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

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Chapter V
Impedance spectra of the flute and clarinet ∗
5.1 INTRODUCTION
Several authors have measured the input impedance spectra of brass and woodwind instruments
(Backus 1974, 1976, Elliott et al. 1982, Caussé et al. 1984, Wolfe et al. 2001a) but such
measurements are often prone to systematic errors and, depending on the excitation signal
used, may take a great deal of time to measure over a wide frequency range. In this chapter, a
spectrometer using three microphones and calibrated on resonant-free loads (see Chapter 3)
is used to measure the input impedance of several flutes and clarinets. Using such impedance
spectra, many differences in tuning and timbre between the instruments are explained.
A database of input impedance spectra for the flute (Wolfe et al. 2001b) has been used to
develop software tools that are widely used by flutists (Botros et al. 2002). In the future it may
be possible to use the measured database of clarinet spectra in an analogous way. In this thesis,
the measured flute impedance spectra are used to fit a semi-empirical model for flutes of arbitrary
geometry. This model forms the basis of a software tool being developed for instrument
makers.
5.2 MATERIALS AND METHODS
5.2.1 Instruments and fingerings
The following instruments were measured:
• modern flute (Pearl PF-661, open hole, measured with both a C foot and a B foot)
• classical flute (made by Terry McGee, Canberra, Australia)
• B♭ and A clarinets (Yamaha Custom CX).
The dimensions of these instruments are provided in the XML files ModernFlute.xml,
ClassicalFlute.xml and BbClarinet.xml in Appendix B. The classical flute, an experimental
instrument, is described in Wolfe et al. (2001a), although several keys have been added to
the flute in the intervening time—it now has four keys, which when operated give the notes F,
B♭, C and G♯ (the flute is designed to play in the key of D without the use of any keys). The two
clarinets measured have the same bore diameter and differ by approximately 6% in length. In
addition to the above-mentioned instruments, the modern and classical flute headjoints were
both measured without the flute body. Some simple T-junctions were also measured, as mentioned
in §5.3.3.
∗ Parts of this chapter have been published as Dickens, P., France, R., Smith, J. & Wolfe, J. (2007), ‘Clarinet acoustics:
introducing a compendium of impedance and sound spectra’, Acoustics Australia 35(1), 17–24.