Minimum bow force measured with a high-precision bowing pendulum

Abstract

The minimum bow force Fmin necessary to establish Helmholtz motion on stringed instruments was widely believed to be proportional to the bow velocity vB, to the reciprocal of the bridge resistance R, and to the reciprocal of the relative bow-bridge distance ß squared [J. Schelleng, J. Acoust. Soc. Am. 53, 26-41 (1973)]. More recently, a study reported independence from vB and an overproportional reciprocal effect of R while confirming the 1/ß² proportionality [E. Schoonderwaldt, Acta Acustica United with Acustica 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 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 Fmin. The empirical data gained from cello strings suggest that HM requires a baseline force Fmin,0 even for very low vB. Fmin,0 depends on R and ß. Fmin, then grows proportionally with vB and with 1/ß rather than with 1/ß².