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Spécial « Congrès Acoustics 2012 »
Acoustical and musical properties of the Deskford carnyx reconstruction
Frequency (Hz)
Pitch
39
D#1 + 5 cents
77
D#2 - 18 cents
169,5
E3 + 49 cents
266
C4 + 29 cents
526
C5 + 9 cents
623
D#5 + 2 cents
696
F5 - 6 cents
Tabl. 1 : Playing frequencies and pitches
Fréquences jouées et leurs emplacements
Two particularly strong played notes were at pitches
E3 + 49 cents (described in the following discussion as
E3) and C4 + 29 cents (described as C4). Frequency spec-
tra of these notes were calculated. The spectrum of E3 is
shown in Figure 8, superimposed on the input impedance
curve. It is evident that the fundamental frequency of the
played note is slightly higher in pitch than the second reso-
nance peak, while the second and third harmonics are
below the fourth and sixth resonance peaks respectively.
This could account for the relative weakness of the upper
harmonics, implying that the lip behaviour is outward stri-
king. A similar comparison of played spectrum and input
impedance is given in Figure 9 for the played note C4.
The frequency match between harmonics and resonance
peaks is much better in this case, and the upper harmo-
nics much stronger.
Another way to visualise the relationship between played
notes and the input impedance curve is shown in Figure
10. The Equivalent Fundamental Pitch (EFP) for resonance
number n with frequency ƒ
n
is
(2)
where ƒ
r
is an arbitrarily chosen reference frequency.
In Figure 10 ƒ
r
= 87.31 Hz, corresponding to the pitch F2.
The EFP then shows the pitch interval in cents between
the n
th
resonance peak and the n
th
harmonic of F2. A
perfectly harmonic set of frequencies lies on a vertical
line, whose horizontal position shows the deviation from
F2 of the fundamental of the set.
This display can also illustrate the possibilities for playing
notes based on a mode with n > 1. Figure 10 also inclu-
des the harmonic frequencies for the note E3 (based on
the second resonance) and C4 (based on the third reso-
nance).
Fig. 10: Equivalent Fundamental Pitch for carnyx with
superimposed harmonics of played notes E3 and C4
Emplacement fondamental équivalent pour un carynx
avec les harmoniques des notes Mi3 et Do4 superposées
This shows, for example, that the played E3 is nearly 70
frequency spectrum from played C4 cents higher than the
pitch corresponding to the second resonance frequency,
while the played C4 is 11 cents below the pitch of the
third resonance.
Fig. 8: Input impedance curve with superimposed frequency
spectrum from played E3
Courbe de l’impédance d’entrée avec le spectre
de fréquence de la note Mi3 en superposition
Fig. 9 : Input impedance curve with superimposed frequency
spectrum from played C4
Courbe de l’impédance d’entrée avec le spectre
de fréquence de la note Do4 en superposition
