On the playability of stringed instruments
As first noticed by Helmholtz, strings vibrate in a “V-shape” when they are bowed correctly and a full tone is produced, where the vertex of the “V” shuttles back and forth along the visible envelope of the string’s motion. If the instrument is bowed incorrectly, i.e. the instrument does not “speak”, then this “Helmholtz motion” is not produced, and the shape of the string as it vibrates will be quite different. The goal of this research is to gather experimental data from a stringed instrument and use it in the on-going development of a theoretical model of the mechanics of the bowed string, which can be used to investigate which aspects of the violin, strings or bow influence the ease with which this “Helmholtz motion” can be produced. The design, testing and application of a robotic bowing machine are described, which has allowed the speed and force of a bow as it plays a cello to be controlled. Extensive measurements of various aspects of the motion of a cello string being bowed by the bowing machine are presented, and compared with predictions from nominally similar theoretical models. Although certain models do reflect the qualitative behaviour seen in experiment under some conditions, all show vast room for improvement. Aspects of theoretical predictions that are at odds with experimental results, and would therefore impede efforts to use theoretical modelling in the design of a more “playable” violin, are subsequently described. Shortcomings of each model are attributed to physical defects of the theories underpinning them, and various modifications are discussed and tested.