String synthesis using individually modeled termination scattering filters

Abstract

In the context of digital waveguide synthesis of string instruments, strings are modeled as pairs of digital waveguides which encounter a scattering junction at each boundary. The string scattering junction at the bridge can be modeled to match the measured driving point admittance at the bridge of a physical instrument, and is used in calculating the radiated sound. The string termination at the nut, or fingering end of the string, is typically modeled with a single scalar attenuation, independent of the fingering. However, driving point admittance measurements are presented confirming that string reflectance is a function of both frequency and fingering. A model is proposed which uses a unique, frequency-dependent string reflection scattering junction for each fingering position. The fingering location scattering junctions are calculated using a modal architecture based on driving point admittance measurements made on an acoustic guitar at the bridge, nut, and frets 1 through 13. These synthesized strings are compared to recordings of the physical instrument, as well as to the widely used scalar attenuation model.