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

5.3. RESULTS AND DISCUSSION 93
10 8
10 7
m
s
(Pa
10 6
|Z|
− 3 )
10 5
model
experiment
10 4
0 1 2 3 4
f (kHz)
Figure 5.28: Impedance spectra (experiment and model) for the fingering C♯5 on the classical
flute with empirical correction.
correction used in §5.3.4 would suffice. As can be seen in Figure 5.30, this results in a model
prediction that is too flat, particularly in the frequency range 1.5–2 kHz.
The length corrections identified in Chapter 4 for closed holes were then included in the
model (Figure 5.31). The fit to the experimental data is better, justifying the use of explicit
length corrections for closed finger holes. The overall flattening effect of closed holes is to some
extent ameliorated for closed finger holes, since the protrusion of the finger into the hole reduces
the hole shunt compliance, in some cases making it negative. The series impedance
is also different for closed finger holes, although the effect of the series impedance is usually
much less than that of the shunt impedance.
5.3.5.3 One keyed hole open
The fingering for F4 and F5 on the classical flute uses one open keyed hole. In Figure 5.32
the model is tested on this fingering, using the same length corrections for open keyed holes as
were used for the modern flute. However, keyed holes on classical flutes usually do not have a
chimney and so the radiation impedance of an infinite flange is more appropriate than that of
a circular flange as used in §5.3.4. The model was altered to accommodate open keyed holes
without chimneys. As can be seen in Figure 5.32, the model copes with the open keyed hole
quite adequately.