An extended geometric model for analysis of string crossings in bowed-string instrument performance

In earlier motion capture studies of fast repetitive bowing patterns across two and three strings in violin performance it was shown that string crossings were consistently timed earlier than bow reversals. This behavior might have a plausible acoustic explanation: a good attack on the new string requires that bow force is built up before the string can be set in motion. An earlier used feature-extraction model fails to adequately describe the transfer of bow force between strings because it considers string positions and bow inclination transition angles between strings as fixed. An improved model is proposed that (1) takes the compliance of the strings and the bow hair explicitly into account, and (2) includes a correction of string crossing angles for stopped strings. The model requires knowledge of the tensions of the strings and the bow hair, as well as the depth of the fingerboard below the strings. It will be shown how these quantities can be obtained via simple calibrations. The model allows for an accurate calculation of control parameters to drive a virtual violin, allowing to study the relation between bowing movements and the quality of attacks in complex bowing pattern