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

6 CHAPTER 1. INTRODUCTION
1.5 ACOUSTIC IMPEDANCE: PREDICTING THE PLAYING QUALITIES OF A FLUTE
Many of the acoustical characteristics of a flute may be quantified by its acoustic impedance
spectrum. Acoustic impedance is the ratio of pressure to flow at the input to the instrument
and describes how the flute will ‘respond’ to exciation at a particular frequency. The magnitude
of the acoustic impedance of a flute varies over the frequency range of the instrument and
has many maxima and minima. Because the flute is open to the air at the embouchure, the
minima correspond to the possible standing waves, and the notes the flute can play are close
in frequency to these minima. The impedance spectrum can also tell us about the tonal characteristics
and playability of a note. Generally, if for some fingering there are many impedance
minima with frequencies in a harmonic relationship to each other, then the note produced will
be harmonically rich (bright); if not the note will be more pure (or dull sounding). Playability
of a note depends upon many factors, such as how deep its impedance minima are, and
whether or not there are other minima nearby. Each fingering for the flute produces a different
impedance curve, with different possible standing waves.
Many methods may be used to measure the acoustic impedance of woodwind instruments.
At the least, some source of acoustic energy is needed (such as a loudspeaker) along with a
means of measuring or inferring both the pressure and the flow. A review of many methods
that have been used is provided in Chapter 3, which also documents the development of a
novel, high-precision measurement and calibration technique.
The acoustic impedance of a flute can be modelled by treating the flute as a one-dimensional
network of cylinders and cones. We may then calculate the impedance properties of each
element and derive the impedance of the entire flute. Figure 1.4 illustrates such an approach.
Starting at the downstream end of the flute, the impedance of the last cylindrical segment is
calculated (Z 1 ), as is the impedance of the last tone hole (Z 2 ). These impedances are combined
in parallel and the result used in the calculation of the impedance at the next section. The
impedance is calculated in an iterative manner until the entire flute is modelled. If the geometrical
lengths of the flute segments are used without correction to calculate the impedance,
it will not be accurate. This is because of various effects that are not adequately modelled by
the one-dimensional network described above. However, adequate results can be achieved if
measured length corrections are used. The tone hole segments (but not the bore) in Figure 1.4
are shown with length corrections added.
1.6 TUNING, TRADITION AND THE ‘STANDARD FLUTIST’
Musicians can be (understandably) resistant to people meddling with their instruments, and
a flute judged to be perfectly in tune by one person may be out of tune to another. Musical
instruments usually evolve, as instrument makers adapt to changing musical tastes and playing
styles. Musicians are taught to compensate for their instrument’s peculiarities, and with
years of practice they do this remarkably well. For this reason it is often difficult to convince
musicians that a new design is better than the existing one, since adopting the ‘improved’ instrument
will entail ‘un-learning’ some of their technique. Furthermore, the concept of an