Acoustics of the yidaki or didjeridu

This page is an appendix to two scientific papers, one experimental and one theoretical about the yidaki or didjeridu (didgeridoo) and its interaction with the vocal tract . It presents sound files, videos and spectra. It also shows some measurements of the acoustical impedance spectrum of the player's vocal tract, measured just inside the lips, while he was playing.

There is also an introductory page of Acoustics of the Yidaki/ Dijeridu, which has a wider range of sounds.

Lip motion

When playing the yidaki, the lips move much like those of a tuba player. The image and video clip below were taken with a camera operating at 1000 frames per second. The "yidaki" in question was made with glass panels. A mirror is positioned so that, while the main image is from the front, a side view of the lips is shown at right. The scales on the left and right are in millimetres. The same transparent "yidaki" was also used to make schlieren images of the air jet from the lips. These are shown in the animation below and in Figure 8 of the experimental paper.) Click on the image for video clip.

Circular breathing

One of the features of yidaki playing is the use of "circular breathing". In the sound file below, the player begins with a steady, sustained note. This is followed by a series of alternations between normal playing and inhalations. During the inhalations, which are made through the nose, the player continuges to play using air stored in the mouth cavity, which is isolated from the nasal cavity by the soft palate. The air is expelled from the mouth using tension in the muscles of the distended cheeks. The part of the sound file with the three circular breaths is analysed in Figure 10 of the experimental paper.)
    wav file 400k . . . Download sound file in .wav format (400 k)

Vocal tract resonances

The differences in sound between the inhalation and normal playing phases are due, in part, to the difference between the resonances in the player's mouth alone (inhalation phase) and in the vocal tract (normal playing).

Players can also make spectacular changes in the spectral envelope of the sound produced using the position of the tongue to change the frequency response of the vocal tract. In particular, positioning the tongue close to the hard palate (the "high tongue" position) produces a strong formant between 1 and 2 kHz, its exact value depending on details of the mouth geometry. With the tongue low in the mouth, this formant disappears.

The next 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)
As we explain in the papers mentioned above, the spectral envelope of the sound produced when playing the yidaki depends strongly on the resonances of the player's vocal tract. A maximum in the acoustic impedance of the tract at a particular range of frequencies inhibits flow into the instrument at those frequencies and thus produces a broad minimum in the spectral envelope. Conversely, a minimum in the impedance of the tract produces a formant or enhanced band of frequencies in the output sound.

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.

In our papers 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.

Vocalisation while playing

Another feature of yidaki playing is the use of "circular breathing". In the sound file below, the player (LH) begins with a steady, sustained note -- without vocalisation. This is followed by a series of segments in which the drone is played with the lips while the player vocalises (sings, or allows his vocal folds to vibrate) at a range of pitches. The third sound segment in this sound file is analysed in Figure 11 of the experimental paper. One can hear the vocalisation at a musical fifth above the drone, so its frequency is 3/2 times that of the drone. One can also hear a strong harmonic partial a musical seventeenth above the drone, because the fifth harmonic lies in the formant of the radiated sound: it is strongly emphasised by the tract resonance near that frequency.
    wav file 400k . . . Download sound file in .wav format (400 k)

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.

 

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