We turn to the final family of wind instruments, the air-jet instruments like the flute, recorder and flue organ pipe. Looking back over previous sections of this chapter, the logic behind the organisation should now become clear: we started with the best-understood instruments, and we have progressively moved to the ones where physical understanding is more challenging, and therefore more rudimentary.
For reed instruments like the clarinet, we were able to construct a fairly simple physical model with quantitative experimental support for all aspects. The pipe acoustics was anchored in measured input admittance which could be interpreted via simple theory, while the nonlinear characteristics of the reed mouthpiece were based on uncontroversial theory with some direct measurements in support. The result was a simulation model with some claims to realism. This could be used to explore questions about how the player might control the instrument to maximise the range of musical options, and also how the instrument maker might help by “playability” improvements.
Moving on to the brass instruments, our understanding of tube acoustics was still supported by direct measurements of input impedance, but the model for the lip dynamics was less convincing. We used essentially the same model as for the reeds, except for a reversal of sign to reflect the opening-reed behaviour of lip vibration as opposed to the closing-reed character of the reed woodwinds. This super-simple model, with just a single degree of freedom, can only be expected to give a rather crude representation of the vibration of the squashy flesh of lips. Nevertheless, the resulting simulation models gave qualitatively plausible results, correctly reflecting many aspects of the behaviour of this family of instruments.
When we moved to the free reed instruments, things got more complicated. This time, the behaviour of the reeds themselves was reasonably uncontroversial, but it was far from clear what additional physics needed to be included in order to model the excitation mechanism with any claim to realism. For some problems, with strong acoustical feedback from a well-characterised system, it was easy to complete a model in the same style as the original clarinet model and obtain quite convincing agreement with experiments.
But in other cases we met snags of two different kinds. First, no impedance measurements appear to have been made on instruments like the concertina, let alone on the harmonica for which the player’s vocal tract is a significant part of the system. Second, we saw strong hints that acoustical feedback is not always the predominant excitation mechanism, suggesting that something more complicated is needed. Initial modelling efforts have been made, based on idealised analysis of the fluid flow in the immediate vicinity of a vibrating reed, but the story is by no means complete.
Now we turn to the air-jet instruments, and we are squarely faced with problems involving non-trivial fluid dynamics. These instruments have no moving parts analogous to reeds or brass-player’s lips. The behaviour of the instrument is determined by the interaction of the internal acoustics of the instrument tube with air-flow from a mouthpiece slot or from a flute-player’s lips. The tube acoustics can be characterised by measured input impedance (or its inverse, input admittance: as we saw back in section 11.1, an air-jet instrument is expected to play notes determined by peaks of admittance, or antiresonances of impedance). But the fluid dynamics governing how an air jet interacts with the solid part of a mouthpiece and with the internal acoustical field is far more complicated than anything we have grappled with in previous sections.