Physics of the didgeridoo (didjeridu or yidaki)

This page is an appendix to a scientific paper on the vocal tract and the sound of the yidaki (also known as didjeridu or didgeridoo). It presents sound files, spectra and impedance measurements from experiments in which the acoustical impedance spectrum of the player's vocal tract was measured, during performance, just inside the lips.

For an introduction to the acoustics of the yidaki, see Acoustics of the Yidaki/ Dijeridu.

Here we explain the production of strong formants in the sound of the instrument. This sound file consists of a sample of the "high tongue" sound, followed by a sample the "low tongue" sound. This pair of samples is repeated three times. Spectra of the two sounds are shown below.

mp3 file 470k . . . Download sound file in .wav format (700 k)

To produce the "high tongue" or high drone sound, the tongue is held close to the hard palate to make a narrow constriction. Consequently, the acoustic impedance has high values at the resonances, as shown in the figure at left below. The frequencies at which the impedance is high correspond to resonances that have pressure antinodes and velocity nodes near the lips. Consequently, there is very little acoustic flow into the instrument at these frequencies, and so a minimum in the spectral envelope (figure at left). Between these minima, the flow is not impeded so much, and so there are formants, or peaks in the spectral envelope, at frequencies at which the impedance is low. To produce the "low tongue" sound, the tongue lies low in the mouth (figure at right). Even at the resonant frequencies, the acoustic impedance is lower, because of the larger aperture. Consequently, the acoustical flow at these frequencies is not inhibited substantially and there are no strong formants. Note the absence of the strong formant in both the spectrum and the sound files. Note that, in the sound files, the pitch as well as the timbre is changed by the tongue position. We have reported on this effect in the trombone in another study.

graphs of tract impedance and output sound spectra for high tongue configuration

Sound spectrum and vocal tract impedance for "high tongue" configuration

graphs of tract impedance and output sound spectra for low tongue configuration

Sound spectrum and vocal tract impedance for "low tongue" configuration
The curves are typical. In the high tongue configuration (left), maxima in of the spectrum of the output sound correlated well with minima in the impedance spectrum (a correlation coefficient 0.98 for 46 measurements on three players).

In the sound file, although the sound is clearly that of a yidaki with a pitch below that of the normal human voice. Nevertheless, it sounds a little like someone alternating between the sound "ee" (the vowel in the English word "heed") and an indistinct vowel something like "aw" (the vowel in "hoard" or "hot"). In a previous study, we measured the resonances of the vocal tracts during speech. Vocal tracts pronouncing "heed" have a strong resonance at about 1.8 kHz, while tracts pronouncing "hoard" or "hot" have no resonances between 1 and 2 kHz.

Another important tract configuration is that used for 'circular breathing', during which the soft palate seals the mouth from the nasal cavity, allowing the player to inhale from nose to lungs while expelling air stored in the inflated cheeks into the instrument. This is studied as part of a much larger study on the yidaki.

In our paper on the yidaki, we briefly discuss the importance of the glottis (the aperture left open between the vocal folds) in the production of strong resonances in the vocal tract in the kHz region. When the vocal folds are nearly closed, as they are for speech, the reflection coefficient for sound waves travelling down the vocal tract is high for all but very low frequencies. When the vocal folds are relaxed and open, the reflection coefficient for frequencies near 1 kHz is much lower: sound waves in the upper airway are more readily transmitted to the lower airway and to the highly lossy lungs. Consequently, the resonances of the vocal tract are weaker.

It is both practically and ethically problematic to measure, with a nasendoscope, the opening of the glottis of a human yidaki player during performance. For this and other reasons, we have made studies using an artificial system for playing the yidaki, in which the "glottis" opening in the artificial vocal tract can be accurately controlled. Measurements on such systems show weaker resonances and weaker formants when the glottis is open. This is in agreement with simple mathematical models. Both the artificial playing system and the physical models are the subjects of extended papers to be presented elsewhere.


The yidaki project combines several different elements. On the experimental side, the major advance has been the development of a system that can measure the acoustical impedance of the vocal tract during performance on the yidaki. In this situation, the sound level in the mouth can be 100 dBA, which seriously complicates the making of mesaurements. Other aspects of the project involve theoretical modelling of the instrument, the lips, the vocal tract and the lower airway and their interaction. Much of this work is applicable to other musical instrument-player interactions, and indeed to other aspects of acoustics.

Several people have worked or are working on various aspects of the yidaki project:
Alex Tarnopolsky [1], Neville Fletcher [1,2], Benjamin Lange [1], Lloyd Hollenberg [3], John Smith [1] and Joe Wolfe [1].

[1] The University of New South Wales, [2] The Australian National University and [3] The University of Melbourne.

We gratefully acknowledge the support of the Australian Research Council.

 

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Joe Wolfe / J.Wolfe@unsw.edu.au
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picture of yidaki player

Benjamin Lange, one of the authors of this paper, is a member of the Mara people of Northern Australia, where he learned to play yidaki in the traditional style. He recently graduated in Electrical Engineering at the University of New South Wales, where he worked on the yidaki project on a vacation scholarship.

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