M2: Prevailing Empirical References

Illustration: including radiation factor/radiation impedance

For a more differentiated graphic illustration, showing a 12db/octave slope of the source and a 6dB/octave intensity increase because of the radiation impedance, see Ladefoged (1996, p. 104), Figure 7.7 and the related comment: “Figure 7.7 shows a source-filter view of the production of a vowel. The spectrum of the glottal pulse is shown on the left of the figure. In this case we have taken the vocal folds to be vibrating at 100 Hz, so the components are at 100 Hz intervals. To the right of the spectrum is the set of curves specifying the vocal tract response. The output of the vocal tract can be regarded as the input to another box entitled ’radiation factor,’ which we must now take into account. […] these vibrations […] inside the mouth […] are not themselves the variations in air pressure that we hear. The air in the vocal tract vibrates so that the air particles at the open end between the lips move backward and forward. It is these movements that start the air outside the lips vibrating. The air between the lips acts like a piston, a source of sound producing variations in air pressure that radiate out from the lips just as the variations in air pressure radiate out from a source of sound such as a tuning fork. The movements of this piston of air are more effective in causing variations in pressure in the surrounding air at some frequencies than others. The higher the frequency, the greater the response of the surrounding air to the action of the air vibrating in the vocal tract. This effect, which we have termed the ‘radiation factor’ (‘radiation impedance’ is the term used in more technical books), can be regarded as a kind of filter that boosts the higher frequencies by 6 dB per octave. The curve representing the radiation factor is shown above the third box in figure 7.7.
The output produced at the lips depends on the vocal cord source, the filtering action of the vocal tract, and the further modifications produced by the radiation factor. Normally the vocal cord source is the same for each vowel, apart from variations of pitch. The vocal folds may be vibrating at 100 Hz, or at 200 Hz, as in the examples we have been considering, or at any other frequency in the range of the human voice. But irrespective of the fundamental frequency, the spectral slope of the cord pulse will usually be approximately −12 dB per octave. The filtering action of the vocal tract will be different for each position of the vocal organs, thus producing formants (peaks in the resonance curve) at different frequencies. The spectrum of the waveform beyond the lips (shown on the right of figure 7.7) will have peaks in regions which depend on the filter characteristics of the vocal tract. The general slope of the output spectrum will be influenced by the slope of the spectrum of the glottal pulse (−12 dB/octave) and the radiation factor (+6 dB/octave). Taken together these two slope factors account for a − 6 dB/octave slope in the output spectrum. The major characteristics of the output spectrum – the formant peaks – are superimposed on this general slope. They are primarily dependent on the filtering characteristics of the vocal tract.” (Ladefoged, 1996, pp. 104–105)

Formant statistics by Fant et al.

With regard to the study of Fant (1959; see Section 2.1, Table 3), see also the later study of Fant, Henningsson, and Stalhammar (1969) concerning statistical formant patterns for long Swedish vowels produced by men.

Formant statistics for Standard German

Older studies concerning formant patterns of German vowels were published by Jørgensen (1969), Iivonen (1970, 1986), Rausch (1972), Wängler (1981), and Ramers (1988). For further indications of formant statistics for Standard German, see the online digital version of the materials.

Formant statistics for other languages

//For further indications of formant statistics of other languages, see also the online digital version of the materials.//