Analysis and reproduction of the frequency spectrum and directivity of a violin

This research was adopted as an internship at IRCAM, Paris. Many groups in the world, are, like the institute, interested in the combination of electronic music and acoustic instruments. A violin was taken as an example for the acoustic instrument, because of its typical frequency-dependent sound radiation. Previous research has shown that different resonances, or modes, of the violin body cause this radiation pattern. To determine the radiation pattern and resonance frequencies, an inverse measurement method is adopted as has been described by Weinreich[3]. In this point of view, the violin was excited externally by a loudspeaker and the vibrations at the violin bridge were picked up by a single calibrated piezo-electric sensor. The results were analysed by a simple peak-searching algorithm and by spatial Fourier decomposition, expressing the violin characteristics in a limited number of parameters. A cube with 6 digitally processed loudspeakers, called La Timee applies the 3D reproduction of the radiation. The system is capable of producing a sound field corresponding to all possible combinations of the spherical harmonics of order 0 and 1. The sound signals are generated by a physical modeling synthesis engine based on the modal theory, called Modalys. This software simulates the vibrations of the different modes of the violin parts, like the strings, bridge and also the violinist’s fingers. A vibrating plate represents the resonant body; its parameters for the resonance frequencies, damping and radiation patterns have been matched to the measurements. A tune is made in the program and played on the loudspeaker system. The results were promising, though a disproportionate rate of frequencies above 2kHz was seen in the measured spectrum. Furthermore, it showed that combinations of monopoles and dipoles up to 1.8kHz could describe the characteristics. This is also approximately the maximum frequency that the used version of La Timee can handle, so no information was lost. However, the radiation of the violin is also interesting for frequencies above 1.5kHz, so further development is recommended to reproduce higher frequencies.