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Vowel Spectra

Vowel Spectra. √ . Last time we saw that the neutral ([ ´ ]) vocal tract could be compared to a tube with a uniform cross-sectional areas that is closed at one end (the glottis) and open at the other (lips). What about other vowels?.

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Vowel Spectra

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  1. Vowel Spectra

  2. √ Last time we saw that the neutral ([´]) vocal tract could be compared to a tube with a uniform cross-sectional areas that is closed at one end (the glottis) and open at the other (lips). What about other vowels? Some vocal tract shapes can be approximated by connecting together two or more uniform tubes with different cross-sectional areas: Open-closed tube: f = c / 4l, 3c / 4l, 5c / 4l, . . . Closed-closed or open-open tube: f = c / 2l, 3c / 2l, 5c / 2l, . . . Closed-narrow opening tube F1 = c A2 (Helmholtz resonator): 2 A1l1l2 A1 A2 l2 l1

  3. = + lb lb lf lf Let’s apply this to [A] and [i]. Some vocal tract shapes can be approximated by connecting together two or more uniform tubes with different cross-sectional areas: [A] Recall f = c / 4l, 3c / 4l, . . ., which holds for front and back cavities. The front cavity is slightly longer than the back cavity (lf > lb), so the lowest resonance, F1, is affiliated with the front cavity. F2 is affiliated with the back cavity. F1 and F2 are relatively close in frequency. F1 is higher, and F2 lower, than those of [´]. (Actual fs are not perfectly predicted from the formula because we have oversimplified the model.)

  4. Ab Helmholtz resonator front cavity back cavity lb lf f = c / 2l, 3c / 2l, ... F1= c A2 2 A1l1l2 f = c / 4l, 3c / 4l, ... √ • [i] • F1 is determined by the natural frequency of the Helmholtz resonator and higher formants by the front and back cavity resonances. Af

  5. PERTURBATION THEORY The relation between the configurations and resonances of the vocal tract can also be examined in terms of formant-frequency changes due to perturbations (local constrictions) along the length of the tract. We return to a single-tube model, but instead of a tube with a uniform cross-sectional area (as for [´]), we’ll consider the acoustic consequences of introducing a perturbation. The effect of the perturbation on formant frequency (F) depends on whether the constriction is near a velocity node or antinode. Node: volume velocity maximum; pressure minimum Antinode: volume velocity minimum; pressure maximum A constriction near a node lowers F; an increase in tube area near a node raises F. A constriction near an antinode raises F; an increase in tube area near an antinode lowers F.

  6. Effects of vocal tract perturbations on formant frequencies (1) Vocal tract length: the longer the vocal tract, the lower the formant frequencies Oral constriction (≈ high vowel): lowers F1 Note: tube is constricted at velocity maximum for F1. (3) Pharyngeal constriction (≈ low vowel): raises F1 Note: tube is constricted at volume velocity minimum for F1. (4) Back constriction (≈ back vowel): lowers F2 Note: tube is constricted at volume velocity maximum for F2. (5) Front constriction (≈ front vowel): raises F2 Note: tube is constricted at volume velocity minimum for F2. (6) Lip rounding: lowers formant frequencies a. lip compression constricts tube at velocity maximum for all F b. lip protrusion lengthens the tube.

  7. To think about: What are the acoustic similarities between the consequences of lip rounding and back tongue body configuration? What cross-linguistic pattern of vowels can you think of that might be explained by these acoustic similarities?

  8. F2 0 1500 Hz i u e o ´ F1 500 Hz A Relative formant frequencies of some American English vowels (keeping in mind considerable cross-dialectal variation...) Stressed /e/ and /o/ are diphthongal.

  9. Frequency F2 F1 Schematic spectrographic representation: Listening for formants: F1: flick glottis test F2: whisper test

  10. F2 Frequency F2 F1 F1 [aU] [aI] Time DIPHTHONGS Diphthongs are vowels that have two different, sequential targets of vocalic gesture. Thus, acoustically, diphthongs are described in terms of the formant frequencies of the two vowel targets, and the time-course of the transition from one to the next.

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