. Similarly in our

study some participants adopted a coordinative structure in which two limbs remained integrated to the third limb, but not each other. This third limb could be thought of as a central limb on which the other limbs’ performance depended. This single decoupling structure may be coping with the increased demands of maintaining the patterns at faster rates by subordinating the performance of two of their limbs to the third limb in a way similar to the results of Summers et al. (1993). We also observed many instances in which one limb completely decoupled from the other two, i.e. a mixed timing structure.

The limb performing in parallel to the remaining two formed its own independent coordinative unit while the remaining integrated limbs appeared to be coordinated as a pair. The presence of these two structures unique in our study exemplify that the perceptual-motor system can rely on more complex organizations to accomplish the goal of accurately maintaining multilimb coordination.

It is not clear yet what factors influence which coordinative structure is likely to emerge when parallelism occurs; however, Korte’s Law is likely a driving influence in those results. From the eight possible coordinative structures that could be observed in our 3-limb conditions, the structures where either one or both of the hands performed in parallel from the foot were most frequent. In the single decoupling case, we observed approximately five times more cases of the foot decoupling from one of the hands and either the left or right hand being the central limb. There was no preference as to whether the left or right hand was central, though the numbers suggest it depended on the polyrhythm being performed. When mixed timing occurred there was a clear bias towards both hands performing as an integrated unit separate from the foot. The full

distribution of coordinative structures is seen in Figure 2. These coordinative structures provide more support for a Korte based interpretation of how the limbs are organized in our perceptual-motor system since the distribution of these structures favors those where the furthest limb (the foot) functioned in parallel to either or both of the two limbs closest to each other (the hands).

Pattern effects on parallel performance

An interesting post-hoc question that arose was whether properties of the patterns themselves would drive what performance structure would emerge. It should be possible for the perceptual-motor system to take advantage of simple relationships between beat patterns to better coordinate the limbs performing them. The 4:2 component pattern, which was present in all the 3-limb polyrhythms, is reducible to a simple 2:1 pattern. We expected this reduction would result in higher prevalence of integration between the limbs that were performing that component. Phrased differently, the limbs performing the

4-beat and the 2-beat in a polyrhythm would be less likely to perform in parallel.

Similarly, the 3:2 component pattern has the distinct characteristic that the second beat of the 2-pattern falls perfectly between the second and third beat of the 3-pattern. The way these beats lineup in the 3:2 pattern make it relatively easier to perform as a unit and therefore could also result in less parallelism occurring between the limbs performing it.

Given these potential pattern effects, we tested the hypothesis that limb pairs performing the 4:2 and 3:2 component patterns had less parallel performance than limbs performing the 4:3 pattern. The ANOVA surprisingly revealed neither a main effect of

pattern nor a speed interaction with pattern. The test suggests that it is no more likely for limb pairs performing a 4:2 pattern to decouple than limb pairs performing a 4:3 pattern.

Even in the ANOVA for bimanual conditions, the results were the same. Strictly bimanual conditions of 4:2 were as likely to perform in parallel as the 4:3 and 3:2 polyrhythms. Furthermore, the proportion of parallel performance ( [number of parallel pairs in a group] / [total number of limb pairs] ) were very close for the bimanual conditions (39% for 4:2, 38% for 3:2, and 33% for 4:3) and for the component patterns in the 3-limb conditions (31% for 4:2, 36% for 3:2, and 36% for 4:3).

What is particularly surprising about these results is that previous studies have found that coordinating distinct movements that are dependent on different timings tend to simplify. In a study by Klapp, Nelson, and Jagacinski (1998), they trained a group subjects to perform a 3:2 polyrhythm by learning two beat-patterns separately for each hand. When tested on their ability to put the two hands together, subjects were unable perform the correct polyrhythm and instead simplified their hands’ beat ratios to either a

1:1, 2:1, or 3:1 pattern. Similarly, in a study done by Kelso, Southard, and Goodman

(1979) subjects were asked to move one of their hands from a starting position to a target.

Subjects could generate this movement quicker to a close target (low difficulty) than when asked to move a distant target (high difficultly). However, when they were asked to use the right and left hand to do both simultaneously (mixed difficulty), according to

Kelso et al. both movements synchronized as to when they started, reached peak velocity, and ended. These distinct movement patterns simplified to an integrated timing structure.

The results from Kelso et al. are interpreted differently by Schmidt and Lee

(2011) in their book Motor control and learning: A behavioral emphasis. According to their chapter on coordination, the two hands do not actually fully synchronize in their timing behavior, but rather the hand doing the high difficulty task “exerted a strong determining influence on the other limb” (p. 272). They provide another experiment to support this interpretation from a study in which subjects had to simultaneously move both their hands to two similar targets, with one of the hands having a hurdle placed in front of it along its movement path. The height of the hurdle was increased through the experiment. As expected the time it took the hand getting over the hurdle to reach its target increased with hurdle height. Surprisingly, the hand that had no hurdle in front of it increased relative to hurdle height as well. This showed that the two limbs had a tendency to produce coupled movement patterns, though not necessarily exactly the same. This interpretation suggests timing coupling between hands is strong, but not completely dependent.

Given these interpretations of coordinative coupling, it might not seem so impossible that in our study participants were not only able to perform 4:2 patterns in parallel, but also did so at the same rate as the more complex polyrhythmic patterns in the study. It is possible that participants adopted a “relatively parallel” performance mode from executing polyrhythmic conditions that enhanced decoupling between their limbs.

This parallel mode could have influenced performance of their 4:2 pattern. We do not know how much control a participant can have on this mode switching (if any), but

evidence from the auditory domain suggests there is an ambiguity in when stimuli can be perceived as integrated or parallel.

In Bregman’s book chapter on Sequential Integration (1990, p. 59-61) he discusses an experiment in which subjects listened to a two tone alternating sequence in which one tone’s frequency kept sweeping up and down. They were asked to hear it as an integrated unit and signal when they heard it as two streams. They also performed the reverse of this task in which they were instructed to hear it as two separate streams and signal when it perceptually integrated for them. These two boundaries were not the same

(i.e., hysteresis), and the difference between when these tones integrated or streamed could be modulated by speed. He stresses that at slower speeds the difference between these boundaries is great enough that “listeners have their choice about whether to hear the sequence as one or as two streams” (1990, p. 59).

The participants in our study may have experienced an analogous phenomenon.

Once participants were able to perform one of the polyrhythms in a parallel mode, they changed their structuring of other conditions to parallel perceptual-motor coordination.

Even the 4:2 pattern which would typically favor an integrated structure between the two limbs was influenced from this representational change, which is why we failed to find significant differences between instances of parallelism for all three pattern types (4:2,

3:2, & 4:3). Evidence of representational changes can be seen in a study replicating Kelso et al.’s (1979) study in which participants in the mixed difficulty condition of this experiment were given feedback on their limb’s performance with a Lissaous plot that integrated their easy-target and difficult-target hand movements into a single visual

representation. This study found that given this integrated feedback subjects could generate dissimilar timing in their hands’ movements to the two targets (Shea, Boyle, &

Kovacs, 2012). Complex interlimb coordination can be achieved regardless of context driven organization (e.g. timing relations in the task) when subjects use a different representation of the task.

In addition to exploring how the component patterns in the polyrhythms might affect parallel performance, we tested whether there might be a difference in parallelism between the bimanual conditions and the 3-limb polyrhythmic conditions. We hypothesized that the added complexity of coordinating an additional limb (i.e. the perceptually-distant foot) in the 3-limb patterns would result in more parallel performance. The test comparing the prevalence of parallel performance in the two types of conditions found no significant effects of bimanual against 3-limb polyrhythms, and no interaction effects with speed. Even with the added complexity of coordinating the foot, the rate of parallelism was comparable between bimanual and 3-limb performance at both slow and fast speeds. The proportion of limb pairs that performed in parallel for the bimanual conditions was 34%, and for 3-limb conditions it was 33%. These findings suggest the perceptual-motor system handled limb coordination similarly under both complexity contexts, with the only difference being that parallel performance favored pairs that involved the foot when it was present.

We did find a difference when testing the prevalence of decoupled pairs in the bimanual conditions to hand-hand decouplings in the 3-limb conditions. The ANOVA showed that the bimanual conditions (i.e., strictly hand-hand limb pairs) were exhibiting

more parallel performance than when the hands were in a 3-limb context (33% of the hand-hand pairs decoupled in the bimanual conditions versus 19% in the 3-limb conditions versus). If Korte’s Law is governing this behavior, one would conclude that the perceived distance between the hands is not constant. Instead, the perceived distance between the hands is less in the 3-limb context. This smaller distance resulted in the reduced hand-hand parallelism that we observed in 3-limb conditions. In other words, we hypothesize that the perception of interlimb distances varies as a function of the entire set of actions being coordinated. This is a hypothesis that will require much more testing.

Based on all these results, we interpret that the challenge of interlimb independence is guided by the cognitive limitations of the perceptual-motor system. For many drummers it is challenging to accomplish what one drummer described as “the holy grail of performance”, coordinating each of our four limbs independently of one another.

Still, parallelism of some form may be more attainable than previously thought. It might not be limited by the number of limbs being coordinated, though according to previous works, timing relations between those limbs may favor simplified structures. However, studies involving perceptual-motor tracking have shown that integrated feedback might overcome timing limitations in coordinating disparate limb movements. When disparate movements need to be generated rather than tracked, performance speed and perceptual- distance affected how frequently limb pairs exhibited parallelism.

Variability of performance

The effect of polyrhythmic complexity on performance consistency in bimanual tapping has been analyzed in many previous experiments. These relationships were summarized in a review article by Jagacinski, Peper, and Beek (2000) that showed that as rhythmic complexity rose performance instability rose as well. To define how unstable participants’ performance was, experimenters calculated the coefficient of variation for the beat-intervals each hand was generating. The beat intervals were defined for the left and right hand by the polyrhythm and speed being performed, with certain relationships between beats in a polyrhythm resulting in much more variable performance.

We examined this complexity effect on performance in our own study; we therefore calculated coefficients of variation for the beat-intervals in our polyrhythmic conditions. However, we incorporated an additional measure of variability in our study, mean absolute distortion (Summers, Rosenbaum, et al., 1993). The value of this measure, which is the difference between a subjects’ performed beat-interval duration and its respective ideal duration, gave us a measure of how much the subject distorted the ideal pattern. Utilizing both of these measures of performance we were able to test polyrhythmic complexity effects.

We analyzed the effects of complexity on variability and distortion in both bimanual and 3-limb polyrhythmic conditions. The results from the bimanual condition mostly aligned with previous findings; coefficient of variation values for bimanual performance showed both a pattern effect and a speed effect (Figure 7). The speed effect consisted of larger coefficient of variation values at the faster speed, and the pattern

effect was driven by larger coefficient of variation values for the 4:3 polyrhythm. The results suggested that the 4:3 relationship is not just the most complex in our study, but also that 3:2 and 4:2 were comparable in difficulty to produce. These same results were found when looking at absolute distortion in bimanual performance. Speed was found to contribute to polyrhythmic distortion marginally, with faster performances resulting in more distortions. The polyrhythmic pattern being performed was found significant in determining differences in distortion values. The 4:3 pattern was the most distorted polyrhythm while the 3:2 and 4:2 were comparable. These results differ somewhat from the articles reviewed in Jagacinski et al. (2000) with regard to how the 3:2 and 4:2 patterns behaved. By their definition the 4:2 rhythmic relationship is reducible to a simple

2:1 rhythmic relationship and therefore should result in the lowest values of variability and distortion. Our findings contradict this result in that the 4:2 and 3:2 pattern were equally simple or challenging to perform.

When analyzing these same variability measures for the 3-limb polyrhythms, the data again showed that participants had higher values for distortion and coefficient of variation when performing at the faster speed. It is relevant to note this effect is present even though participants were not performing that much faster between the two speed conditions (30 cycles per minute versus 50 cycles per minute) compared to the larger range used in Krampe et al.’s (2000) experiment (their slowest condition was about 7 cycles per minute, while their fastest condition was about 75 cycles per minute for a 4:3 rhythm). In addition, after removal of an outlier subject in the coefficient of variation data, a marginally significant pattern effect emerged. The pattern effect was driven by the

4:3:2 polyrhythm (right hand = 4, left hand = 3, and foot = 2) possessing lower coefficient of variation values than the 3:2:4 and the 4:2:3 polyrhythms, both of which appeared to be of equal difficulty to participants. Since the relationship of the beat patterns is the same in each of the three polyrhythms, we interpret this result as suggestive that in this case the main difference between the complexities of the three polyrhythms may actually have to do with the foot component of the performance.

Some participants noted that keeping a 2-beat on the foot is not unlike the typical rhythm keeping they are used to doing with their foot during drumming performances.

Therefore, a potential explanation for the pattern effect observed is that participants struggled when their foot performed either of the two higher beat-pattern components in the more challenging polyrhythmic conditions, i.e. the 4- and 3-beat on the foot. Both of these conditions involve the foot in the more difficult 4:3 rhythm with one of the hands.

This interpretation was supported by our analysis on individual limb performance within each polyrhythmic condition. Analysis on distortion revealed that the foot pattern was most distorted when performing the 3-beat or the 4-beat. The most inconsistent performance for the foot was when performing the 4-beat pattern (Figure 9). Verbal reports from some participants suggest that the reasons for why performing either the 4- or 3-beat on the floor is challenging may differ for the two patterns. Relative to the other beat patterns, the 4-beat’s tapping frequency was the most physically challenging to participants. Most participants did not express this same issue when considering the 3- beat, but rather thought it was difficult to maintain because they were used to “keeping

the beat” with their foot. That particular description seems to point to some cognitive challenge of coordinating the 3-beat onto the foot.

We examined this further by testing the effects of foot presence. We did this by comparing the distortion and coefficient of variation values in bimanual-only conditions to hand-hand performance in the context of a 3-limb polyrhythm (e.g., 4:3 alone against the 4:3 component of the 4:3:2). The comparison revealed that having the foot present during polyrhythmic conditions resulted in higher distortion and coefficient of variation values in participants’ hands. Essentially, it was more challenging for subjects to maintain their hands’ beat patterns if they were also required to coordinate the foot with them. Additionally, we found an interaction between foot presence and speed (Figure 8).

During the faster conditions the 3-limb hand-hand performance was more distorted and more variable than the strictly bimanual conditions. This supports the notion that coordinating the hands while also coordinating the foot becomes more difficult at the faster performance speed. This is in contrast to the direction we were hoping to find this interaction since we hypothesized the foot would be more likely to perform in parallel to the hands at the faster speed based on our Korte description. As a result of this, we expected to see greater stability in the hands’ performance due to reduced interference on the hands’ patterns from the foot.

Covariates of individual differences

A very surprising finding in our study was the large extent to which performance could vary from subject to subject. Some subjects overall favored more integrated performance, while one subject performed almost completely in parallel for every condition. Variability measures also varied widely between drummers in this study.

Subject 11 was a particularly interesting case. His performances showed moderate instances of parallelism, but his absolute distortion values and coefficient of variation values were more than 4 standard deviations above all the others in the study. We had to exclude him almost completely when analyzing different effects on these variability measures. Subject 15 was another interesting case, in that this drummer performed almost exclusively in parallel, but his distortion and variability measures were not that different from the rest of our participants, with one or two exceptions. This particular subject makes it unclear whether there is a direct relationship between parallelism and consistent performance.

We attempted to explain these individual differences by testing some possible covariates with participants’ performance. Based on our Korte’s Law interpretation of the results, limbs perceived as more perceptually distant from each other will exhibit more parallelism. Therefore, it would be reasonable to conclude that participants who were taller may have exhibited more parallel performance. We did not have many participants in our study, but the heights of these participants varied enough to be able to test whether there was any correlation between the two. We correlated height with overall instances of parallelism in slow conditions, fast conditions, bimanual conditions, and 3-limb

conditions. Though many correlations were moderately high, the only correlation to reach significance given our limited power was between bimanual performance and height

(r = 0.65, p = 0.02). We interpret this result as suggestive that taller participants perceived the distance between their hands as longer and thus had a larger Korte’s d in the perceptual-velocity equation. This larger d would result in taller participants exhibiting more parallel performance between their hands.

In contrast, the relationship between height and 3-limb conditions was not as strong (r = 0.34, p = 0.27). Both bimanual and 3-limb conditions showed nearly the same percentage of limb pair decouplings (33% and 34%, respectively), so something about the

3-limb context is different enough that height had a lesser association with the coordinative structure that arose. A possible explanation is that in the 3-limb polyrhythms the foot, which has a larger Korte’s d relative to the hands, is already more likely to decouple than the two hands. If we assume the perceptual-motor system’s default organization is to coordinate the foot in parallel, then the foot would not become more parallel simply because of being taller, hence the weaker relationship between height and

3-limb parallelism.

In addition to height, we tested whether individual differences in performance correlated with high frequency heart rate variability. We found some moderately strong correlations (r ≥ 0.4), but most did not reach statistical significance. It is possible that the relationship between performance and baseline heart rate variability measures was not fully captured by our study due to limited power. Even given this limitation, we were able to identify a statistically significant positive correlation (r = 0.587, p < 0.05) between

Day 1 baseline heart rate variability and parallelism in slow performance, as well as a significant correlation between Day 4 baseline heart rate variability and bimanual parallelism (r = 0.578, p < 0.05). Both slow performance and bimanual performance are conditions that favor integrated coordination between the limbs; therefore, the relationship found between parallelism and heart rate variability in these conditions suggests that heart rate variability is related to participants’ Korte’s thresholds. One hypothesis is that high heart rate variability is associated with lower Korte thresholds in participants, which led to the individual differences observed in participants that demonstrated parallel coordination when the system was not being pushed towards parallelism by factors such as speeding up movement. High frequency heart rate variability may be a means to predict which participants will adopt parallelism more easily.

We also found a marginally significant negative correlation between 3-limb distortion and Day 1 baseline heart rate variability (higher heart rate variability relates to lesser distortion, r = -0.496, p = 0.051, one-tailed). However, none of the other correlations between performance variability and heart rate variability were significant, so we are hesitant to draw conclusions. We were expecting to find stronger evidence for a relationship between heart rate variability and other performance measures, since we found some evidence for a relationship between heart rate variability and parallelism.

In addition to heart rate variability as a measure of individual differences, we hypothesized that one of the reasons our perceptual-motor system switches to a parallel mode is to control performance variability. We examined the correlation between

instances of parallelism and performance and found a positive significant correlation between how much parallelism a subject exhibited and how variable their performance was (i.e., measured by coefficient of variation), as well as other relationships seen in

Table 4. None of the correlations with absolute distortion were significant, but all of them were negative.

Given the limited power in our study we are extremely cautious to draw conclusion from all the correlations we tested due to an inflated probability for Type I errors. However, as a strictly exploratory analysis we believe these results suggest there is a relationship between heart rate variability, parallelism, and performance. Heart rate variability might relate positively to individuals’ ability to adopt parallelism. The advantage of this mode is to keep mean performance timing closer to the desired pattern

(i.e, negative correlation between parallelism and distortion), but it comes at the cost of being more variable in performance (i.e., positive correlation between parallelism and coefficient of variation). Even though our correlations were not strong enough to be conclusive, this interpretation seems to be supported by the negative correlations found between heart rate variability and 3-limb distortion. The hypothetical model can be seen in Figure 10.

Figure 10: The diagram above illustrates possible relationship between parallelism, heart rate variability, and performance measures.

Biomechanical effects on parallelism

The major argument of our experiment is that parallel coordination is driven by perceptual-motor factors relating to Korte’s Law. However, it could be that biomechanical factors influence inter-limb coordination. In particular, the foot movements are being generated by the much larger muscles of the leg which may have a lower frequency bandwidth then the smaller muscles of the arm, wrist, and hand. Since the foot would have a harder time keeping up performance at faster speeds, it is possible that biomechanics is affecting why the foot appears to more often perform in parallel to the hands, i.e., biomechanically driven decoupling rather than cognitively driven.

While we certainly agree that biomechanical limitations can have an effect on foot performance at fast speeds, our data do not suggest that the leg performance was fast enough for biomechanical limitations to be a major factor. Our data argue for a more cognitive interpretation, the evidence of which can be seen in Figure 2 showing the limb and speed effect on parallel performance in 3-limb polyrhythmic conditions. What is important to notice is that parallel performance still occurred more frequently between hand and foot pairings at the 30 cycles per minute speed where the foot performed only 1,

1.5, or 2 taps per second. There is a statistically significant difference between hand-foot and hand-hand coordination ( t(11) = 2.92, p < 0.01, ¯x HF/2 = 0.96, ¯x HH = 0.33 ) at this slow speed where we expect the least (if any) biomechanical effects. We suggest this difference would not be driven by the biomechanics of the foot trying to keep up to the hands’ performance; instead, this serves as support that even at the slow performance speed, differences in the representation of the hands and foot in perceptual-space result in more parallel coordination to emerge.

Additionally, in Figure 2 there is no interaction between hand-hand parallelism as a function of speed. Biomechanical limitations should especially increase instances of parallelism for the hand-foot pairs at the faster speed. This trend is not present in Figure

2; there was not a statistically significant interaction. Similarly, an interaction would also be predicted for absolute distortion and coefficient of variation with speed and limb performing, in which the foot should become more variable than the hands at the faster performance speed. These interactions were not found (distortion: F(2, 18) = 1.31, p = 0.30; coefficient of variation: F(2, 18) = 0.89, p = 0.43); the only interactions that

were found can be seen in Figure 9. The right foot distorted the performance of the 3-beat pattern the most, but was most variable when performing the 4-beat pattern. This does show that there are biomechanical differences in how the limbs are dealing with coordinating the pattern, but these differences do not seem to reflect the cognitive representations of this coordination. Therefore, our data do not support that parallelism for hand-foot pairs was mostly driven by biomechanical limitations.

Another biomechanical factor to consider is how timing relations between disparate limbs is coordinated. An objective of skilled performance is reduced variation in performance. In tapping tasks, variation comes in the form of interbeat interval inconsistencies that would change the beat-structure of the desired rhythmic pattern.

Error in these perceptual-motor programs may come in two forms as described by Wing

(1990) in his book chapter on timing in responses. One is in the form of variance in the central timekeeper. Timekeepers are described by Wing (1990) as a perceptual system that “emits pulses each of which initiates a motor response” (p. 470). Coordinating these tapping tasks would require our perceptual-motor system to maintain timekeepers for the appropriate interbeat interval lengths between the successive responses within each limb if parallel, or different intervals between each limb if integrated.

The second type of contributor to performance variation is motor delay variability. Motor delays are the time it takes the signal from the timekeeper to reach the appropriate limbs or muscles in a tapping response. Motor delays are added onto the central timekeeper’s initial pulse variability and account for the overall response variability we observe in these rhythmic performance studies. There is an interesting

aspect about motor delay variability observed in tapping studies which separates it from timekeeper variability. From our own results, variability in performance (measured by the coefficient of variation) increases with performance speed; however, Wing noted in his chapter that motor delay variability does not scale with speed. Motor delays are more or less constant regardless of how quickly successive responses need to be made. This important distinction has major implications for the way that participants would maintain a rhythm at various performance speeds.

If participants expect to maintain the rhythmic pattern under various speeded conditions, they would need to account for the motor delay added to their timekeeper signal in the overall resulting response. Imagine a fully integrated tapping performance.

At slower speeds this motor delay will be a very small percentage of the interbeat interval between timekeeper responses. At faster speeds the motor delay may actually distort the rhythmic pattern being produced if it results in taps being generated past their desired arrival. Therefore, to account for this, participants’ timekeepers would need to adjust when the signal is sent to the limbs performing by triggering them sooner in their cognitive program. Two hands performing parts of a polyrhythm would probably share similar motor delay times, so the timekeepers for their hands’ responses would shift equally to preserve the cognitive representation of the limbs performing. However, when the motor delays are not comparable as is the case for hand-foot relations, then distortions to the timekeeper intervals for each limb would be dissimilar, and could result in distorted mental representations of the patterns being attempted (Figure 11). If the perceptual-motor system is to retain an effective timekeeper representation of the

polyrhythm being performed, it would be easier for it to separate the integrated representation into two parallel streams of control, one for the hand and its motor delays and one for the foot and its delays. Then the speed adjustment would simply consist of shifting the foot stream relative to the hand stream.

Figure 11: The principle of rhythmic distortion on the performance of a 3:2 polyrhythm is seen here with vertical bars representing the timekeeper signals. Motor delays are represented by the slanted lines, with longer lines representing longer delays. Hand taps (H) and foot taps (F) are triggered at different points in the timekeeper perceptual-motor programs to achieve ideal performance. In the integrated plan the overall rhythmic pattern looks very different than the ideal pattern, whereas the parallel plans allows for little distortion within each perceptual stream and still achieve the desired pattern by simply shifting the foot’s perceptual-motor plan.

Our study did not directly test whether rhythmic distortion is accountable for the changes in coordinative performance structures seen in participants, though we did find

that limb pairs incorporating the foot performed in parallel more often than bimanual limb pairs. A better test of this principle would be a study in which the same polyrhythm is performed by a strictly bimanual limb pair and a hand-foot limb pair, and compare whether parallelism occurs differentially in the two cases. If rhythmic distortion were driving parallelism, then we would expect to find hand-foot polyrhythmic performances showing more parallelism at faster speeds than hand-hand performances.

However, we argue that since Figure 2 clearly demonstrates no interaction between speed and limb pairing on parallelism, rhythmic distortion would not be an adequate explanation of our results. An interaction would be predicted by this hypothesis since distortions would be at their greatest in hand-foot pairs performing at 50 cycles per minute. The lack of interaction in our experiment is support that neither biomechanical limitation nor rhythmic distortions are the primary factor in the prevalence of parallelism we observed in limb pairs involving the foot. Instead the observed effects are better interpreted in terms of Korte’s Law.

Variability effects on parallelism

Neither biomechanical limitations nor rhythmic distortion could account for why bimanual polyrhythmic performances might display parallelism. Instead, a possible explanation may have to do with how our perceptual-motor program is dealing with variability. In a study by Krampe, Engbert, and Kliegl (2002) they examined the effects of speed of performance on interbeat interval variances for expert and amateur pianists performing a 4:3 bimanual polyrhythm. In their experiment they showed that variance for

interbeat intervals increased with interval length (i.e., longer intervals had larger variances). This variance affects performance when it is integrated, since pianists had to adapt their timekeeper intervals to the varying interbeat interval lengths produced by between hand taps. At faster speeds the interbeat intervals become very short, so Krampe et al. argue expert pianists adapt a parallel structure to “take advantage of isochronous within-hand structure and the related relatively long target durations” (Krampe, Engbert,

& Kliegl, 2002). The longer interbeat target durations within each hand presumably allow more time for error correction at fast speeds.

We do not completely agree with Krampe et al.’s interpretation, but argue something similar in our results. Recall we measured variability with the coefficient of variation, and showed that the relative variability of intervals lengths being produced by participants’ taps went up at the faster speed. Speed of performance not only increased variability in performance but it also decreased the interbeat interval length between tapping responses in the motor program. If bimanual performances were fully integrated it would require timekeepers of different interval lengths corresponding to the interbeat intervals between left and right hand taps. As those interbeat intervals shrink from speeding up and relative variability increases from speeding up, it would become very challenging for our perceptual-motor system to accurately reproduce the desired pattern consistently for the smallest intervals in the integrated pattern. The perceptual-motor system could split this integrated unit into two parallel units whose interbeat response intervals would now be larger than they were in the integrated pattern. The variability due

to speeding up would be reduced and have a less detrimental effect on the larger intervals produced by the parallel streams.

Conclusion

Though we appear to be capable of controlling our limbs independently, results from bimanual tapping in laboratory environments could not generally find evidence for it. Our study was able to confirm Krampe et al.’s (2000) findings that skilled drummers can in fact exhibit this form of control we call parallelism. The drummers in our study were able coordinate their hands and foot in complex polyrhythmic tasks. Even though participants’ performance still typically favored full integration between the limbs, when they performed faster their fully integrated coordinative structures changed into partially or fully parallel structures. We interpreted these organizational changes from a Korte’s

Law perspective. Speed and perceived-limb distance between limb pairs were the major determiners of the coordinative structure participants exhibited.

In addition to these effects, we still wish to explore how attention can drive the coordinative structures being exhibited. We wonder whether it is possible to induce specific parallel units in multilimb tapping tasks by having participants focus on specific components or limbs in their performance. We also wonder whether these results are restricted to skilled populations or can be applied to more general groups. Could training techniques be developed that exploit the way our perceptual-motor system handles performance information? A final question we may explore is whether there are neuron

groups we can detect with EEG that might classify people’s performance as parallel or integrated.

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