The method 

I searched for a method by which the passive acoustic properties of more complex didgeridoo internal forms are calculable.
 

That aim in mind, I started a private project in early 2003. After extensive research in scientific literature and discussions with physicists, I opted for the method of transmission line modelling, which I developed further with my own ideas and findings.

With this method, a didgeridoo is mathematically split into a finite number of cylindrical and conical pieces. The acoustic chain matrix in the complex numbers sector can be resolved for thus modelled inner cavities of didgeridoos, taking into account the uneven inside walls. In this way one obtains the so-called input impedance spectra, from which the resonant frequencies of the air column and the back-pressure of the drone (fundamental tone) and toots (series of overblows) can be read. By coupling the impedance spectra with the respective simulated overtone spectra when playing the drone or toots, one obtains additionally the sound spectra for the drone and the first toot. These simulated sound spectra match well with the practically analysable FFT (Fast Fourier Transformation) spectrograms when the individual instruments are played.

In the context of this website I will predominantly work with absolute frequency data. In order to be able to achieve an allocation to the musical tone designations at any time, the respective frequencies are assigned to the tones in table 1.

Table 1

Audio frequencies in Hz; The range marked in grey shows the fundamental tone frequencies in which most didgeridoos resonate.
 

The following example shows the sound simulation of actual measurements of one of Walter Strasser’s didgeridoos and the accompanying practical analysis of the FFT spectrogram with an FFT analysis programme.

Walter Strasser’s didgeridoo; black: simulation of the toot sequences (drone and overblows);
grey: Simulation of the sound spectrum when the drone is played;
(L=135 cm, dMouth=30 mm, dBell=110 mm; Drone E1, first toot A3+ ) characterised by “singing” third overtone at E3 louder than the drone E11

Practical analysis of the FFT spectrum when playing the drone; the sound level depicted is a relative logarithmic value expressing the difference between acoustic pressures. However, to interpret these spectra the subjective perception of volume of the concurrently sounding frequencies is important. Without wanting to delve any deeper into that aspect, it can be assumed that from the highest peak (i.e. the loudest frequency) only those frequencies still significantly influence the sound character which are up to about 40 dB below the highest peak. All quieter frequencies are overlaid by the louder ones. That means that for every FFT spectrum there exists a sound level section (green box=, that significantly determines the sound characteristic.

Wave pattern for this didgeridoo

Current outcomes of the project are various prototype software tools by which, in dependence of complex internal forms, the toot sequences (drone and overblows) and the sound spectra of the drone and 1st toot can be simulated/calculated. Presently these tools are to hand as non-self-explanatory work versions still under development.

The following example shows the sound simulation of a very interesting interior form with parallel amplified 4th and 5th harmonic overtone. The first overblow is located an oktave and a tone over the fundamental tone and should be very easily to play. The building of a Didgeridoo with this sound characteristic by suitable software produced templates is documented in the crafting example.

Simulation of a didgeridoo with parallel amplified 4th and 5th harmonic overtone
- sound spectrum of the fundamental drone: dark green
- sound spectrum of the 1st overblow: light green
- series of overblows / resonances: white

Using the method developed opens up the following possibilities:

1) Didgeridoos with complex internal shapes can be projected in such a way that the drone and the playable toot sequences can be predetermined.

2) So-called “singing” didgeridoos can be made in which one or two desired overtones are strengthened by higher acoustic impedance peaks in the range of e.g. 350-750 Hz. In the scene such didgeridoos are usually rarities.

3) Didgeridoos can be modelled which have pronounced acoustic impedance peaks between the first harmonic overtones. In these frequencies the voice is especially strengthened and is easier to use in an accentuated manner.

4) FFT spectra can be recorded of interesting didge sound characteristics available as recordings to model internal forms that can come very close to the desired sound characteristics. Due to the fact that the internal forms essentially determine the passive sound characteristics, in principle these internal forms are reconstructable from the sound spectra analysed.

5) In a relatively short time the sound characteristics of so many different internal forms can be simulated that are practically impossible to realise with classical crafting methods. Despite that, however, the know-how of experienced didgeridoo craftsmen is needed to practically implement the simulated internal forms optimally.

The simulation of sound spectra of many hundreds of didgeridoo interiors with a computer makes clear that just small changes of the inner form can open up a “universe” of possible sound spectra. The ultimate didgeridoo that realises all possible wishes about sound characteristics is not calculable. What is possible, though, is an almost endless variety of didgeridoos with unique sound and playing qualities.
 

For anyone with a deeper interest in this theme, I can recommend the book “Das Didgeridoo-Phänomen”. The chapter “Simulation of sound spectra of complex internal didgeridoo forms – Computer Aided Didge (Sound) Design” describes in detail the methodology, the physical correlations and the possibilities for didgeridoo building.

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