Resonator.
The frequencies of the formants are determined by the shape of the resonator. In the case of non-nasalized sounds the resonator consists of the pharynx and mouth cavities. In vowels these cavities constitute a tube resonator which may be regarded as closed at the glottal end and open at the lip end. The average vocal tract length for males is generally considered to be 17·5 cm. A tube of that length and having a uniform cross-sectional area would display a series of resonances falling close to the odd multiples of 500 Hz. However, as the cross-sectional area of the vocal tract is not constant, the formants deviate from these frequencies. The vocal tract shape is determined by the positions of the articulators (i.e. the lips, the jaw, the tongue, the velum and the larynx). The positions of these articulators are continuously varied in singing and in speech, so that the formants are tuned to various target frequencies. Thus each vowel sound corresponds to a certain pattern of articulator positions.
The dependence of the formant frequencies on the articulatory configuration is rather complex. Only a few factors have the same type of effect on all formant frequencies; for instance, all formants drop in frequency more or less when the vocal tract length is increased, by protrusion of the lips or lowering of the larynx or both, and when the lip opening area is decreased. Moreover, certain formants are more dependent on the position of a specific articulator than are others. The first formant frequency is particularly sensitive to the jaw opening: the wider the jaw opening, the higher the first formant frequency. The second and third formant frequencies are especially sensitive to the position of the tongue body and tongue tip respectively. The highest frequencies of the second formant (2–3 kHz) are obtained when the tongue body constricts the vocal tract in the palatal region, as in the vowel of ‘keep’. The lowest values of the third formant (around 1500 Hz) are associated with a tongue tip lifted in a retroflex direction.
provides examples of articulatory configurations associated with some vowels.
These guidelines apply to oral sounds; in nasalized sounds the dependence of the formants on the articulator positioning becomes considerably more complex. The nasal tract introduces minima in the sound transfer of the vocal tract resonator. The acoustical effect of nasalization varies between vowels, but a general feature is that the lowest partials are emphasized.
For both oral and nasalized sounds the two lowest formant frequencies are generally decisive in the vowel quality perceived. Frequencies typical of male speakers are given in fig.56. Females have shorter vocal tracts and therefore higher formant frequencies. On average for vowels, the three lowest formant frequencies of female voices are 12, 17 and 18% higher, respectively, than those of male voices. Children, having still shorter vocal tracts, possess formant frequencies that are 35–40% higher than those of males (see Fant, 1973).
The amplitudes of the partials emitted from the lip opening depend on the sound transfer ability of the vocal tract. This ability depends not only on the partials’ frequency distance from the closest formant, but also on the frequency distance between formants. Thus a halving of the frequency distance between two formants increases the sound transfer ability by 6 dB at the formant frequencies and by 12 dB midway between the formant frequencies, other things being equal. Another factor important to the amplitudes of the radiated partials is the sound radiation properties of the lip opening, which boosts the entire spectrum envelope by 6 dB per octave. For this reason, the amplitudes of all spectrum partials tend to increase with the pitch even when there is no change in vocal effort.