19th INTERNATIONAL CONGRESS ON ACOUSTICS
MADRID, 2-7 SEPTEMBER 2007
THE ACOUSTICS OF THE PLAYER-DIDJERIDU SYSTEM
PACS: 43.75.Fg
1
1,2
3
1
1
Wolfe, Joe ; Fletcher, Neville ; Hollenberg, Lloyd ; Lange, Ben ; Smith John ; Tarnopolsky,
1
Alex
1
School of Physics, University of New South Wales, Sydney, Australia; J.Wolfe@unsw.edu.au
2
Dept. Electronic Materials and Engineering, Australian National University, Canberra, Australia
3
School of Physics, University of Melbourne, Parkville, Victoria, Australia
ABSTRACT
The didjeridu is a eucalypt trunk, hollowed out by termites, and originally played in Northern
Australia. It is blown like a tuba and produces just one or a few notes. Its musical interest lies in
striking changes in timbre, produced by strong, varying formants, some of which are determined
by the pattern of 'circular breathing'. A range of other timbres involves vocalisation during play.
We compare the spectra of the sound produced with simultaneous measurements of the
acoustical impedance spectrum Ztract of the player's tract. Sufficiently strong peaks in Ztract in the
1-2 kHz range are strongly correlated with minima in the envelope of the output sound
spectrum, showing that peaks in the acoustic pressure spectrum at the lips diminish acoustic
flow into the instrument. In this range, instrument resonances are weak and have no systematic
harmonic relation with the playing frequency. Consequently, by varying the tract resonance with
various mouth configurations, players can 'sculpt' the spectral envelope to produce formants.
During vocalisations, simultaneous vibration of the player's vocal folds and lips, usually at
different frequencies, which can be detected by applied electrodes, produce sum and difference
tones.
INTRODUCTION
The didjeridu is a musical instrument capable of a vast range of timbres and effects, which are
produced by a relatively strong coupling between the player’s vocal tract and the bore of the
instrument [1-5]. Originally a traditional instrument played only in Northern Australia, it has now
found niches in pop music, world music and concert music. Apart from the intrinsic interest of
the instrument itself, the bore-tract interaction is generally interesting in music acoustics
because, although the interaction is less spectacular in Western instruments than in the
didjeridu, it is still considered musically important [6,7].
In typical performance, a single note drone is played at the frequency of the first resonance, and
only occasionally are notes sounded at the second or very rarely third resonances. An
uninterrupted sound is maintained by ‘circular breathing’: the player inflates the cheeks with air,
which is expelled into the instrument during brief inhalations. The mouth configuration used
during the inhalations changes the timbre and the regular alternation between the phases of
breathing provides a basic rhythm structure in idiomatic performance. The musical interest
arises from ornamenting these structures with further contrasting timbres (Figure 1). Some are
produced by changing the tongue position and mouth shape, which have strong effects on the
spectral envelope. The player may also ‘vocalise’: i.e. produce vibration of the vocal folds at a
frequency usually different from that of the lips, thereby producing interference tones. The
modulation of the spectral envelope and the interference tones are the principal subjects of this
paper.
The instrument itself is superficially simple: a eucalypt tree whose trunk or branch has been
hollowed out by termites is harvested and cut to a length of typically 1.2 to 1.5 metres. A ring of
beeswax makes a comfortable mouthpiece. Its interior is thus like a pipe with a small flare angle
and a complex surface texture. The instrument belongs to the lip valve family, and the player’s
lips operate like somewhat like those of a trombonist.
Figure 1. A spectrogram showing some of the spectral envelope variations
that may be produced above the sustained drone. Sound file at [8].
In this paper we present acoustical impedance spectra of instruments and of the player’s vocal
tract during performance and the spectra of the output sound. We use these to show how the
player uses the tract resonances to modulate the spectral envelope of the output sound. We
also report simultaneous measurements of the motion of the lips and the vocal folds, made
using electrical conduction through the tissues, and compare these with the sound produced.
MATERIALS AND METHODS
The impedance spectra of real didjeridus and of plastic pipes (used to allow reproduction of
measurements) were measured using a spectrometer described elsewhere [9,10] The tract
impedance was measured using an adaptation of the capillary method, with a current source
supplied through a small pipe placed, with a probe microphone, just inside the player’s lips from
the corner of the mouth [5]. For this section, the players were three of the authors (LH, BL, AT).
BL is a member of the Mara people of Roper River in Northern Australia, and learned to play in
the traditional style. LH is an experienced player of contemporary styles and AT learned for the
purposes of the study.
Measurements of the lips and vocal folds of a player (JW) were made by attaching a pair of
metal electrodes coated with conducting gel above and below the player’s lips and another pair
on the throat at the level of the glottis. They were held in place by straps around the head and
neck. The electrical admittance Y between each pair of electrodes was measured at 2 MHz,
which conveniently allowed display of Y(t) on the timescale (~10 ms) of the vibrations. Sounds
were measured at 10 cm and 100 cm from the instrument output.
RESULTS AND DISCUSSION
The impedance spectra Z(f) of instruments (Fig 2) show a series of maxima and minima,
qualitatively similar to but less regular than those of an open cylinder. (The instrument at right is
ranked higher than that at left in a study of quality and acoustics reported at the satellite ISMA
meeting.) Lip valve instruments play at frequencies near the maxima of Z(f) [11,12]. Because of
the slight flare, the maxima are ‘stretched’ somewhat with respect to the odd harmonic series
associated with a cylinder [1,3]. Consequently, there is no systematic coincidence of harmonics
of the lip motion with maxima in Z(f), and so no systematic impedance matching of the
harmonics by resonances of the bore, as is the case with orchestral lip valve instruments. When
this harmonic coincidence does occur, local maxima in the spectral envelope may occur, but
this effect is modest compared to that produced by the player’s vocal tract [5].
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Figure 2. The impedance spectra of two didjeridus.
Vocal tract effects
One of the most common sounds produced in idiomatic didjeridu playing is the 'high-tongue
drone', in which the tongue provides a constriction near the hard palate. This produces a
formant or band of enhanced frequencies somewhere in the range 1-2 kHz, a range in which
speech formants also occur. Human perception is likely to be well adapted, either by evolution
or exposure, to changing formants in this range. In this frequency range, the impedance
maxima of didjeridus, (and especially of good didjeridus [10]), have magnitudes that do not
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much exceed 1 MPa.s.m . This is much smaller than the values measured in orchestral lip
valve instruments, which have much narrower bores at the input and a narrow constriction in the
mouthpiece. A consequence is that the resonances in the player’s vocal tract may have
impedance maxima whose magnitude may exceed that of the didjeridu.
Fig 3 shows the impedance spectrum Ztract of a player's vocal tract, measured just inside the
lips, and compares it with the spectrum of the sound output by the instrument [4].
Figure 3. The impedance spectrum of the player's vocal tract Ztract(f) compared
with the output sound spectrum p(f) produced at the same time.
Maxima in Z tract correlate strongly with the minima in the spectral envelope of the sound, and
vice versa. This is shown statistically in Fig 4.
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Figure 4. The frequencies of maxima and minima in the spectral envelope of the sound
vs those of minima and maxima in the vocal tract impedance, for three players.
The correlation is also observed in the results in a simple mathematical model of the forces
acting on the vibrating lips and on the air flow through them [13]. The maxima in Ztract(f) occur at
frequencies much higher than that of the vibration of the lips, so these resonances have little
effect on the motion of the lips, but may have considerable effect on the air flow between them.
At frequencies of maxima in Ztract(f), there is little air flow into the didjeridu and so little power at
these frequencies. In contrast, the harmonics of the lip motion that fall in frequency bands
where Ztract is small produce substantial air flow at the lips. The efficiency with which these
frequencies are radiated by the instrument depends to some extent on the harmonic
coincidence effect mentioned above, but most are radiated strongly in comparison with the
frequencies that are inhibited by high values of Ztract.
The vocal tract resonances in the frequency range about 1-2 kHz are strongly dependent on the
position and shape of constrictions made by the tongue. Consequently, players can 'sculpt' the
spectral envelope with movements of the tongue. This is a very important part of traditional
technique. Further, during the inhalatory phase of circular breathing, the isolation of the mouth
from the airway by the velum and the dilated cheeks together shift the frequencies of the
resonances of the tract. This produces controllable features in the spectral envelope and timbre.
Vocal fold effects
Vocalisation refers to the vibration of the vocal folds while playing: players describe it as singing
or shouting into the instrument. The technique is used in some traditional narrative playing
styles to imitate animal cries. It is widely used in contemporary performance technique.
It is possible to observe the motion of the lips directly using a transparent didjeridu [5,14,15], but
this is not possible for the vocal folds. We therefore monitored the motion of both valves by
measuring the high frequency electrical admittance Ylips between a pair of electrodes mounted
either side of the player's lips and the admittance Yfolds between another pair mounted either
side of the throat at the level of the vocal folds. Y is strongly correlated with the extent of lip
contact and of vocal folds. Fig 5 shows an example of Ylips, Yfolds and the microphone signal, all
measured simultaneously.
The instrument played for Fig 5 is largely cylindrical, with a small flare at the output end. It has a
length of 112 cm. It plays at a frequency f = 82 Hz or E2, which is approximately the frequency
of the first resonance. Although vocalisation is present here, the spectrum of the sound signal
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shows a strong spectral peak at 82 Hz and the oscillogram is approximately periodic with a
period 1/f = 12 ms. Note, however, that the 12 ms ‘cycles’ do not repeat exactly, but alternate in
shape: the real period is 2/f = 24 ms, and the spacing of the peaks in the sound spectrum is 41
Hz, for reasons we discuss below. The pitch of a sound is strongly dependent on the spacing of
its harmonics in the range several hundred Hz, and the perceived pitch in this case is a little
ambiguous: one can hear both the missing fundamental E1 (41 Hz) and also E2 and B2.
Figure 5. The top panel shows the sound signal output from the instrument – waveform
left and spectrum right. The middle and lower panels show the lip and vocal fold signals
Ylips, Yfolds The vertical scales are linear and uncalibrated.
Similar comments apply to the electrical admittance across the lips: it is exactly periodic at 41
Hz (= f/2), but nearly periodic at 82 Hz, the resonance of the instrument. Comparing spectra of
lips and sound, we see that, while the second and third harmonics of the lip motion (2f and 3f)
have nearly equal magnitude, the third harmonic is radiated more efficiently. This is because the
third harmonic falls close to the second resonance of the instrument, which is not far from being
cylindrical. Consequently, 2f is weak in the sound spectrum.
The vocal fold signal most clearly shows the period of 24 ms, corresponding to f/2 = 41 Hz. The
player in this case reports that he is vocalising at a frequency g = 123 Hz which is 3/2 times the
frequency f of the sound, or a perfect fifth above it. By this, the player means that he aims to
produce a pitch a fifth above, and also that this is what he hears and feels. The spectrum of the
electrical admittance of the vocal folds does indeed shows a strong component at frequency g =
123 Hz. As well as the peak at g = 123 Hz, the glottal oscillogram shows an equally strong
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component at f = 82 Hz. This is not surprising: the lips are vibrating strongly, and are being
driven by a resonator with a very high Q. Thus a strong acoustical pressure wave in the vocal
tract is strongly affecting the motion of the folds themselves. The player is also aware of this: it
is somewhat difficult to control the vibration of the vocal folds precisely. However, the condition
of harmonic consonance (g = 3f/2) feels significantly different from non-consonant ratios. We
remark in passing that this significant modification of glottal behaviour by a pressure wave in the
vocal tract may have significant implications for the phenomenon of resonance tuning in singing,
which is the subject of another paper in this conference [16].
The glottis-tract-lips-didjeridu system has two strongly non-linear elements: the air flows through
the glottis and lip apertures are nonlinear functions of the pressure difference across them. In a
simple model [13], the nonlinearity comes from the dissipation of kinetic energy of the jet
downstream of the aperture (see [5,8] for schlieren images of the jet). This gives rise to
interference tones with frequencies gf, g+f and ng±mf, which are clearly visible in all three
spectra. The case chosen for discussion in this paper is one of the simplest possible examples.
Both traditional and contemporary performance technique use vocalisations with frequencies
that may be fixed at different intervals above the drone, or that may vary in time, giving rise to
exotic effects. Some demonstrations (both sound and spectrogram) are available [8].
CONCLUSIONS
Two of the most important features of didjeridu performance – the rhythmical timbre changes
associated with circular breathing and the shifting formants accomplished with mouth
configuration changes – are explained by the modulation of the spectral envelope using the
acoustical impedance of the player’s vocal tract. A third, the production of interference tones, is
demonstrated by simultaneous measurements of lip motion, glottis motion and output sound.
The sound wave generated in the mouth by the lip motion has a profound effect on the motion
of the vocal folds.
ACKNOWLEDGMENTS
This project was supported by the Australian Research Council. The Didjshop kindly provided
the instruments shown in Fig 1. BL worked on the project on a UNSW vacation scholarship.
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