Tuning of transient-excited musical instruments through optimized structural modification and modal techniques

Tuning is a very important aspect for any musical instrument, not only concerning proper pitch but also the tonal quality of the instrument. In this paper, we address bar instruments as an application. Marimbas and vibraphones, have their first bending modes carefully tuned, being typically the first modal frequency ratios of 1:4:10. Such tuning is usually achieved by shaping the bar profiles with precision machine tools, a delicate and highly specialized task. In this paper we investigate the possibility of obtaining similar results using suitably designed tuning masses attached to the bars. Two application areas are illustrated: (1) Obtaining adequate tuning from common bars of constant cross- section loaded with masses; (2) Correcting badly tuned bars with a minimal set of loading masses. From a numerical point of view, such objectives are achieved by coupling structural modification techniques with effective optimization schemes. Two tuning approaches are proposed: the first one uses a full-sized finite element model of the mass-loaded bar, while the second one is based on a very effective reduced model built using the modes of the non-corrected bar. After presenting the developed tuning methods, we illustrate them on the above mentioned applications, based on simulated data. Validation experiments are currently being prepared.