Parametric Electric Guitar Synthesis

The electric guitar is one of the most common musical instruments today. Several synthesis algorithms have been created to synthesize its sound (Sullivan 1990; Karjalainen et al. 2006; Pakarinen, Puputti, and Välimäki 2008; Smith 2008). However, these previous synthesis models lack a few features that contribute to, or alter, the characteristic electric guitar tone. Firstly, the magnetic pickup used in electric guitars alters the sound radically. The magnetic pickup acts as a bandpass filter and causes a comb filter–like effect as a function of its position (Jungmann 1994). In addition, the response of the magnetic pickup has been found to be inharmonic, as are the vibrations of the string. Secondly, when using a distortion effect, the details of the attack and the sustain part of a tone are brought to an audible level, which is not the case with acoustic instruments. This is caused by the radically increased gain (0–120 dB) and the inherent compression of the distortion effect. Thirdly, the instrument can be played very expressively: The player has total control of the plucking event (plucking angle, force, and width) and can bend the string to alter the pitch.

This article proposes a new parametric synthesis model that enables the creation of these sonic features. The synthesis model is based on the waveguide method (Jaffe and Smith 1983; Smith 1992; Karjalainen, Välimäki, and Tolonen 1998) with novel alterations. A new excitation model is introduced that recreates the plectrum scrape and the first displacement pulse created during the plucking event. The excitation model also accounts for different plucking forces, and the angle of the virtual plectrum is controllable. The string model is a time-varying one, where the parameter controlling the decay time is varied and the amount of pitch glide is mapped to different plucking forces. The magnetic pickup model recreates the level and timbre changes that occur when the distance of the magnetic pickup to the strings is altered. Moreover, the inharmonicity of the magnetic pickup is modeled with a cascade of allpass filters. Sound examples are available on-line (Penttinen, Välimäki, and Lindroos 2011).

Electric Guitar Sound Analysis

A Fender Stratocaster (American Deluxe model) guitar, equipped with three magnetic pickups and a Fishman Powerbridge piezoelectric under-saddle pickup, was used in this study. The piezoelectric pickup was used for the excitation and string-sound analysis, because it offers a broader bandwidth than does a magnetic pickup and hence a clearer “view” of the plucking event and the vibrations in the string. The output signals of the guitar were fed into a PC through a sound card (Edirol UA-101, f_s = 44.1 kHz, 16 bits) with the ability to record the piezo and the magnetic pickup signals simultaneously in separate channels, as shown in Figure 1.

Excitation Analysis

Electric guitar strings are usually excited with the fingertips, fingernails, or a plectrum. Most commonly the electric guitar is excited with a plastic plectrum. Hence, this work concentrates on excitations done with a plectrum. As shown in Figure 2, the beginning of the electric guitar tone can be split into three parts: plucking noise, excitation pulse, and the first reflection from the nut. The plucking noise is generated while the plectrum slides over the string but before the string has been released. This plucking noise is audible, especially when the guitar is played through a distortion unit. Two transverse waves travel in opposite directions from the plucking point when the string is released (Fletcher and Rossing 1991; Penttinen and Välimäki 2004). The wave travelling directly from the plucking point to the under-saddle pickup is the second part of the excitation. The third part of the excitation is the first reflection, the wave reflecting from the nut and travelling to the under-saddle pickup.

Figure 1.

Electric guitar tone signal of an open 6th string (f₀ = 82.5 Hz), with plucking point d = 32.6 cm, as a function of time in the piezoelectric under-saddle pickup (top) and the magnetic neck pickup (bottom...