Download Low-order allpass Interpolated Delay Loops
This paper presents empirical and theoretical results for a delay line cascaded with a second-order allpass filter in a feedback loop. Though such a structure has been used for years to model stiff vibrating strings, the complete range of behavior of such a structure has not been fully described and analyzed. As shown in this paper, in addition to the desired behavior of providing a frequencydependent delay line length, other phenomena may occur, such as “beating” or “mode splitting.” Associated analysis simulation results are presented.
Download Pitch glide analysis and synthesis from Recorded Tones
Pitch glide is an important effect that occurs in nearly all plucked string instruments. In essence, large amplitude waves traveling on a string during the note onset increases the string tension above its nominal value, and therefore cause the pitch to temporarily increase. Measurements are presented showing an exponential relaxation of all the partial frequencies to their nominal values with a time-constant related to the decay rate of transverse waves propagating on the string. This exponential pitch trajectory is supported by a simple physical model in which the increased tension is somewhat counterbalanced by the increased length of the string. Finally, a method for synthesizing the plucked string via a novel hybrid digital waveguide-modal synthesis model is presented with implementation details for time-varying resonators.