The acoustics of wind instruments – and of the musicians who play them

In many wind instruments, a non-linear element (the reed or the player's lips) is loaded by a downstream duct – the bore of the instrument – and an upstream one – the player's vocal tract. Both behave nearly linearly. In a simple model due to Arthur Benade, the bore and tract are in series and this combination is in parallel with the impedance associated with vibration of the reed or player's lips. A recent theme for our research team has been measuring the impedance in the mouth during performance. This is an interesting challenge, because the sound level inside the mouth is tens of dB larger than the broad band signal used to measure the tract impedance. We have investigated the regimes where all three impedances have important roles in determining the playing frequency or the sound spectrum. This talk, illustrated with demonstrations, presents some highlights of that work, looking at several different instruments. First order models of the bore of flutes, clarinets and oboes – the Physics 101 picture – are well known and used as metaphors beyond acoustics. Of course, they are not simple cylinders and cones, so we briefly review some of the more interesting features of more realistic models before relating performance features and instrument quality to features of the input impedance spectrum. Acousticians and sometimes musicians have debated whether the upstream duct, the vocal tract, is important. Setting aside flute-like instruments, the bore resonances near which instruments usually operate have high impedance (tens of MPa.s.m or more) so the first order model of the tract is a short circuit that has no effect on the series combination. In this country, that model is quickly discarded: In the didjeridu, rhythmically varying formants in the output sound, produced by changing geometries in the mouth, are a dominant musical feature. Here, the impedance peaks in the tract inhibit flow through the lips. Each produces a minimum in the radiated spectrum, so the formants we hear are the spectral bands falling between the impedance peaks. Heterodyne tones produced by simultaneous vibration of lips and vocal folds are another interesting feature. In other wind instruments, vocal tract effects are sometimes musically important: as well as affecting tone quality, the vocal tract can sometimes dominate the series combination and select the operating frequency, a situation used in various wind instruments. In brass instruments, it may be important in determining pitch and timbre. Saxophonists need it to play the altissimo register, and clarinettists use it to achieve the glissandi and pitch bending in, for example, Rhapsody in Blue or klezmer playing. Now, how to play the flute. Well you blow in one end and move your fingers up and down the outside. – Monty Python. In a simple model of a musical wind instrument, the bore is a cylindrical or conical pipe, either open-open (flute family) or closed-open (most others). This acts as a resonator, which loads a nonlinear element (air jet, reed or player’s lips) that converts DC air flow at higher pressure into AC. Together, the system oscillates at a fundamental frequency near one of the lower resonances of the bore and its higher harmonics are impedance matched to the radiation field by the higher resonances. In this model, the role of the player is to vary the length of the resonator (using keys, valves or slide), to supply the air at high pressure and to control some parameters of the nonlinear elements. Of course this is not enough, as Figure 1 demonstrates. In this paper, we shall look at just a few of the reasons why. We begin with a quick look at the pressure-flow behaviour of one simple nonlinear generator. Next we review Benade’s argument about how the ducts load the generator. Next we look at some of the subtleties and complications of the ducts that are real musical instruments, including one that explains the puzzle in Figure 1. Source: Dickens et al. (2007a) Figure 1. A sound spectrum of the same note played by a flute (open-open pipe) and a clarinet (closedopen). But which is which? 23-27 August 2010, Sydney, Australia Proceedings of 20th International Congress on Acoustics, ICA 2010 2 ICA 2010 One complication is that the reeds of woodwinds or the lips of a brass player are acoustically loaded by two ducts: the instrument bore is located downstream; the player’s vocal tract, upstream. We look here at some examples where the tract resonances have dominant musical roles. Separating the two ducts is the autonomous (self-sustaining) oscillator, the nonlinear element mentioned above. A clarinet or oboe reed tends to close when the upstream pressure increases, whereas the lips of a brass player tend to open into the mouthpiece, or to move sideways. A model of all three types is given by Fletcher (1993). As an example, we look first at a clarinet reed.