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

70 CHAPTER 5. IMPEDANCE SPECTRA OF THE FLUTE AND CLARINET
The position of the cork in the head joint of the modern flute was set at 17.5 mm from the
centre of the embouchure hole, and the tuning slide was set at 4 mm. These are typical values
used by flutists playing at standard pitch. For the classical flute the cork was set at 19 mm and
the tuning slide at 12.8 mm (this was determined empirically by the maker Terry McGee as the
correct position for the flute to play at A 440, although his playing style may not be typical).
All standard and many alternative and multiphonic fingerings were measured for the modern
flute with both C and B foot. Classical flutes currently available differ widely in design and
hence no authoritative standard exists. For the measurements in this chapter, the fingerings
given in Porter (2005) were used. In all cases the fingerings are shown on each graph of the
results.
The impedance of the clarinets were measured over the range from E3 to E7 (written) for all
standard fingerings and a selection of multiphonic and alternate fingerings.
5.2.2 The impedance spectrometer
The details of the impedance spectrometer have been described in Chapter 3. The impedance
spectra are measured between 200 Hz and 4 kHz for the flute and between 120 Hz and 4 kHz
for the clarinet (a range that encompasses the fundamental frequency of all of the instruments’
notes and includes their cut off frequencies).
A 7.8 mm inner diameter brass measurement head is used in addition to the 15 mm head
described in Chapter 3. In all other respects this impedance head is identical to the 15 mm
version. The 7.8 mm impedance head may be used to measure the input impedance of flutes
and clarinets as the outlet fits within the embouchure hole of a flute and the mouthpiece of a
clarinet. (The cross-sectional area of this head is comparable with the area through which air
flows between clarinet and mouthpiece, i.e. the gap between reed and mouthpiece. It is also
comparable with the area of the hole at the embouchure of a flute when played.)
The impedance head is calibrated as described in Chapter 3 using a solid stop (infinite impedance
load) and a 7.8 mm semi-infinite pipe.
5.2.3 Attachment of instruments
The flutes were coupled to the impedance head as in Wolfe et al. (2001a) (see also Smith et al.
1997) with a concave attachment matching the curvature of the embouchure striker plate (Figure
5.1 (a)). The thickness of the concave attachment was accounted for in calibration, so that
the reference plane for impedance measurements was situated at the embouchure hole. For
the spectra presented in this chapter and in Appendix A the impedance of a stub of length
5 mm and diameter 7.8 mm was added to the measured impedance to account (at least approximately)
for the radiation impedance baffled by the player’s face and lips (see Wolfe et al.
2001a). The impedance was thus measured upstream of a discontinuity, since the diameter of
the embouchure hole on the outside of the instrument is greater than 7.8 mm for both headjoints
measured. This measured impedance will be different to the impedance that would be
measured by an impedance head with diameter matched to the input radius of the instrument.
However, in the played instrument a similarly sized discontinuity exists, since the player’s lips
occlude the embouchure hole to a significant extent.