TUNING OF TRANSIENT-EXCITED MUSICAL INSTRUMENTS THROUGH OPTIMIZED STRUCTURAL MODIFICATION AND MODAL TECHNIQUES

摘要

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