Full Text for Manuscript for Isma 2007-02-13

An experimental study of the upper and lower bow force limits for bowed violin strings is reported. A bowing machine was used to perform bow strokes with a real violin bow on steel D and E strings mounted on a rigid monochord and on a violin, respectively. Measurements were systematically performed for 24 values of bow force and 11 values of relative bow-bridge distance at four bow velocities (5, 10, 15 and 20 cm/s). The measured string velocity signals were used to compile Schelleng diagrams, showing the distribution of different classes of string motion (multiple slipping, Helmholtz motion, raucous motion). It was found that the maximum bow force limit for Helmholtz motion corresponded well to Schelleng’s equation in modified form, taking the shape of the (hyperbolic) friction curve into account. The minimum bow force was found to be independent of bow velocity, which is in clear contradiction to Schelleng’s prediction. Observations and simulations suggested that the breakdown of Helmholtz motion at low bow forces involves a mechanism related to ripple and corner rounding which was not taken into account in Schelleng’s derivation of minimum bow force.