Automatic multi-modal tuning of idiophone bars

Abstract

Idiophones generate sound through the vibration of their beam-like “keys”. The musical sound generated depends on the natural bending vibrations of the free-free beams. The tonal quality of the idiophone bar is achieved by tuning the second and third natural bending frequencies in relation to the fundamental natural frequency. Tuning these harmonic overtones becomes one of the primary tasks for making idiophone bars. It is achieved by removing material from the underside of the beams. This thesis focuses on the accurate prediction of the geometry of the beam underside (undercut) shape of marimba bars1 and the fine tuning process for correcting the unavoidable uncertainties of wood during automated tuning.The correct underside shape of the marimba bar was predicted using Timoshenko beam receptances. The underside shape predictive model predicts the resulting natural bending frequencies based on the undercut geometry of the bars. A search algorithm was implemented to find the correct geometry of the undercut for the multi-mode frequency requirements. A CNC machine tool was adapted to mill the specified underside shape from a wood blank, and this machine tool was combined with the predictive model and automatically controlled by the hardware controlling program. A fine tuning program was developed to incrementally approach the target natural frequencies from above, thereby correcting for the unknown non-homogeneity and anisotropy of wood.Manufacture of wooden bars showed that the underside shape predictive model was very accurate when the elastic properties of the test material are accurate. For non-homogeneous and anisotropic material the improvement of the actual results made by the fine tuning program were observed. A physical machining centre, which combines the underside shape predictive model, the fine tuning program, the hardware controlling program, the frequency measuring program and a self-built CNC machine, have been developed to automate the tuning process.