Motion, control, and performance of a cello bowing pendulum

Abstract

This documentation contains eight short movies to document the performance of the bowing pendulum. The pendulum is designed to facilitate controlled bowing of string instruments, e.g. for physical studies. Bowing is controlled by applied forces rather than by a motor or by otherwise predefined velocities. With the applied forces, the bowing will take place in a self-organized way. That means that the bow and the string together define the bow velocity in a synergistic process given the applied forces and the physics of the stick-slip action at the point of friction. This process also defines the amplitude and the regime of playing such as regular Helmholtz motion, or bifurcation, or noise.

The pendulum uses an eccentric suspension to translate the circular movement of a pendulum into a straight movement necessary for bowing. A schematic of the total setup can be found in this documentation (SchematicTotal.jpg). The more generalized geometry can be found in

Mores, R. (2015). Precise cello bowing pendulum. Proceedings of the Third Vienna Talk, 16-19 Sept. 2015, University of Music and Performing Arts Vienna.

The proceeding paper is also part of this documentation (PreciseCelloBowingPendulum.pdf).

The pendulum is located in Hamburg at the Arts and Media Campus Finkenau and can be used by any researcher.

The pendulum and the approach of self-organization are key to resolve the differing proposals of four existing theories on maximum bow force. The result is published in Mores, R. (2016). Maximum bow force revisited. The Journal of the Acoustical Society of America, 140(2), 1162-1171.

The pendulum and the approach of self-organization also encouraged to revisit he issue of minimum bow force with the results published in Mores, R. (2017). Complementary empirical data on minimum bow force. The Journal of the Acoustical Society of America, 142(2), 728-736.

The construction principle – translating the circular track of a pendulum into a straight track – should be useful in other applications as well, for instance for simple bridges.

There is no patent on this construction and everybody is welcome to use this without any license fee. This documentation should effectively preempt future patent applications from other parties.

Content of the eight movies:

1_HeightCompensated: this movie shows the motion principle of the pendulum. The circular curve of the pendulum is compensated by an eccentric suspension with an effective length of an eccentric lever such as to translate the curve into a straight motion. While moving on a strictly straight path, the issues of potential energy and kinetic energy are not traded any more. The pendulum can rest at any position, potentially.

2_Weight_Copensated: in reality, the pendulum still experiences forces to move to and finally rest at the middle position. This comes from the eccentric suspension itself. The body rotates during the pendulum’s movement. While the rotation point is the top of the triangle body the center of mass is well below this point. This causes the restoring forces. Here, the weight is compensated for with a counter-pendulum. There are also other means to compensate for.

3_BowForceControl_manual: this is to demonstrate how well the height can be adjusted. It is monitored by the force of the bow normal to the string. The motion is done manually to allow a slow enough motion for monitoring.

4_BowForceControl_selforganized: the same monitoring but now under self-organized motion, i.e. a steady-state force is applied horizontally to cause motion.

5_DampingUnit: can be applied optionally for smoother operation.

6_KeepingTrack: the bow itself will keep track without any other support of guidance. In fact, the angle between bow and string usually controls the contact position along the string. Every cello player knows this.

7_SingleShot: this is to demonstrate the superior control capability of this bowing machine. This extreme case of very high bow force in combination with very low velocities is extremely difficult to control. This bowing, again, takes place in a self-organized way without any driving machine or manual operation. There are only applied steady-state forces (redirected forces of gravity).

8_Bifurcations: this is another example to demonstrate an extreme case of control. Steady-state bifurcations are rather difficult to establish during conventional cello playing.