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Spécial « Congrès Acoustics 2012 »
Acoustical and musical properties of the Deskford carnyx reconstruction
Input impedance and transfer function of carnyx
The input impedance of the instrument, measured using the
BIAS apparatus [4], is shown in Figure 5. Three features
of this curve which have implications for musical perfor-
mance can be noted. Firstly, the frequencies of impedance
peaks 1 to 5 are clearly not harmonically related.
Fig. 5 : Input impedance of carnyx reconstruction
Impédance d’entrée de la reproduction du carynx
Secondly, the unusual design of mouthpiece means that
the boosting of impedance peak amplitudes around peak 5,
commonly seen in the impedance curves for cup mouth-
piece instruments, is very weak in this case. Thirdly, at
least 30 peaks can be distinguished, suggesting that the
cutoff frequency is around 2500 Hz, around three times
that of a tenor trombone.
The extent to which the resonance frequencies deviate from
a harmonic series is illustrated by the plot of Equivalent
Cone Length (ECL) [5] in Figure 6. While the fourth and
fifth resonances correspond to those of a perfect cone
of length 2.0 m, the first resonance is that of an equi-
valent cone of length 2.85 m. A strongly mode-locked
regime of oscillation can occur between modes which lie
close to a vertical line on the ECL plot; clearly an oscilla-
tion based on the first or second mode frequency will not
satisfy this criterion.
The frequency dependence of the radiation effciency of
the instrument was investigated by measuring the trans-
fer function T, defined as
(1)
with p(in) the acoustic pressure of a sine wave at the
mouthpiece entrance and p(out) the acoustic pressure
in the radiated sound field, measured at a point 50 cm
from the hinge of the fully open jaw and directly in front
of the opening. The measurement was carried out in an
anechoic chamber. The frequency of the input sine wave
was ramped from 50 Hz to 5000 Hz with an amplitude
suffciently low that effects of nonlinear propagation were
insignificant. The result is shown in Figure 7.
Fig. 6 : Equivalent Cone Length for carnyx reconstruction
Longueur de cône équivalente pour
une reproduction de carynx
Below 1500Hz the minima of the transfer function are close
to the maxima in the input impedance. For an open trombone
bell the overall shape of the transfer function is a rise from
low frequency to the bell cutoff frequency, above which the
function is broadly constant. In contrast, the transfer func-
tion for the carnyx shows a deep minimum around 1500 Hz,
with two strong peaks between 2000 Hz and 3000 Hz.
It appears that the mouth shape and tongue are performing
an acoustic function similar to that of a trombone mute.
Fig. 7: Transfer function of carnyx reconstruction, measured from
mouthpiece entrance to a point 50 cm in front of the jaw
opening on the head, as a function of frequency
Fonction de transfert de la reproduction du carynx,
mesurée de l’entrée de l’embout buccal à un point
placé 50 cm avant l’ouverture de la mâchoire
ouverte, comme une fonction de fréquence
Playing frequencies
A recording was made of John Kenny playing what he consi-
dered to be the natural notes of the instrument. The
playing frequencies and pitches of some of these notes
are shown in Table 1.
