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Source-Filter Theory of
Speech Production II
Introduction • Neutral vocal tracts [] can be modeled as a tube (with uniform cross‐ sectional areas) that is closed at one end (the glottis) and open at the other (lips). • Other vocal tract shapes involve constrictions along their length and 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 (Helmholtz resonator) 2 Low Vowel Example = +[] lb lf lblf 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 []. 5 Non‐low Vowel Example • Vocal tract configurations with a constriction in the middle – Tube closed at both d b k iten s = ac cav y – Tube closed at one end, open at the other = front cavity – Helmholtz resonator 6 Non‐low Vowel Example • Helmholz resonator: an arrangement in which a small body of air acts as a piston oscillating against a l l d b d f √ F1 = c A2 2π A1l1l2 arger enc ose o y o air – back tube + constriction • The natural resonant f f h H l h l A2requency o t e e m o z resonator depends on the relative volumes of air in the back cavity and in the A1 l l2 constriction: – produces an extra‐low resonance (low F1) 1 7 Perturbation Theory U N d • Constrict a node = lower a corresponding formant = o e • N = Node (A and C) frequency • Constrict an antinode = raise a • A = Antinode (B and D) • 1,2 = Formants corresponding formant frequency 10 Perturbation Theory • Labial constriction (rounded vowels): lowers F1 and F2 b/c tube is constricted at volume velocity maximum (node A). • Pharyngeal constriction (≈ low vowel): lowers F2 b/c tube is constricted at volume velocity maximum for F2 (node C). • Palatal constriction (≈ front vowel): raises F2 b/c tube is constricted at volume velocity minimum for F2 (antinode B). 11 Perturbation Theory • Other Locations for constriction (Fraction of Length of vocal tract) – glottis 0 – pharynx 1/4 – uvula 1/2 – velum 2/3 – palate 3/4 l l 7/8– a veo um – lips 4/4 12 Typical Formant Values for
Monopthongal Vowels
Men Women Children
Vowel Fl F2 F3 Fl F2 F3 Fl F2 F3
[i] 270 =2300 =. 3000 300 2800 3300 370 3200 3700
fi] 400 2000 2550 430 2500 3100 530 2750 3600
fe] 530 1850 2500 600 2350 3000 700 2600 3550
[x] 660 1700 2400 860 2050 2850 1000 2300 3300
[a] 730 1100 2450 850 1200 2800 1030 1350 3200
[>] 570 850 2400 590 900 2700 680 1050 3200
{u] 440 1000 2250 470 1150 = =62700 560 1400 3300
[u] 300 850 2250 370 950 2650 430 1150 3250
[a] 640 1200 2400 760 1400 2800 850 1600 3350
[3] 490 1350 1700 500 1650 1950 560 1650 2150
Mean 500 1420 2400 575 1700 ©2800 670 1900 3250
F2/Fl 2.84 2.96 2.84
F3/F2 1.69 1.65 1.71
From: Peterson and Barney (1952)
Distribution of Fl and F2
TH" 1200
Frequency of second formant versus frequency of first
formant for ten vowels by 76 speakers,
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. Frequency F2 F1 F2 [a] [a] F1 Time 17
