Projects:2018s1-192 Karplus-Strong Synthesis of Sound

Project Team

• David McQueen

• Samuel Churches

• Sam Haberman

Supervisors

• Dr Andrew Allison

• Dr Brian Ng

Introduction

The Karplus-Strong (KS) plucked-string algorithm was a computational model developed in the early 1980s as an efficient model for vibrating strings based on physical resonance. It was praised for the rich and realistic timbres it generated despite its simplicity. Briefly explained, the algorithm works by placing a delay element into a positive feedback configuration together with a simple low pass filter. Short noise bursts injected into the feedback loop will resonate in the system at a frequency defined by the delay period, and decay away due to the action of the filter. This model is analogous to a plucked string, with the noise bursts acting as the plucks, and the resonating feedback loop acting as the string medium. By modifying the transient shape and frequency content of the noise burst, and the cutoff frequency and gain of the filter, different pleasing output timbres can be synthesised.

Since its conception, many advances have been made in developing the KS algorithm in efforts to generate more realistic models of instruments and to widen the range of instruments available for simulation through advances in the theory of digital waveguides for the modelling of multi-dimensional systems. Efforts have been made to produce musical synthesisers as products, with patents being applied for in 1986 and 1987 and both Mattel and Yamaha licensing the technology however no products have been brought to market using the algorithm from these efforts.

Some modular synthesiser systems are available that provide sufficient building blocks to run a Karplus-Strong model, but these synthesisers are cumbersome, do not support easy chromatic tuning and require much work to implement polyphony, and as such lack playability via standard MIDI control methods.

Abstract

The goal of the project is to develop two synthesizers based on the Karplus-Strong algorithm. The first will implement the model using analog electronics, with digital electronics to control it and the second will be purely digitally based. The synthesizers will be required to be playable using a MIDI controller (such as a keyboard) and have a user interface that allows the character of the generated music to be intuitively adjusted.

The three main research goals of this project are to:

• Highlight the frequency domain differences between Karplus-Strong synthesisers implemented in the digital domain and with analogue electronics

• Study the subjective perceptual timbral differences between analogue and digital Karplus-Strong synthesisers through systematic surveying

• Investigate the commercial viability of producing a hardware Karplus-Strong synthesiser using analogue electronics.

The basis of the analogue electronics KS implementation are bucket-brigade delay lines, and the digital synthesiser is implemented in the MATLAB environment.