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Cello bowing pendulum

Mores, Robert 

A cello bowing pendulum for precise measurements of physical parameters of bowing is presented. It is designed to hold and play bows of any style and to perform the bowing on a strict line. Such a strict line follows the bowing paradigm of musical play but also eases the instrumentation of the applied bowing forces. Two eccentric suspensions translate the initially circular track of a ballistic pendulum into the desired straight line. This height-compensated pendulum is additionally weight-compensated by means of a counter-pendulum so that the total system is finally free of any restoring forces. An adjustable fraction of the ballistic weight serves as bow force, while the stringed cello is resting beneath the pendulum on a weighing scale which measures this bow force. The tractive force for bowing works strictly perpendicular to the bow force. Both forces in their orthogonal arrangement can be adjusted and measured with centinewton precision. Secondly, bow speed is not predefined by a driving entity but is controlled by the slip-stick interaction. A potential tractive force is provided in combination with a damping unit such that the resulting mechanical impedance will instantaneously adapt to what the actual slip-stick process recommends including a resulting bow speed. This adaptive operation is similar to what a musician senses during bowing and therefore appears to be a valid approach for related performance-based studies of musical acoustics. Such adaptive operation also appears to be preferrable for investigations of bifurkation regimes, of reciprocal inter-instrument pitch-synchronization, physical parameters of slip-stick interaction and of maximum and minimum bow force. Measured signals are organized in multiple data-tuples (every 12 ms of bowing) in order to facilitate statistical analyses and traces. The paper contains the pendulum construction principle, operational modes and ranges, as well as first results from maximum bow force measurements.