For maximally natural interaction between the bow and string, bow-hair dynamics should be included in a proper bow bodel . In addition, the width of the bow should be variable, depending on bow ``angle''. A finite difference model for the finite width bow was reported in [354,355]. The bow-string friction characteristic should employ a thermodynamic model of bow friction in which the bow rosin has a time-varying viscosity due to temperature variations within a period of sound . It is well known by bowed-string players that rosin is sensitive to temperature. Thermal models of dynamic friction in bowed strings are described in , and they have been used in virtual bowed strings for computer music [423,427,21].
Given a good model of a bowed-string instrument, it is most natural to interface it to a physical bow-type controller, with sensors for force, velocity, position, angle, and so on [424,296].
A real-time software implementation of a bowed-string model, similar to that shown in Fig.9.52, is available in the Synthesis Tool Kit (STK) distribution as Bowed.cpp. It provides a convenient starting point for more refined bowed-string models .