Complementary empirical data on minimum bow force

The minimum bow force F_min necessary to maintain Helmholtz motion on stringed instruments was widely believed to be proportional to the bow velocity v_B, to the reciprocal of the bridge resistance R, and to the reciprocal of the relative bow-bridge distance β squared [Schelleng, J. Acoust. Soc. Am. 53, 26-41 (1973)]. More recently, a study reported independence from v_B and an overproportional reciprocal effect of R while confirming the 1/β² proportionality [Schoonderwaldt, Acta Acust. Acust. 94, 604-622 (2008)]. Here, a bowing pendulum is used which facilitates precise control and measurement of related parameters. The string excitation at the contact point is recorded to instantly classify Helmholtz motion (HM) versus non-Helmholtz motion with one (nHM-1) or more additional slips during the stick phase. Monitoring of the classification supports the control of bowing parameters during measurement. These are directed towards the regions of transition between HM and nHM-1 to reveal the parameters related to F_min. The empirical data gained from cello strings suggest that HM requires a baseline force F_min,0 even for very low v_B. F_min,0 depends on R and ß.