Date Published: February 4, 2019
Publisher: Public Library of Science
Author(s): Robert Mores, Jefferson Stafusa Elias Portela.
Research on bowed string motion focuses on transverse waves rather than on torsional waves. These are believed to play only a minor role for stabilizing vibrations and no role for perception. Here, torsion is measured on both sides of the bow contact point for a variety of bridge-bow distances on a cello string. Every periodic string release is preceeded by a reverse torsional motion independent from bowing position or dynamics. Transverse and torsional motions are coupled and there are cases of stabilization, but also cases of perturbation or surrender. Structural and timing analyses of torsional waves suggest that the earlier concepts of differential slipping can be essentially confirmed while the concept of Schelleng ripples cannot be confirmed and the concept of subharmonics is under question.
In bowed string motion not only transverse waves but also torsional waves are excited due to the tangentially applied force at the surface of the string. Early observations of torsion date back more than 100 years as reported by Cremer, chap. 6.1 in . String torsion is generally believed to have little impact on sound, because a rotating string itself will not radiate. The body of the instrument will not radiate either, because the moment to the bridge as determined by the string diameter is very small . Torsion is nevertheless believed to have a stabilizing effect on periodic bowed-string motion . Torsion has therefore played a role in models and simulations of bowed strings. The most recent discussion concludes in the need for more elaborate friction models that could possibly be combined with the already investigated effects of a limited bow width . While these models gain in fidelity, this study seeks to draw some conclusions from experiments and to revisit the relation of general observations and existing concepts. Among these concepts, which relate to torsion, are bow force limits, Schelleng ripples, subharmonics and Friedlander’s instability, limited bow hair width and differential slipping, and friction models.
For most measurements a cello G steel string is used, mounted to a monochord and bowed by a real bow. The monochord is preferred over a real cello because incorporated body resonances would otherwise increase the complexity of vibrational modes and aggravate the interpretation of impulse patterns and stick-slip interactions. String excitation is measured underneath the contact point and string torsion is measured in the vicinity of the contact point, both via electric pick-ups. This location is preferred as to picture impulse patterns departing from and returning to the contact point.
Future numerical simulation might address the challenge to model the coupling between the different vibrational modes, and the transformation between them at the points of contact and termination. This might help to understand how the mechanisms of differential slipping truly work and how this gets synchronized with the main cycle. A lot of the corner rounding seems to be contributed by torsion, which should become clearer when simulation covers coupling and transformation between vibrational modes. Differential slipping is a key to the caused vibrational modes and necessary to adequately describe the m-HM cycles. A two-point contact model should be enough to represent the actions on the bowed string. Differences between up- and downstrokes are apparent. It might be promising to explore alternative concepts of modelling, for instance formulating impulse patterns in coupled systems rather than forces in a geometrical context.
Torsional vibrations are measured on both sides of the contact point for varying bowing positions on an open cello G string, and are related to the transverse motion of regular Helmholtz cycles. The structural analysis of coexisting vibrations suggests that these are mutually coupled, ready for transformation or submission while arriving at terminations or returning at the contact point. It also suggests that the release action provides the main energy impulse for vibrations of both types which will then decline fast, i.e. the transverse wave on the bridge side and the torsional waves on both sides. Secondary energy impulses come from differential slipping which, on the contrary, are rather likely to grow due to increasing forces towards the end of the sticking phase.