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Violin Pedagogy and the Physics of the Bowed String

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Violin Pedagogy and the Physics of the Bowed String Violin Pedagogy and the Physics of the Bowed String by Alexander Rhodes McLeod A thesis submitted in conformity with the requirements for the degree of Doctor of Musical Arts Faculty of Music University of Toronto © Copyright by Alexander Rhodes McLeod 2014 Violin Pedagogy and the Physics of the Bowed String Alexander Rhodes McLeod Doctor of Musical Arts Faculty of Music University of Toronto Abstract The paper describes the mechanics of violin tone production using non-specialist language, in order to present a scientific understanding of tone production accessible to a broad readership. As well as offering an objective understanding of tone production, this model provides a powerful tool for analyzing the technique of string playing. The interaction between the bow and the string is quite complex. Literature reviewed for this study reveals that scientific investigations have provided important insights into the mechanics of string playing, offering explanations for factors which both contribute to and limit the range of tone colours and dynamics that stringed instruments can produce. Also examined in the literature review are significant works of twentieth century violin pedagogy exploring tone production on the violin, based on the practical experience of generations of teachers and performers. Hermann von Helmholtz described the stick-slip cycle which drives the string in 1863, which replaced earlier ideas about the vibration of violin strings. Later, scientists such as John Schelleng and Lothar Cremer were able to demonstrate how the mechanics of the bow-string interaction can create different tone colours. Recent research by Anders Askenfelt, Knut Guettler, and Erwin Schoonderwaldt have continued to refine earlier research in this area. ii The writings of Lucien Capet, Leopold Auer, Carl Flesch, Paul Rolland, Kató Havas, Ivan Galamian, and Simon Fischer are examined and analyzed. Each author describes a different approach to tone production on the violin, representing a different understanding of the underlying mechanism. Analyzing these writings within the context of a scientific understanding of tone production makes it possible to compare these approaches more consistently, and to synthesize different concepts drawn from the diverse sources evaluated. iii Acknowledgements I would like to sincerely thank Dr. Cameron Walter, Dr. Robin Elliott, and Prof. Annalee Patipatanakoon, each of whom offered many hours of patient help and instruction. The main chapter of this paper could never have come together without the help of Dr. Stephen Morris, who patiently walked me through many aspects of the physics which eluded or confused me, or Jason Leung, who challenged and helped me to further expand my research. To Steven Dann, my most recent viola teacher, go many thanks for the inspiration to continue developing as a violist, and for the patience with my divided attention, and to Eric Nowlin, for the opportunity to put some of my ideas into practice in the teaching studio and the guidance which helped me to do so. I would also like to thank Katherine Rapoport, without whom I would never have become a musician, and whose inspired approach to technique set me on the path that ended in this paper, and Johannes Lüthy, who saw me through the most difficult time in my life, both musically and personally, with great kindness and patience. I hope that my own teaching will follow the wonderful examples set for me by each of these four great teachers. My quartet-mates, Sarah Steeves, Linnea Thacker, and Alexa Wilks, who have made playing such a pleasure these last four years, will always have my gratitude for helping me through many setbacks, listening to me rant and rave about the difficulties of writing, and lightening many days with laughter and great music. I would also like to thank my parents, Norman and Elaine McLeod, who have seen me through many difficult times and have always supported me both emotionally and financially, and my grandparents, who also offered much financial support and created a family in which music, physics, and teaching seemed like natural companions. Finally, I would like to profusely thank my loving and patient wife Victoria Leigh who represented an unflagging and invaluable source of support and inspiration during the writing of this dissertation, and my children, Ryleigh and Oliver, who literally give me a reason to get out of bed every morning. iv Table of Contents Introduction................................................................................................................................1 Chapter 1: Literature Review.....................................................................................................4 1 Helmholtz and the Founding of Modern Acoustics...........................................................5 2 Capet and Auer: Ending the 19th Century.........................................................................8 Flesch and Trendelenburg: Launching the 20th Century....................................................10 Pedagogy in the 1960s: Havas, Rolland and Galamian......................................................12 Schelleng, Cremer and the New Science of Violin Physics................................................14 Experimental Developments After Cremer.........................................................................20 Contemporary Pedagogy: Simon Fischer's Basics..............................................................22 Revisiting McIntyre and Schelleng.....................................................................................23 Physics in the Classroom: Cheri Collins.............................................................................25 Chapter 2: Physics for Violinists.............................................................................................26 Note, Tone, and Overtone: Understanding Sound Waves..................................................28 Underlying Forces: Tension, Friction, and Bow Force.......................................................32 1 Tension and Restoring Force...........................................................................................32 2 Static and Kinetic Friction...............................................................................................36 3 Bow Force and Bow Speed..............................................................................................38 The String in Action: Helmholtz Motion............................................................................40 1 Initiating the Stick-Slip Cycle..........................................................................................40 2 The Slip Phase..................................................................................................................41 3 The Stick Phase................................................................................................................43 The Ideal Limits of Helmholtz Motion...............................................................................44 The Rounded Corner: Tone Colour Explained...................................................................47 Friction, Contact Point and Timbre.....................................................................................49 The Bow Hair......................................................................................................................50 Other Factors Affecting the Tone.......................................................................................53 1 String Length and Timbre................................................................................................53 2 The Fingers of the Left Hand...........................................................................................54 The Bow Stick.....................................................................................................................54 v Putting it all Together..........................................................................................................57 Chapter 3: Analysis of Twentieth-Century Pedagogical Works..............................................61 Capet...................................................................................................................................63 Auer.....................................................................................................................................66 Flesch..................................................................................................................................68 Havas...................................................................................................................................71 Rolland................................................................................................................................75 Galamian.............................................................................................................................80 Fischer.................................................................................................................................84 Conclusion...............................................................................................................................89 Ideas for Future Research....................................................................................................90 Bibliography............................................................................................................................93 Appendix: Exercises
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