How important are torsion modes in bowed-string dynamics?

Abstract

In spite of the venerable history of bowed-string research, several aspects are still inadequately clarified. The importance of torsion modes on the motion regimes of bowed strings is one such issue. Experiments involving torsion are difficult to perform and most of the results available pertain to numerical simulations. The authors’ approach differs from previous efforts in two main aspects: (1) the development of a computational method quite distinct from the classic wave-propagation approach pioneered by McIntyre, Schumacher, and Woodhouse and (2) an extensive and systematic analysis of the coupling between torsion and transverse motions. The numerical simulations are based on a modal representation and a friction model that enable accurate representations of the stick-slip friction forces and of the string dynamics, in both time and space. Many relevant aspects of the bowed-string can be readily implemented, including string inharmonic behavior, finite bow-width and torsion effects. Concerning the later aspect, a realistic range of the wave-speed ratio α≡CTors/CTran=2∼7 is investigated, for several values of the bow velocity and normal force. The results suggest that torsion modes can affect both transient durations and steady state regimes, in particular when α<4. Gut strings should then be particularly prone to torsion effects.