Physics of the Didgeridoo

About physical basics that are responsible for the typical sound characteristics of the didgeridoo and lead to its specific playing style.

From the physical point of view the didgeridoo is a more or less irregular shaped pipe which determines the shape of the interior vibrating air column.
According to whether the mouthpiece end is open or closed with the mouth, we find an irregular sequence of resonating frequencies of that air column (intrinsic resonances). The positions and distribution of these intrinsic resonant frequencies depends fundamentally on the shape of the air column.
Slapping with a flat hand on the mouthpiece and keep it closed, you obtain the sound of the intrinsic resonances of the one-end-closed pipe. Opening the mouthpiece right after slapping on it, you obtain those of the both-end-open pipe.
Every intrinsic resonance of the one-end-closed pipe (closed with the mouth) is playable with the vibrating lips (basic drone and the series of overblows or toots). Playing the lowest resonance produces the basic drone, playing the next higher resonances produces the toots.

[This row of the playable intrinsic resonances is not comparable with the nature scale (e.g. row of the playable overtones (flageolett) on a guitar string) because by the irregularity of the inside form at the didgeridoos in comparison to other instruments these are not harmonic. The sounding harmonic overtones during playing the basic drone correspond to the nature scale. But generally these harmonic frequencies don't fit with the frequencies of the intrinsic resonances.]

When playing an intrinsic resonance (at the didgeridoo the lowest to get the basic drone) the harmonic spectrum of the overtones of this intrinsic resonance resounds.
That means the 2, 3, 4, ..., nfold of the fundamental frequency.
In case harmonic frequencies fit with intrinsic resonance frequencies of the air column, these will be amplified and become audible as a singing tone (see below). Harmonics lying between intrinsic resonances are not amplified and are audible only (if at all) indirectly through the sound characteristics evolving. That means, the spectrum of the intrinsic resonances (depending on the interior form of the air column) filters (amplifies or dampens) the spectrum of the resulting harmonic overtones.

[If one sings a note with the voice which falls on an intrinsic resonance, this sung note is also amplified. Additional the mixture frequencies (sums and difference frequencies) still arise from basic drone and sung note which can partly lie under the fundamental frequency. In typical traditional playing techniques of NW-Arnhemland the interaction of the intrinsic resonances with the mixture frequencies (sums and difference frequencies) of the fundamental and the voice are very important.]

The stronger an intrinsic resonance and the more harmonic overtones fit with other intrinsic resonances the higher is the acoustical impedance it can feel as backpressure.
The resulting harmonic spectrum (sound spectrum) is partly transfer onto the wall of the didgeridoo and comes into resonance with it.
The typical sound is transferred to the surroundings directly through the open end by the air column and a little part indirectly by the wall of the didgeridoo.
Additionally to the passive interior form depend intrinsic resonances, in the typical western way of playing the overtones are also influenced (filters, amplifies, dampens) by the variable resonating spaces in the vocal tract.
In typical traditional playing techniques of NE-Arnhemland the dynamic movements of the tongue activates especially the sound of the complete spectrum of intrinsic resonances of the “one-end-closed-pipe” (e.g. with the “cut”) and temporarily of the “both-end-opend-pipe” (e.g. with low-pressure-effects during the fast retroflexing tongue).
This leads to additional percussive drum-like effects and to typical whirring harmonic overtones, amplified alternately by different intrinsic resonances (“wobbling” or “ringing” overtones, see below).
The main sound and playing characteristics are determined by the complete contour of internal cross-sections of the air column in the didgeridoo and are often influenced most distinctly by the interior form of the first third of length beyond the mouthpiece.
Many naturally grown eucalyptus-didgeridoos with interesting sound-features chosen by Aboriginal makers have interesting structures in that area.
That is one reason why sound characteristics of slide didgeridoos or self-made simple drilled instruments are often very restricted because the most interesting area is dominated by the less interesting cylindrical shape.

Oversized bells
(inner diameter >12 cm) often result in a loud instrument. Mostly this volume hides the lack of an interesting sound characteristic but nevertheless is rather interpreted or perceived as a positive sound quality by untrained listeners.

Harmonic wobbles
Quickly alternating amplification (5 – 10 times per second) of different overtones in instruments with a defined alignment between intrinsic resonances and harmonics, obtained by using certain traditional playing techniques.

Singing harmonic
Distinctly perceivable harmonic, amplified by an intrinsic resonance of the vibrating air column.
 

28.3.2006 - Frank Geipel

22.12.2006

Simulations-Grafiken aus einem Didgeridoo Experimental-Vortrag von Frank Geipel

weiß: Impedanzspektrum,
blau-violett: Klangspektrum Grundton
rot-grün: Klangspektrum 1. Overblow

Beispiel für ein Didgeridoo mit ausgeprägtem Sington (5.Oberton)
Example of a didjeridu with a prominent singing 5.harmonic
 

Beispiel für ein obertonwobbelfähiges Didgeridoo (zwischen 4. und 5. Oberton)
Example of a didjeridu with a harmonic wobble pattern between 4. and 5. harmonic
 

Beispiel für ein Didgeridoo mit sehr gut anspielbaren 1.Overblow und verstärkten 2. und 5. Oberton
Example of a didjeridu with very good playable 1.overblow and prominent 2. and 5. harmonics
 

Beispiel für ein Oktav-Didgeridoo (1. Overblow eine Oktave über Grundton, 2. und 3. Eigenresonanz verstärkt 2. und 3. Oberton des Grundtones)
Example of an octave-didjeridu (1.overblow one octave above the fundamental) 2. and 3. intrinsic resonance amplifies the 2. and 3. harmonics
 

Beispiel für ein „trocken“ klingendes Didgeridoo mit Impedanzpeaks zwischen dem 1., 2. und 3. Oberton, was die Verstärkung von Mischfrequenzen aus Grundton und Stimme fördert
Example of an „dry“ sounding didjeridoo with intrinsic resonances between 1., 2. and 3. harmonics (it could amplify mixed frequencies of fundamental and voice)