Acoustics of the banjo: measurements and sound synthesis

Abstract

Measurements of vibrational response of an American 5-string banjo and of the sounds of played notes on the instrument are presented, and contrasted with corresponding results for a steel-string guitar. A synthesis model, fine-tuned using information from the measurements, has been used to investigate what acoustical features are necessary to produce recognisable banjo-like sound, and to explore the perceptual salience of a wide range of design modifications. Recognisable banjo sound seems to depend on the pattern of decay rates of “string modes”, the loudness magnitude and profile, and a transient contribution to each played note from the “body modes”. A formant-like feature, peaking around 500–800 Hz on the banjo tested, is found to play a key role. At higher frequencies the dynamic behaviour of the bridge produces additional formant-like features, reminiscent of the “bridge hill” of the violin, and these also produce clear perceptual effects.

Acoustics of the banjo: theoretical and numerical modelling

“…For the simplest idealisation, treating the resonator and the rest of the banjo structure as rigid, the lowest mode of the membrane will couple to the Helmholtz resonator formed by the vented back. As shown in Figure 6 of the previous paper [1], the result is a pair of modes involving combinations of both types of motion. This behaviour is very familiar from simple models of guitar bodies [19], and also from the analysis of ducted loudspeaker enclosures (see e.g.…”

“…In fact, it will be suggested that a "square banjo" like this would not sound very different from a normal circular one: indeed, non-circular banjo-like instruments, including rectangular ones, really exist in various corners of the world. In addition, audio demonstrations based on the model to be developed here were presented and discussed in the earlier paper [1] and the website [4]: the examples Sound B.1 and Sound B.2 on that website give a direct comparison between synthesis based on measured admittance and on the square banjo model. Later in the present paper the frequency response behaviour of the model will also be compared with that of the detailed FE/BE numerical model.…”

“…Membranes, however, have been relatively little studied, and the behaviour is different (see chapter 14 of [9]). Waves on a membrane are non-dispersive, and it appears that for any realistic parameter values for a banjo or drum membrane, the wave speed is slower than the speed of sound in air [1]. This means that an infinite ideal membrane can only generate evanescent waves: there is no critical frequency, and far-field sound radiation can only occur through finite-size effects.…”

“…In a preceding paper [1], measurements of vibrational response were presented for an American 5-string banjo (a Deering Eagle II [2]), and contrasted with corresponding results for a steel-string guitar (by Martin Woodhouse [3]). The measured mechanical admittance functions at the bridges of the two instruments were then used as the basis of a synthesis algorithm, to find out whether the differences captured by those measurements were sufficient to allow recognisable and convincing versions of "banjo sound" versus "guitar sound" to be produced.…”

“…Some parameter *Corresponding author: jw12@cam.ac.uk values for the tested banjo are listed in Table 1. Figure 1 of the previous paper [1] included a cross-sectional diagram of the banjo body, showing the configuration of the pot and resonator back.…”