Figure 1: Spectrum of a velar-like voice produced by me (for the audio file click here). F0 = 211 Hz. The 13th harmonic is 21 dB stronger than its flanking harmonics.
It is a velar-like voice; the tongue approximates the soft palate but does not press on it. This vocal technique is similar to the "one-cavity overtone singing" described by Tran Quang Hai. As the occurrence of this sharp formant is associated with the narrowing of the soft palate, I hypothesize that the surface wave of the soft palate modulates the airflow, producing the strong component at 2.7 kHz. Because of this narrowing, (1) flow separation can occur, and (2) the flow volume velocity is sensitive to the surface wave.
Figure 2: Surface wave of the soft palate. The tongue approximates the soft palate as to pronounce /ng/.
Low-frequency vibration of the soft palate during snoring has been investigated as a classic problem of aeroelasticity (e.g. Huang 1995). It is observed that the soft palate vibrates at its eigenfrequency during inhalation.
High-frequency surface waves of the soft palate may be triggered by the acoustic pressure and grows in amplitude through the fluid-structure interactions. Varicose oscillations of the airflow could be generated when it separates from the soft palate. This hypothesis of the velar-like voice with a sharp formant is similar to the model of surface waves of the false vocal folds during Sygyt singing. The eigenfrequency of the false vocal folds is very low (<70Hz). But the frequency of its surface wave can be higher than 1 kHz, which is assumed to be determined by the acoustic pressure.
If the surface wave of the soft palate is verified by experiments, this model may explain some types of velar or nasal voices with strong harmonics in the range of 2.5-3.5 kHz, e.g., voices of male roles of Chinese opera. In a traditional Chinese singing style, Nanguan (about 800 years old), a female singer can produce velar-like voices with a sharp formant at 3.8 kHz. It is important to note that Nanguan singers only use the chest register.
Figure 3: Spectrum of a Nanguan singing voice (with accompanying instruments) produced by a female singer in the chest register (for the audio file click here). F0 = 422 Hz. The 9th harmonic is more than 22 dB stronger than its flanking components.
If the assumption of soft palate surface wave is invalidated by experiments, however, the varicose jet oscillation should be attributed to the pressure fluctuations at the flow separation point. The issue of varicose jet oscillations and wall vibrations could be related to the two questions:
# Why some people can whistle loudly and I cannot?
# Is the human whistle associated with the surface vibrations of the tongue and the hard palate?
These questions may be still open. However, it is interesting to note that human 4 kHz pure tonal vocalizations are found to be associated with the surface vibrations of the false vocal fold (Tsai et al. 2004).
Figure 4: Pressure recovery in an ancient Egyptian double reed. Adapted from [Hirschberg 1995:350].
In human vocalizations, the pressure recovery downstream of the glottis is recently found to play a key role in the effect of the vocal tract on the vocal folds during voiceless consonant production (Van Hirtum et al. 2004).
Other constriction structures in the vocal tract can be (1) the false vocal folds, (2) the aryepiglottic folds, and (3) the soft palate. When the jet separates from a constriction structure, high-frequency varicose oscillations may be induced by the local acoustic pressure.
When the aryepiglottic folds are adducted, for example, I observed a sharp formant at 1.4 kHz of the growl voice. The generation mechanism of the component at 1.4 kHz may be a loop composed of the varicose jet and the acoustic feedback.
Figure 5: Spectrum of a growl voice produced by a famous Peiking opera actor with the aryepiglottic folds adducted. For the audio file click here.
This model of pressure recovery/varicose jet/acoustic feedback might also shed new light on the nonlinear mechanism of the singer's formant. However, it is unclear whether flow separation occurs at the narrowing of the epilarynx tube of a baritone.
Van Hirtum, A., Ruty, N., Pelorson, X., Fuchs, S., and Perrier, P. (2004) Laryngeal adjustment in voiceless consonant production: II physical modeling. International conference on voice physiology and biomechanics, Marseille (France), August 18-20, 2004.
Huang, L. (1995) Mechanical modeling of palatal snoring. J. Acoust. Soc. Am. 97, 3642-3648.
Huang, L. (2001) A theoretical study of duct noise control by flexible panels. J. Acoust. Soc. Am. 109, 2805-2814.
Huang, L., and Ffowcs Williams, J.E. (1999) Neuromechanical interaction in human snoring and upper airway obstruction. J. Applied Physiology 86, 1759-1763; see also pp. 1757-1758.
Paidoussis, M. P. (1998) Fluid-Structure Interactions, Vol.1, Academic, San Diego.
Tanida, Y. (2001) Stability of a soft plate in channel flow (aerodynamic aspects of palatal flutter). JSME International Journal 44, 8-13.
Tsai, C.G., Shau, Y.W., and Hsiao, T.W. (2004) False vocal fold surface waves during Sygyt singing: A hypothesis. International Conference on Voice Physiology and Biomechanics, Marseille (France), August 18-20, 2004.