Terhardt, E. (1990). A systems theory approach to musical stringed instruments: Dynamic behaviour of a string at point of excitation. Acustica 70, 179-188

The systems theory approach to musical stringed instruments makes it particularly apparent that the dynamic behaviour of a sting at the point where it is excited plays a key role. This behaviour can properly be described by (1) the complex impedance as a function of frequency; (2) the step- or impulse-response of force; and (3) the step- or impulse-response of velocity. In the frame of a general structural model with time-variant excitation mechanisms, and employing bilaterl Laplace-transformation, theoretical solutions fo the above characteristics are given for the case of small excursions of a flexible, non-torsional string. The results are compared with experimental data and their relevance for less restricted conditions is discussed. It is concluded that in spite of the simplifications involved, the theoretical results facilitate the understanding of stringed instruments and can serve as a reference for experimental investigations on the musical quality of instruments.

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