The bowed string

The complex function of musical instruments has traditionally fascinated scientists and engineers. This resulted in a field of study, namely Music Acoustics, where sound generation by musical instruments is one of the main subjects. In this project the focus lies on the bowed string. The interaction between a bow held by a musician and the string of a bowed-string instruments (such as a violin, viola or cello) also taking into account any feedback from the instrument`s body, has been under investigation over the past decades. However, there are still open questions regarding how the bow is causing the motion of the string. This is eventually transferred to the wooden body of the instrument, which is set into vibration and radiates sound in the surrounding area. In order to shed more light into this interaction, experiments will be carried out in three main categories: (i) the performance of real musicians will be analysed using sensor technology that can capture their actions (similar to motion-capture technology used for animating digital character models in computer animation); (ii) a robot arm will be instructed to perform in a similar manner to human musicians. This allows to run experiments for longer durations while ensuring that the robot is always performing in exactly the same way, something that is impossible in practise for human players; (iii) information gathered by both types of measurement approaches will be used in order to develop a computer algorithm that, based on physics principles, will be able to generate synthetic sounds similar to those performed by the musicians. Having a so-called physical model of a musical instrument that takes the actions of the performer into account and has been validated via experimental measurements, allows to systematically study the effect of every part of the system (in this case the player-bow-string-instrument system) on the generated sound. This can be achieved, since in a computer simulation the user may change only one system parameter (e.g. the velocity of the bow) while keeping everything else constant, in order to assess the effect of that single parameter. Such a systematic study is extremely difficult, if not impossible in real experiments, because changing a system parameter usually also affects other parameters. The findings of this study, besides enhancing our understanding of the function of bowed-string instruments, may also provide students and teachers with illustrative examples of sounds that result from specific bowing actions, could yields results that are of interest to instrument makers regarding the role of certain instrument parts and will also generate valuable research tools for future studies in Music Acoustics. Finally, the resulting algorithms may be used for sound synthesis applications within contemporary electroacoustic composition and sound design.

This project investigated the interaction between the musician's bow and the string of a bowed string instrument. This interaction is still not fully understood, due to the complex physical phenomena related to frictional forces between bow and string. In order to simplify the problem, the system under study was reduced to a monochord: a string with fixed boundary conditions excited by a bow. Analysis was carried out using experimental measurements and physical modelling. Experiments consisted of a bow controlled by a robotic arm, while the string oscillations were monitored by measuring the string forces at its boundaries. Analyses revealed the resulting oscillation regime depending on the control parameters (bow position, velocity, acceleration, and force), the relationship between string velocity and bow force, and how these may vary subject to string properties. A vast dataset has been generated and published in Zenodo, which could be valuable for further research in the areas of musical acoustics and mechanical engineering. Physical modelling aimed at replicating time-domain waveforms measured experimentally. To this end, an elasto-plastic friction model has been employed, and its parameters were optimised in order to match the experimental measurements. Results show that model parameters need to be fine-tuned in order to match waveforms generated under different control parameters. This led to a model refinement, where the friction-related parameters are subject to the relative velocity between the bow and the string and, hence, to temperature variations. Sound synthesis was carried out, also considering the effect of the instrument's body. While an improvement of the model has been observed, further measurements of different type, focusing on temperature variations, are necessary in order to validate newly developed models.