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An Empirical Investigation of Bow-Force Limits in the Schelleng Diagram

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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. Measurements were systematically performed for 11 values of relative bow-bridge distance and 24 values of bow force 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. The influence of damping showed only qualitative agreement with Schelleng's predictions.
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Document Type: Research Article

Publication date: July 1, 2008

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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