Flute acoustics: measurement, modelling and design - School of ...

82 CHAPTER 5. IMPEDANCE SPECTRA OF THE FLUTE AND CLARINET
10 8
10 7
|Z| (Pa s m −3 )
10 6
10 5
10 4
model
experiment
0 1 2 3 4
f (kHz)
Figure 5.13: Impedance spectra (experiment and model) for an open modern headjoint after
adjustment of parameters.
empirical parameters is entirely reasonable, since turbulence generated at discontinuities is a
lossy process.
Experimental and modelled impedance spectra for the two measured headjoints (open and
closed) are shown in Figures 5.13–5.16.
Clearly, the empirical parameters used to model the headjoint are optimised for the modern
and classical flute. If a flutemaker were to design a headjoint with wildly different dimensions,
then this model may not predict the input impedance accurately. Thus a more comprehensive
study is in order. However, the headjoint parameters are unlikely ever to deviate greatly from
these examples, since they are constrained by the player’s face geometry and the physics of the
air jet. For a more detailed discussion of the acoustics of flute head joints, see Benade & French
(1965) and Fletcher et al. (1982).
5.3.4 Modelling the modern flute
Given an accurate model of the modern flute headjoint, we may now use the measured impedance
spectra for the flute under different fingering conditions to test and refine the flute model,
paying particular attention to the modelling of open and closed tone holes.
5.3.4.1 All holes closed
The modern flute with C foot plays the note C4 with all holes closed. The model was first
tested on this fingering. Figure 5.17 shows the performance of a primitive model for this fingering.
The headjoint model as derived in §5.3.3 was used but no account was made for the closed