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.

Background

Karplus-Strong Synthesis

Karplus-Strong (KS) synthesis produces musical notes by impulsing a filtered positive feed- back delay line with short bursts of noise. The method was presented in 1983 as a way to digitally synthesise musical notes using as little computational overhead as possible. KS synthesis works as a simplified physical model of a plucked string, such as that found on a guitar, cello or harp. The noise burst represents the energy stimulation (pluck) imparted on the string. The delay element encapsulates the time delay between the energy wave on the string, as a result of stimulation, travelling between each reflective ends of the string. The low pass filter attenuates high frequency components in the ’reflected’ wave (delayed impulse), imitating the same dampening effect found in real plucked strings due to viscosity in the air medium they travel on, and the energy transferred to the reflective element. Gain control in the feedback path regulates the sustain effect of a plucked string, with a lower feedback gain leading to a shorter note sustain time. Gain control is limited to unity, or below, such that the output signal will always decay to zero. Finally, the summing element of the feedback loop adds the reflected waves back into the signal path, to be delayed and filtered again.

By tuning the delay period to be that of the frequency of a desired note, and using appropriate filtering and gain parameters, the Karplus-Strong model can synthesise realistic plucked string timbres.

Bucket-Brigade Devices

Bucket-brigade devices (BBD) are discrete time, continuous voltage analogue signal delay lines. They function as a queue of electrical charges stored in capacitors, shifted along by switching MOSFETs using alternating clock signals. The high price of bucket brigade devices is the past was prohibitive of their use in affordable synthesisers, but now these devices are affordable, which has encouraged their use in this project. Additionally, to precisely control the delay line, a highly precise digitally controlled clock signal is required, the implementation of which has only become cost effective for use in synthesis in recent years.

Transient Envelopes

A common control signal used in synthesisers is called an envelope. An envelope is triggered by note a gate and/or a trigger signal, which are engaged by a new keyboard note event, and outputs a control voltage which will typically control either a filter cutoff frequency or the gain of a note output signal. An typical envelope has four control parameters: attack, sustain, decay and release (ADSR). Attack controls the time from the start of the note event to the envelope reaching its peak level. Decay controls the time from the envelope reaching its peak level to reaching its sustain point. Sustain controls the level of the sustain point. Release controls the time from the note gate ending to the envelope reaching zero.

Market Analysis

Analogue electronics based instruments and effects units are currently seeing a renaissance in the music technology market. Consumers are returning to older music technology, embracing their subtle imperfections and rich tonality compared to their digital counterparts, which are perceived as comparatively sterile [5]. Karplus-Strong synthesis is also receiving more attention in recent times, as the computational power required for detailed, polyphonic, real time KS synthesis becomes cheaper and more readily available.

At this point in time, no fully integrated KS synthesiser implemented using analogue electronics exists. It is predicted that due to the current state of the market, there may be a consumer demand for this product. The function of this project is to determine whether such an analogue implementation is different enough to warrant bringing this product to market.