A modified Mersenne Law governs the inter-mode patterns in bundengan string vibrations

The bundengan, a folk zither instrument from Indonesia, has a unique timbre because its strings are added with small bamboo clips. The non-homogeneous mass distributions allow the strings to imitate the sound of metal percussions in the gamelan ensemble. Moreover, the clever design of the bamboo clips allow the bundengan timbre to be controlled easily by sliding the clips along the strings. Using computer simulations, we have systematically varied both the position and the mass of the bamboo clips, resulting in a rich catalogue of vibration spectra. In these spectra, we have observed peculiar patterns in the graphs of vibration-frequency -vs- clip-position. These patterns, which occur across different vibration modes, evolve as the mass of the bamboo clips are increased. In the extreme case where the bamboo clips are very heavy, these patterns can be explained by a modified version of the Mersenne’s Law.