Sitar String Physical Model
As a second challenge in the seminar on how objects vibrate, taught by Miller Puckette at UCSD,
we were asked to simulate the non-linear way a sitar string interacts with the sitar bridge. In a typical
string, like on a guitar, the string maintains a fixed length regardless of whether it is moving upward
or downward. Since a sitar bridge is a wide, flat object, with tapered edges, the string comes into contact with different
amounts of the bridge depending on its direction of travel.
The bridge / string interaction looks something like this:
When the string travels upward, it comes into contact with the outside edge of the bridge, causing the string to have length N. When the string travels downward, it comes into contact with the inside edge of the bridge, which shortens the length of the string. The string is now something like N – X, where X is the width of the bridge. Part of the characteristic sound of the instrument comes from this alternating shortening and lengthening of the string during the course of a note. My extension to this model, which was proposed to the class, was to imagine the bridge as not simply two termination points, but as a curved surface:
Depending on how far “down” the string travels, its length shortens according to the curvature of the bridge. The image below shows the length of the string during one period of vibration. When the string is moving downward, the string length shortens proportionately. When the string is moving upward, the string length is fixed.
Here’s an image of the string simulation patch:
I made one final modification to the original idea by adding a set of 13 sympathetically tuned string simulations. Each is a simple Karplus-Strong string model tuned to a specific pitch. This helps to generate the characteristic harmonic activity of the sitar.
Finally, here is a video showing the simulation in action:
Musician/hacker living in San Diego, CA. Studying computer music at UCSD. 