The dependence of viola top plate mode frequencies and shape on string tension

Abstract

The normal mode vibrations of a viola’s top plate impact the tone quality of the radiated sound. Luthiers pay some attention to the body mode frequencies during fabrication of the instrument, though specific tuning of modes does not seem to be a priority over other considerations. Interestingly, the normal mode vibrations of the instrument body are modified by the downward force of the bridge feet on the top plate due to the string tension. Different string materials result in different string tensions for proper tuning, so the final body mode frequencies are not strictly predictable. We will present ESPI studies of the top plate normal mode frequencies and mode shapes of a viola as the string tension is increased from zero (strings as bridge removed) to in-tune values for all four strings. The changes of resonant frequency and mode shapes will be discussed in terms of their sensitivity to string tension and the resultant tuning of the final instrument behavior. Knowing the sensitivity of the instrument body to string tension variation may help in understanding the importance of body resonance tuning during the fabrication process.