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 By 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 ii 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. iv 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 v 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 ix 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