All this buzz about the sitar: Cphysically modelingly speaking

In this paper, we present recent research results in physical modelling of the sitar, an ancient Indian stringed instrument. Although a plethora of literature is available for modelling of classical western guitars, the depth of study of the sitar has seemingly been, for whatever reason, shallow in both theory and implementation. We present three different approaches in modelling the sitar focusing on the sitar's idiosyncratic "buzzing" timbre as analyzed from the string's perspective and directly addressing the sitar's unique bridge shape itself. We start with the Karplus-Strong plucked-string model and extend it to produce the sitar timbre. The first two approaches concentrate on what happens to the string and the final method focuses on the sitar's nonlinear bridge structure. Approach 1: Dynamic Delay Length: Due to the particular shape of the bridge, the contact amount between the string and bridge surface changes during the lifetime of the string's vibration. Thus, the string length can be regarded as dynamically changing. This is simulated by a subtly changing dynamic digital delay line. Approach 2: Inverse Comb Filtering: Viewed from the perspective of "harmonic dampening" of the string, the buzzing characteristic can be considered as a dynamically shifting inverse-comb-filter applied on the basic string model which can be exploited to mimic pluck position dampening a string's harmonic structure. The buzzing is thus simulated by dynamically altering the "pluck position" after each "actual" pluck. Approach 3: Bridge Waveshaping: Due to the nonlinear surface of the bridge, nonlinear string distortion results for the string. Thus, via modelling the shape of the bridge through waveshaping, we can shape the string's waveform directly for each feedback cycle. Additional issues including sympathetic string vibration and its body's resonant structure are also discussed with sound examples downloadable from the Internet.