The acoustic input impedance of the air columns of four traditionally crafted didgeridoos were measured as a function of frequency. The peaks in input impedance correspond to the resonant frequencies of the air column. In none of the instruments did the resonant frequencies come close to forming an harmonic series. Western wind instruments are designed so the resonances of their air columns come as close as possible to forming a harmonic series: many harmonics of the note being played will match air column resonances , and are thereby amplified. Very few of the harmonics fo the didgeridoo sound, however, match the instrument resonances, reducing the intensity of the lower harmonics, apart from the fundamental. In the sample curve in figure 4 there are clearly strong resonances out to 2000 Hz, which do not disappear altogether until 4000 Hz. This is because the open end of the didgeridoo is not flared- in contrast to the trombone, for example, which has a large flared bell and shows no resonances above 800 Hz. Low frequency oscillations in the air column are poorly radiated from a small opening, so are largely reflected back into the instrument instead, where they set up standing waves. The higher frequency harmonics of the didgeridoo sound are radiated well, allowing the formant to be clearly heard. Hence the crude structure of the instrument is quite important for bringing out the high frequency formants, since it acts as a filter, allowing changes in the higher harmonics to be heard.

Casual sounding of the didgeridoo, even by experienced brass players, does not create strong formants. The lips must be forced by playing as loudly and harshly as possible. Films of the lip motion were made both when blowing hard to make a 'dirty' tone and when blowing slightly more softly to make a loud but 'cleaner' tone, and these permitted the curves in figure 5 to be generated. In both cases the lips were in fact closed for a large portion of the cycle. When playing with a 'dirty' tone the lips opened for a shorter time, creating an even more chopped input to the instrument. From Fourier analysis it is clear that such a pulsed input must have a rich spectrum of harmonics. The oscillatory release of air into the instrument also sets up standing waves in the vocal tract where, as we have seen earlier, there is a resonance tuneable from 750 to 2750 Hz. This resonance is excited by the higher harmonics in the pressure oscillations leaving the lips. It is also important that the frequency of the vocal tract resonance is considerably higher than the frequency of the lip oscillations (~60Hz), as this allows several cycles of the vocal tract resonance to be transmitted to the instrument during the time the lips are open.

The didgeridoo player can control the timbre of the sound produced through a complex combination of instrument structure and playing technique. The shape of the instrument and the random profile of its bore cause a suppression of lower harmonics. By forcing the lips very hard and tuning the vocal tract resonance to a high frequency, strong oscillations can be set up in the vocal tract and transmitted to the instrument. This technique is radically different from that used in classical brass technique, which explains why the possibility of the vocal tract resonance having a large effect on tonal quality has largely been overlooked.

Graham C. Wiggins
Clarendon Laboratory, Oxford

Addendum:
My original research project was inspired by a paper by Dr. Neville Fletcher (N. H. Fletcher, "Acoustics of the Australian didjeridu", Journal of the Australian Institute of Aboriginal Studies 1 (1983)). After my article in Physics in Action was published, he wrote to me and suggested a further explanation for how the vocal tract resonance is communicated to the instrument. He pointed out that the diameter of the vocal tract is very similar to the diameter of the hole inside a didgeridoo. This will lead to "impedance matching", whereby the similarity of the two tubes will allow oscillations to be transmitted easily from one to the other. This situation is generally not the case with western brass instruments, where there is a cupped mouthpiece which leads to a small diameter tube at the start of the instrument. A common-sense explanation of this concept, which I find very important in understanding the didgeridoo, is that the instrument is in some ways simply an extension of your throat and mouth, and what happens inside your body comes out in the sound of the instrument.