Western Washington University Western CEDAR The Edna L. Sterling Collection Western Libraries and the Learning Commons 1990 Polymetric Performance by Musicians Kate Grieshaber University of Washington Follow this and additional works at: https://cedar.wwu.edu/sterling_collection Part of the Music Education Commons, and the Music Performance Commons Recommended Citation Grieshaber, Kate, "Polymetric Performance by Musicians" (1990). The Edna L. Sterling Collection. 3. https://cedar.wwu.edu/sterling_collection/3 This Book is brought to you for free and open access by the Western Libraries and the Learning Commons at Western CEDAR. It has been accepted for inclusion in The Edna L. Sterling Collection by an authorized administrator of Western CEDAR. For more information, please contact [email protected]. 589758 GIFfOF THE RACHEL ROYSTON PERMANENT SCHOLARSHIP FOUNDATION OFTHE DELTA KAPPA GAMMA SOCIETY (J..'r\u.. L. Stzr,ltnq ~source (t"tM,r Polymetric Performance by Musicians by Kate Grieshaber A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 1990 Approved by Program Authorized to Offer Degree Date b. t.--,, 11, l'ffO PERMISSION In consideration of financial support received from the Rachel Royston Permanent Scholarship Foundation, I hereby grant permission to said Foundation and to any instit·1tion[sJ it may designate as Resource Center[s], to reproduce and distribute copies of all or any part of the following work during the full duration of its copyright, for purposes of study, scholarship, and research, in accordance with my obligations as a scholarship recipient: I understand I am entitled ·to retain copyright in the work, subject to the above grant of permission, and assume full respon­ sibility to disclose the existence of this permission to any sub- sequent publish~r, assignees, and licensees of the work • . DATED thisgL_ day of ~7 UNIVERSI1Y Of WASHINGTON Dare: December 13, 1990 We have carefully read the diMertatioo entid,Pd Polymetric Performance by Musicians _____________________________ubmitted by _K_a_t_e_G_r_ie_s_h_a_b_e_r________________ ~io partial fuUillmeot of the requirements of the degree 0L£_..J.D1J.o~c;_i,,t~o..1..r___J,l.o.1...f__.Pi;:__,ihu..1u·lL...1.011:.swot..µp..u.b.'I-Y----------• and recommend its acceptance. In support of this recommendation we present the following joint statement of evaluation to be filed with the dissertation. Kate Grieshaber has undertaken an investigation of musicians' complex motor activities, particularly two-handed performances of polymetric patterns found in music. Her subjects were highly trained percussiomsts and pianists. In addition to behavioral data, Ms. Grieshaber also obtained subjective opinions from each of the participants as to effectiveness and points of difficulty. What is especially important about this study is the use of computer graphics to reveal precise descriptions of performance patterns. Her data refine our understanding of the limits of timing control which musicians exercise during music performance, revealing that some performers demonstrate precision within ten milliseconds. She has demonstrated a clear understanding of the application of scientific procedures to musical problems. Her findings have import beyond music to theories of neural timing and motor behavior. Copyright by Kate Grieshaber 1990 Doctoral Dissertation In presenting this dissertation in partial fulfillment of the requirements for the Doctoral degree at the University of Washington, I agree that the library shall make its copies freely available for inspection. I further agree that extensive copying of this dissertation is allowable only for scholarly purposes, consistent with "fair use" as prescribed in the U.S. Copyright Law. Requests for copying or reproduction of this dissertation may be referred to University Microfilms, 300 North Zeeb Road, Ann Arbor, Michigan 48106, to whom the author has granted "the right to reproduce and sell (a) copies of the manuscript in microform and/or (b) printed copies of the manuscript made from microform." Date j University of Washington Abstract Polymetric Performance by Musicians by Kate Grieshaber Chairperson of the Supervisory Committee: Professor James c. Carlsen School of Music This study measured musicians' ability to perform complex motor activities, seeking to provide empirical foundation for theories of neural timing behavior. In individual sessions, each of twenty-nine right-handed undergraduate or graduate percussionists or pianists performed three polymeters (2:3, 3:4, and 4:5) with two hand combinations (L:R, R:L) in six cuing contexts: (1) Uncued, without having heard the pattern, (2) Pulse­ with the first pulse of each measure provided, (3) Imitate 1-in synchrony with a computer-generated pattern heard over a loudspeaker, (4) Continue/Pulse­ after matching the pattern, continuing with the first pulse of each measure, (5) Imitate 2-again matching the pattern, and (6) Continue/Uncued-after matching the pattern, continuing on without cues. Tap evenness scores (standard deviation around each beat) served as the dependent variable. Factors found to be significant included hand (right more accurate than left), meter (fast more accurate than slow), hand combination (left hand performed slow meter least accurately), pattern (2:3 more accurate than 3:4, with both more accurate than 4:5), and cuing context (imitation contexts were more accurate than contexts in which first beats were provided). These effects, however, are affected by significant interactions of hand/meter and hand/meter/pattern. Very high and consistently accurate performance was observed, with many subjects performing with standard deviations under 10 milliseconds. Some musicians performed some contexts with near mathematical precision and others with systematic variation (non-random lags and anticipations). In post-experiment interviews, subjects were asked whether they had difficulties with certain aspects of performance (e.g., hand difficulty, changing hand combination, mathematically precise stimuli). Subjects also were asked about relative difficulty of polymetric pattern and performance strategy use. These reports corresponded closely with empirical performance data. Subjects reported using tactile, visual, and auditory cues and verbal mnemonics, and often reported switching between focusing on one meter or hand and focusing on the resultant rhythm of both hands together. Although high correspondence between subjects' reported cognitive activity and motor production was observed, more baseline data are needed before formulating models of rhythmic perception. Findings have implications for musicians (especially educators) and researchers in various fields examining neural aspects of motor behavior. JI TABLE OF CONTENTS Page List of Figures vi List of Tables viii CHAPTER 1-HYPOTHESIS DEVELOPMENT 1 Introduction 1 Handedness Issues 8 Issues Related to Timing 11 Interactions of Handedness and Timing. 15 Cuing Context/Tapping Task 22 Proficiency ..... 25 Summary of Experimental Hypotheses 27 CHAPTER 2-ADDITIONAL ISSUES . 30 How Accurate Are the Best Performers? .. 31 Are There Identifiable Types of Errors? . 41 Is There a Pattern of Systematic Variation? ........ 43 Do Performers Descriptions of Accuracy Correspond to Their Actual Performance? . 50 What Strategies Do Performers Use? 51 Other Information ..... 57 TABLE OF CONTENTS (cont.) Page CHAPTER 3-METHODOLOGY 59 Experimental Design .. 59 Subject Selection .. 61 Data Collection Instrumentation .. 63 Pilot Study. 74 Procedures . 75 Critique of Methodology. 77 CHAPTER 4-PREPARATION OF DATA FOR STATISTICAL ANALYSIS . 80 Removing Artifacts 80 Displaying the Data in Pictorial Timelines ........... 83 Extracting "Complete" Measures 85 Normalizing Data/Superimposing Measures .•........ 86 Computing Tap Evenness 90 CHAPTER 5-STATISTICAL ANALYSIS: RESULTS AND DISCUSSION ..... 98 Preparation for Analysis of Variance 98 Findings and Discussion of Experimental Hypotheses ............. 103 iii TABLE OF CONTENTS (cont.) Page CHAPTER 6-DESCRIPTIVE ANALYSIS: RESULTS AND DISCUSSION ..... 116 Accuracy 116 Identifiable Types of Error 122 Evidence of Systematic Variation 124 Descriptions of Performance Accuracy 134 Descriptions of Strategies Used. 143 Additional Subject Comments 148 Summary . 159 CHAPTER ?-SUMMARY, IMPLICATIONS, AND RECOMMENDATIONS .•... 160 Limitations 161 Summary and Implications of Research Findings. 169 Recommendations. 182 Conclusion 185 BIBLIOGRAPHY . 187 APPENDIX A-GLOSSARY 209 APPENDIX B-SELECTED EXAMPLES OF MUSIC FEATURING POLYMETERS ............ 213 iv TABLE OF CONTENTS (cont.) Page APPENDIX C-FORMS AND INSTRUCTIONS 220 Solicitation Flyer 221 Solicitation Letter. 222 Solicitation Letter Response Form. 223 Consent Form 224 Instructions to Participants 226 Edinburgh Handedness Inventory 227 Musical Background and Experience Inventory 228 Post-Experiment Interview Form . 229 APPENDIX 0--VIDEO MONITOR INSTRUCTIONS 230 APPENDIX E-COMPUTER PROGRAM DESCRIPTIONS . 233 APPENDIX F-SAMPLE STATISTICAL SUMMARY SHEET 237 APPENDIX G-INDIVIDUAL ACCURACY SCORES . 240 APPENDIX H-SUBJECT RESPONSES AT EXIT INTERVIEW. 247 V LIST OF FIGURES Number Page 1 Example of the Polymeter Two Against Three (2:3) . .... 2 2 A Ga Tune with Rhythmic Accompaniment 3 3 Examples of Polymeters in Music 4 4 Comparison of 3:4 and 4:3 17 5 Summary of Cuing Contexts 24 6 Experimental Design 60 7 Data Collection Configuration 64 8 Two Views of the Dual Pulse Recorder.