Measuring Bow Force in Bowed String Performance : Theory and Implementation of a Bow Force Sensor

A sensor has been developed which allows measurement of the f orc exerted by the bow on the string (bow force) during violin performance. The bow force is deduced from measureme nt of the transversal force at the termination of the bow hair at the frog. The principle is illustrated with an experiment th at demonstrates how the bending of the stick and variations i n bow hair tension influence the measurements. The design of the se nsor is described and performance characteristics are disc ussed. A thorough calibration procedure is described and tested. Fi nally, the use of the sensor is demonstrated through measure ments in real playing situations. I. I NTRODUCTION Bow force is one of the three main control parameters in bowed string playing, the two others being bow velocity and bowbridge distance. In particular, a rapid establishment of He lmholtz motion during the attack is dependent on the coordin atio of bow force with acceleration and bow bridge distance [6][11] . Also, for the control of timbre, bow force is the main parame ter, bow-bridge distance playing a secondary role [7]. The interest for measuring control parameters in playing is encouraged by the advancements in the study of musical instruments by physical modeling. One advantage of this app roach is that the control parameters of the model become the same as for the real instrument. On the other hand, measuring the control parameters in normal playing without interferi ng with normal playing conditions presents a challenge, in par ticular for wind instruments. The bowed stringed instrumen ts are seemingly straight-forward to approach as the string and bo w are of reasonable size and the motions associated with bowi ng are accessible for measurement. Application of motion capt ure techniques is an obvious approach for measuring bow velo city and bow-bridge distance in playing, while bow force measure ments will require application of sensors to the bow or the vi olin. The first reliable measurement of control parameters in viol in playing during real performance were made by Askenfelt [1 ], [2]. A bow was modified to measure bow position, bow velocity, bow-bridge distance and bow force. Bow position refers to the position of the contact point between bow hair and string elative to the frog or tip. The bow position was measured by a resistance wire running among the hairs in the outer layer of the bundle of bow hair contacting the string. The string divi ded the wire in two parts which were used in a branch of a Wheatston e bridge. Bow-bridge distance was measured in a similar manner, using the parts of the string on each side of the bow (w ire) in a second Wheatstone bridge. Bow velocity was obtaine d from the bow position signal through differentiation. Bow f orce was measured by gluing the bow hair to two metal strips at the frog and at the tip, respectively, and measuring the defle ction of the strips by strain gauges. Later, Young used the bending of the bow stick to estimate the force on the string in playing. Two pairs of strain gauges wer e glued to the stick in order to measure the bow force (normal to the string) as well as the lateral force component (in the str ing direction) [13]. Recently, the present author [4] proposed an improvement of Askenfelt’s work by designing detachable sensors which could be attached to any bow, and treating the sensor si gnal from the frog and tip independently. Later implementa tions of this idea for real-time measurements have been presented by Guaus et al [5]. The following presentation gives a descri ption of the basic idea, theory, design, and calibration of a detac hable bow force sensor. II. I NTRODUCTORY EXPERIMENT AND THEORETICAL CONSIDERATIONS The basic idea of the force sensor was to determine bow force i ndirectly by measuring the resulting transversal forces at the bow hair terminations. In this section, the principle is illustrated and the influence of the mechanical behaviour of the bow is analysed. A simple model based on measurements is used to q uantify the contributions from the bending of the bow stick and changes in bow hair tension to the observed behaviour. A. General description of the bow The bow consists of a bow hair ribbon fastened to the head of th e bow stick at one end and to the frog at the other end (see Fig. 1a). As the bow hair is brought up to tension by turni ng the frog screw, the hair pulls the head back, and the initia l camber of the stick is reduced. Keeping the frog fixed horizon tally, the tip is lowered until an initial displacement h0t has been reached, at which the restoring force resulting from the str aightening of the stick counteracts the static hair tension (see Fig. 1b). The displacement of the tip is measured relative to a hor izontal reference line extending from the underside of the f rog, as if the frog was resting on a table (see Fig. 1). 1 Screw Frog Ferrule Bow stick Bow hair Head