M8.1: Dependence of Vowel-Specific, Relative Spectral Energy Maxima and Lower Formants ≤ 1.5 kHz on Fundamental Frequency

Content of illustration

Figure 1 shows examples of sounds of the vowels /o, ø, e / produced at different F0 by a woman (/o /), a man (/ø /) and a child (/e /; age 8). In the frequency range of F0 of c. 200–400 Hz, the second partial is generally dominant thus indicating a shift of the lowest spectral peak with rising F0, which is also indicated by the corresponding calculated F1. In more detail: For the sound series of the vowel /o /, the shift in F0 is 170–400 Hz, the frequency shift of the dominant second harmonic is 340–800 Hz and the shift of calculated F1 is c. 380–800 Hz. (Note that for the sound at F0 = 400 Hz, the first calculated formant value at 560 Hz is ignored here because it is associated with a bandwidth of 928 Hz and, as a consequence, the LPC filter curve does not show a corresponding peak.)—For the sound series of the vowel /ø /, the shift in F0 is c. 110–360 Hz, the frequency shift of the dominant harmonic (third harmonic up to F0 = 167 Hz, then second harmonic) is c. 330– 720 Hz and the shift of calculated F1 is c. 350–710 Hz.—For the sound series of the vowel /e /, the shift in F0 is c. 210–360 Hz, the frequency shift of the dominant second harmonic is c. 420–720 Hz (dominance is weak but constant) and the shift of calculated F1 is c. 420–720 Hz.

Figure 2 shows examples of sounds of the vowels /u, y, i / produced at different F0 by a woman (/u /), a child (/y/; age 13, transition to adolescence) and a woman (/ i /). For all sounds, the first partial is generally dominant thus indicating a shift of the lowest spectral peak with rising F0, which is also indicated by the corresponding calculated F1. (Note that for higher levels of F0, the calculation of F1 is methodically unsubstantiated; however, the calculated values correspond to the dominant first harmonics.) In more detail: For the sound series of the vowel /u /, the shift in F0 is c. 220–870 Hz, as is true for the frequency shift of the first dominant harmonic and the shift of calculated F1 is c. 230– 870 Hz.—For the sound series of the vowel /y/, the shift in F0 is c. 210– 710 Hz, as is true for the frequency shift of the first dominant harmonic, and the shift of calculated F1 is c. 380–740 Hz. (Note the problem of automatic calculation of F1 for the example in Figure 2-14.)—For the sound series of the vowel / i /, the shift in F0 is c. 210–830 Hz, as is true for the frequency shift of the first dominant harmonic and the shift of calculated F1 is c. 240–900 Hz.

Note the very pronounced spectral differences for the three sounds of / i, y, u / in the frequency range of F0 of 700–800 Hz which reinforces the thesis of a parallelism between differences in perceived vowel quality and related acoustic differences, that is, the thesis of vowel-specific harmonic spectra of high-pitched sounds.

However, as mentioned in Section 8.1, indications for an F0-dependence of the lower spectral peaks and lower formants ≤ 1.5 kHz are not systematic: above all, the indications in question relate to frequency ranges of F0, to vowel qualities and to single speakers and their phonation characteristics, including vocal effort.

Concerning the F0 ranges, the indications for the F0-dependence in question are generally weak or absent for F0 < c. 200 Hz for the sounds of all vowels (see, for example, Figure 1 in this chapter, the corresponding sounds of /ø /).

Concerning vowel quality, the indications of the F0-dependence in question are particularly evident in the sounds of / i, y, e, ø, o, u / but often unsystematic, weak or even absent for the sounds of /ɛ / and of /a–ɑ /. In terms of an illustration, Figure 3 shows examples of sounds of /a–ɑ / produced by a child (age 13, transition to adolescence) on different F0. The harmonic spectrum strongly varies and peak and formant estimation is difficult to conduct. However, no clear indication of a relation between F0 and the lower spectral envelope is evident.

Concerning single speakers and their phonation characteristics, including vocal effort, Figure 4 shows examples of sounds of /o / produced at different F0 by a woman; in contrast to the corresponding sound series in Figure 1, only a very weak indication of a relation between F0 and the lower spectrum is evident.

But, as mentioned in Section 8.1, although the indications for the dependence discussed here prove to be unsystematic, the findings of intelligible vowel sounds at fundamental frequencies > 500 Hz (see next chapter) and of formant pattern ambiguity (see Chapter M9) force us to relate the lower spectral peaks and the lower formants to fundamental frequency.

In addition, such a dependence can also be observed for the second formant for cases of sounds of back vowels (see, for example, Section 10.1, Figure 1).

In the context of such F1 shifts with rising F0, “inverted” frequency levels of the lowest spectral peak and of calculated F1 can be observed for two sounds of two different vowels: where statistical values give lower formant frequencies for F1 for one vowel quality than for the other, higher values can be found for sounds of the former than for sounds of the latter if F0 variations are included into the investigation. Figures 5 shows examples of such cases in terms of sound pairs of /o, u / and /e, i /. (The sound pairs produced by children, women and men are presented separately.) The lowest spectral peaks < 1.5 kHz for the sounds of /u / are above those of the sounds of /o /, as is the case for the sounds of / i / compared with the sounds of /e /. Moreover, no clear indication of a second peak < 1.5 kHz and a corresponding marked F2 is manifest for the sounds of /o, u /, and the calculated F2 for the sound pairs of /e, i / are also “inverted”, i.e. F2 for the sounds of / i / is found below F2 for the sounds of /e /.

This observation foreshadows formant pattern ambiguity of vowel sounds, as documented in detail in Chapter M9.

For earlier accounts, see Maurer, Landis, and d’Heureuse (1991), Maurer and Landis (1995, 1996, 2000); see also Traunmüller (n.d.) for synthesised examples.

Link to the spectra of the Figures

Figure 1: Sounds of /o, ø, e/, produced at different F0 by a woman (/o/), a man (/ø/) and a child (/e/), which indicate a shift of the lowest spectral peak as well as of calculated F1 with rising F0.

>> Link to Figure 1

Figure 2: Sounds of /u, y, i/, produced at different F0 by a man (/u/), a child (/y/) and a woman (/i/), which indicate a shift of the lowest spectral peak as well as of calculated F1 with rising F0.

>> Link to Figure 2

Figure 3: Sounds of /a–ɑ/ produced at different F0 by a child, for which there is no clear indication of a relation between F0 and the lower spectral envelope.

>> Link to Figure 3

Figure 4: Sounds of /o/, produced at different F0 by a woman, for which there is only a very weak relation between F0 and the lower spectrum.

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Figure 5: Three sound pairs of /o, u/ and three sound pairs of /e, i/, produced by children, women and men, exhibiting a higher first spectral peak frequency for /u/ than for /o/, and for /i/ than for /e/, respectively.

>> Link to Figure 5