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

CHAPTER 5. IMPEDANCE SPECTRA OF THE FLUTE AND CLARINET 89
10 8
10 7
m
(Pa s
10 6
|Z|
− 3 )
10 5
model
experiment
10 4
0 1 2 3 4
f (kHz)
Figure 5.27: Impedance spectra (experiment and model) for the fingering C♯5 on the classical
flute without empirical correction.
5.3.5.1 All finger holes open
The fingering for C♯5 on the classical flute has all finger holes open and all keyed holes
closed. In Figure 5.27, the model is tested on this fingering using the equations in §2.2.10 and
the low-frequency correction (2.29) to model the radiation impedance of open finger holes.
The small length correction for closed keypads used in §5.3.4 is retained for classical flutes.
A better fit to the experimental data is obtained if we include a length correction for open
holes of
t open hole = −0.15b, (5.7)
as shown in Figure 5.28. This length correction is opposite in sign to the length correction used
for open keyed holes, which is not surprising—open finger holes do not have an overhanging
keypad to increase the inertance. The small negative length correction may be in part due to
the fact that finger holes are usually undercut to some degree.
5.3.5.2 Most finger holes closed
The fingering for D4 on the classical flute has all holes closed except for the two holes at
the end of the instrument which are always open. In Figure 5.29 the model is tested on this
fingering, but with the effects of closed holes deliberately ignored. As expected, the model prediction
is clearly sharp compared to experiment. In Figure 5.30 the same fingering is modelled
and the standard length corrections for closed (keyed) holes are used. This was done to test
whether finger hole length corrections need be explicitly included in the model, or whether the