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24.963 Linguistic Phonetics
Fall 2005
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24.963
Linguistic Phonetics
Acoustic parameter
Quantal Theory
I
II
III
Articulatory parameter
Image by MIT OpenCourseWare. Adapted from Stevens, K. N. "On the Quantal Nature of Speech." Journal of Phonetics 17 (1989): 3-46.
Reading for week 7:
• Johnson chapters 7 and 8.
Assignments:
• 3rd acoustics assignment
Quantal Theory
Acoustic parameter
Quantal relationship between articulatory and acoustic parameters
(Stevens 1972, 1989, etc)
• The acoustic difference between I and III is large - qualitatively
different (Johnson’s example: glottal aperture and voicing).
• The acoustic parameter is relatively insensitive to change in the
articulatory parameter within regions I and II, hence:
– articulation need not be precise.
– continuous movement through the region will yield acoustic steady
states.
I
II
III
Articulatory parameter
Image by MIT OpenCourseWare. Adapted from Stevens, K. N. "On the Quantal Nature of Speech." Journal of Phonetics 17 (1989): 3-46.
Quantal Theory
Claim:
• Linguistic contrasts involve differences between
regions I and III.
• More specifically, quantal relations provide the
basis for distinctive features:
‘The articulatory and acoustic attributes that occur
within the plateau-like regions of the relations are,
in effect, the correlates of the distinctive features’
(p.5)
Voicing and glottal aperture
• This example is not Stevens’s, but it’s a nice illustration of
the insight behind the quantal theory and the potential
complications it faces:
• Gradual change in articulatory parameters can result in
abrupt, qualitative change in acoustic output - voicing is
qualitatively different from voicelessness.
• Glottal aperture is only one of many parameters that affects
voicing - glottal tension and pressure drop across the glottis
are relevant also. How does this affect the identification of
quantal regions (particularly as a basis for features)?
• Languages also contrast breathy vs. modal voice vs. creaky
voice. Are these quantal distinctions?
Voicing and glottal aperture • Glottal aperture is only one of many parameters that affects
voicing - glottal tension and pressure drop across the glottis
are relevant also. How does this affect the identification of
quantal regions (particularly as a basis for features)?
400
0.5
Oscillation onset
PL(Pa)
Phonation threshold pressure, Pth (kPa)
0.6
200
1
0.4
2
Oscillation offset
0.3
0
-1
0
1
2
3
Prephonatory glottal halfwidth, ξ o (mm)
3 4
0
0.05
0.1
ξo (cm)
Image by MIT OpenCourseWare. Adapted from Titze, Ingo R., Sheila S. Schmidt, Image by MIT OpenCourseWare. Adapted from Lucero, J. C. “The Minimum
and Michael R. Titze. “Phonation Threshold Pressure in a Physical
Lung Pressure to Sustain Vocal Fold Oscillation.” Journal of the
Model of the Vocal Fold Mucosa.” Journal of the Acoustical Society of
Acoustical Society of America 98 (1995): 779-784.
America 97 (1995). Quantal theory applied to vowels
4
4
3
3
Frequency
Frequency
• Regions of stability (quantal regions) for vowel formant
frequencies occur where two formants converge.
2
Ac=0.5 cm2
0
1
A1=0.5 cm2
2
A1 =0
1
0.2
0
0
0
2
4
6
8
10
12
14
2
4
Length of back cavity
A1
Ac
A2
A1
l1
lc
l2
e1
6
8
10
Length of back cavity
12
14
A2
e2
Images by MIT OpenCourseWare. Adapted from Stevens, K. N. "On the Quantal Nature of Speech." Journal of Phonetics 17 (1989): 3-46.
Quantal theory applied to vowels
• The three most common vowels cross-linguistically are [i. a. u]. Stevens argues that these are quantal vowels.
4
• High front [i] is produced at
the convergence of F2 and F3
created by a
narrowconstriction in the
palatal region.
Frequency
3
2
Ac=0.5 cm2
0
1
0.2
0
0
2
4
6
8
10
12
14
Length of back cavity
A1
l1
Ac
lc
A2
l2
Images by MIT OpenCourseWare. Adapted from Stevens, K. N. "On the Quantal Nature of Speech." Journal of Phonetics 17 (1989): 3-46.
Quantal theory applied to vowels
• Regions of stability (quantal regions) for vowel formant
frequencies occur where two formants converge.
4
3
Frequency
• Low [#] is produced at the
convergence of F1 and F2
created by a narrow back
cavity and a wide front cavity
of equal length.
A1 =0.5 cm2
2
A1 =0
1
0
2
4
6
8
10
Length of back cavity
12
14
Image by MIT OpenCourseWare. Adapted from Stevens, K. N. "On the Quantal
Nature of Speech." Journal of Phonetics 17 (1989): 3-46.
A1
e1
A2
e2
Image by MIT OpenCourseWare.
Quantal theory applied to vowels
• Regions of stability (quantal regions) for vowel formant
frequencies occur where two formants converge.
• High back rounded [u] is
produced near a minimum
in F2, in a region where F1
is relatively stable.
4
Frequency (kHz)
3
2
1
0
0
2
4
6
8
10
12
14
Length of back cavity (cm)
Image by MIT OpenCourseWare. Adapted from Stevens, K. N. "On the Quantal
Nature of Speech." Journal of Phonetics 17 (1989): 3-46.
Quantal theory applied to vowels
• Are all convergences of F1 & F2 or F2 & F3 quantal
regions?
4
• Convergence of F2 and F3 at
4cm is said to be quantal
vowel [3].
• Note that this vowel is crosslinguistically relatively
unusual.
3
Frequency
• Some are not anatomically
feasible - e.g. convergence of
F2 and F3 at 12cm.
A1=0.5 cm2
2
A1=0
1
0
2
4
A1
e1
6
8
10
Length of back cavity
12
14
A2
e2
Images by MIT OpenCourseWare. Adapted from Stevens, K. N. "On the Quantal
Nature of Speech." Journal of Phonetics 17 (1989): 3-46.
Quantal theory applied to vowels
• Are mid vowels [e, o] quantal?
• We have suggested that the difference between high and
mid vowels can be modeled as an increase in the area of the
constriction.
• What is the effect on the formants?
Ac
c2
,
ΔF =
X
2
A
2π lcl2Fn
A1
l1
F1 =
Ac
lc
c
2π
Ac
Vlc
A2
l2
Image by MIT OpenCourseWare. Adapted from Stevens, K. N. "On the Quantal Nature of Speech." Journal of Phonetics 17 (1989): 3-46.
Stability with respect to multiple parameters
• There is no quantal relationship between constriction area
and formant frequencies
• In fact formants are maximally sensitive to constriction area
at the points of formant stability.
• Is a quantal relationship between one articulatory parameter
and one acoustic parameter sufficient?
• Stevens seems concerned about this case - argues that:
–although there is no minimum, the relationship between
formants and constriction area is a shallow slope.
–there may be non-monotonicity in the relationship
between muscle atcivity and constriction area (p.15).
Stability with respect to multiple parameters
• What is the effect on F2 and F3 of varying constriction
length? Consider the configuration where F2 and F3
converge.
Fb =
A2
Cavity length (cm)
=
Ac
Back cavity
5
Front cavity
0
l1
lc
l2
Image by MIT OpenCourseWare. Adapted from Stevens, K. N. "On the
Quantal Nature of Speech." Journal of Phonetics 17 (1989): 3-46.
Frequency (kHz)
Ff
c
4l f
c
2lb
10
A1
2.5
F3
2.0
F2
2
3
4
5
Constriction length, lc (cm)
Image by MIT OpenCourseWare. Adapted from Lindblom, B., and O. Engstrand.
"In what Sense is Speech Quantal?" Journal of Phonetics 17 (1989):
107-121.
Stability with respect to multiple parameters
• Vowel formants vary monotonically with degree of lip
constriction.
• How undesirable is articulatory precision?
• Languages do not appear to take full advantage of the
imprecision that quantal regions allow - e.g. differences
between Danish and English [i].
• Note that Stevens has recently suggested that the quantal
distinction between front and back vowels is based on the
frequency of F2 relative to the first sub-glottal zero, not on
convergence of F2 with F1/F3.
Lindblom’s Theory of Adaptive Dispersion
• Liljencrants and Lindblom (1972), Lindblom 1986, 1990a,b
• An alternative explanation for the cross-linguistic
preference for the vowels [i, a, u]: these vowels are at the
extremes of the formant space of physiologically possible
vowels.
• These vowels are maximally distinct from each other and
therefore less likely to be confused by a listener.
Lindblom’s Theory of Adaptive Dispersion
• A shift in perspective: preferred systems of contrasts vs.
preferred sounds.
• There are many generalizations about possible inventories
of contrasting sounds.
Lindblom’s Theory of Adaptive Dispersion
• Common vowel inventories:
i
u
i
u
e
o
a
Arabic,
Nyangumata,
Aleut, etc.
i
e

a
Spanish,
Swahili,
Cherokee, etc.
u
o
ɔ
a
Italian,
Yoruba,
Tunica, etc.
• Unattested vowel inventories:
i
i

e
e

a
a
i

u

Lindblom’s Theory of Adaptive Dispersion
• Lindblom’s approach takes these generalizations as prior to
generalizations about sounds: a preferred speech sound is
one that appears in many preferred inventories.
• Specifically, sounds in a language are selected so as to best
satisfy requirements that derive from the communicative
function of language:
– Maximize perceptual distinctiveness
– Minimize effort
Liljencrants and Lindblom (1972)
• The role of perceptual contrast in predicting vowel
inventories.
• The space of articulatorily possible vowels:
1500
2.0
3.0
2000
4.0
1000
.5
2.5
250
.5
500
.75
750
MEL 1500
1000
First Formant (F1)
1.5 1.0
500
MEL
2.5
1500
Third Formant (F3)
.5
1.5
kHz
First Formant (F1)
1.5 1.0
MEL
2.5
MEL
Third Formant (F3)
kHz
Second Formant (M2)
500
Second Formant (M2)
Images by MIT OpenCourseWare. Adapted from Liljencrants, Johan, and Bjorn Lindblom. “Numerical
Simulation of Vowel Quality Systems: The Role of Perceptual Contrast.” Language 48, no. 4 (December 1972): 839-862.
Liljencrants and Lindblom (1972)
• Perceptual distinctiveness of contrast between Vi and Vj:
distance between vowels in perceptual vowel space
rij = (xi − xj )2 + (yi − yj )2
where xn is F2 of Vn in mel
yn is F1 of Vn in mel
• Maximize distinctiveness: select N vowels so as to
minimize E
n−1 i −1
1
E = ∑∑ 2
i =1 j =0 rij
2.5
2.0
3
4
5
6
7
8
9
10
11
1.5
1.0
Second Formant (kHz)
• Predicted optimal
inventories
• Reasonable
approximations to
typical 3 and 5
vowel inventories
are derived.
• Preference for [i, a,
u] is derived.
• Problem: Too
many high, nonperipheral vowels.
• Not enough mid
non-peripheral
vowels.
.5
2.5
2.0
1.5
1.0
.5
2.5
12
2.0
1.5
1.0
.5
.2
.4
.6
.8
.2
.4
.6
.8
.2
.4
.6
.8
.2
.4
.6
.8
First Formant (kHz)
Image by MIT OpenCourseWare. Adapted from Liljencrants, Johan, and Bjorn Lindblom. “Numerical Simulation of
Vowel Quality Systems: The Role of Perceptual Contrast.” Language 48, no. 4 (December 1972): 839-862.
Liljencrants and Lindblom (1972)
Second formant frequency (kHz)
• The excess of central vowels arise because measuring
distinctiveness in terms of distance in formant space gives
too much weight to differences in F2 (even after mel
scaling).
• Recent work by Diehl, Lindblom and Creeger (2003)
suggests that the greater perceptual significance of F1
probably follows from the higher intensity of F1 relative to
F2.
2.5
2.0
1.5
7
7
1.0
.5
.2
.4
.6
.8
.2
.4
.6
.8
First formant frequency (kHz)
Image by MIT OpenCourseWare. Adatped from Diehl, R. L., B. Lindblom, and C. P. Creeger. "Increasing Realism of
Auditory Representations Yields Further Insights into Vowel Phonetics." Proceedings of the 15th International
Congress of Phonetic Sciences. Vol. 2. Adelaide, Australia: Causal Publications, 2003, pp.1381-1384.
Liljencrants and Lindblom (1972)
• The absence of interior vowels [, ø] is a result of the
way in which overall distinctiveness is calculated.
• Each vowel contributes to E based on its distance from
every other vowel.
• Interior vowels have a high cost because they are relatively
close to all the peripheral vowels.
• One possible alternative is to maximize the minimum
distance (Flemming 2005).
Problems with Adaptive Dispersion
• Specific instantiations of the model have made specific
incorrect predictions (but some of the broad predictions are
correct and models are improving).
• The model answers an inobvious question: ‘Given N
vowels, what should they be?’ - what determines the size of
inventories?
• TAD predicts a single best inventory for each inventory
size. Why would languages have sub-optimal inventories?
24.963
Linguistic Phonetics
Source-filter analysis of fricatives
Noise source
• Turbulence noise - random pressure fluctuations.
Relative level (dB)
• Turbulence can result when a jet of air flows out of a
constriction into a wider channel (or open space).
30
20
10
0
0.5
1
2
3
5
10
Frequency (kHz)
Image by MIT OpenCourseWare. Adapted from Stevens, K. N. “On the Quantal Nature of Speech.” Journal of Phonetics 17 (1989): 3-46.
Noise source
• Turbulence can result when a jet of air flows out of a
constriction into a wider channel (or open space).
• The intensity of turbulence noise depends on particle
velocity.
• For a given volume velocity, particle velocity will be greater
if the channel is narrower, so for a given volume velocity,
narrower constrictions yield louder frication noise.
Relative Level (dB)
source at glottis
source at glottis
20
source at supraglottal
constriction
10
source at
supraglottal
constriction
Ag = 0.2 cm2
0
0
0.1
0.2
0.3
0.4
Ag = 0.3 cm2
0.5
0
0.1
0.2
0.3
0.4
0.5
Area of Supraglottal Constriction Ac (cm2)
Image by MIT OpenCourseWare. Stevens, K. N. Acoustics Phonetics. Cambridge, MA: MIT Press, 1999.
Noise source
• Turbulence is also produced when an airstream strikes an
obstacle (e.g. the teeth in [s]).
• The orientation of the obstacle to the direction of flow
affects the amount of turbulence produced - the teeth are
more or less perpendicular to the airflow in [s] and thus
produce significant turbulence.
• The louder noise of strident fricatives is a result of
downstream obstacles.
Image by MIT OpenCourseWare. Stevens, K. N. Acoustic Phonetics. Cambridge, MA: MIT Press, 1999.
Filter characteristics
• The noise sources are filtered by the cavity in front of the
constriction.
• In [h] the noise source is at the glottis, so the entire
supralaryngeal vocal tract filters the source, just as in a
vowel.
• So [h] has formants at the same frequency as a vowel with
the same vocal tract shape, but the formants are excited by a
noise source instead of voicing.
• The noise source generated at the glottis has lower intensity
at low frequencies, so F1 generally has low intensity in [h].
SPL in 300 - Hz Bands
(dB re 0.0002 dyne/cm2)
70
60
Periodic
source
50
40
Overall
noise source
30
20
0
1
2
3
4
5
Frequency (kHz)
Image by MIT OpenCourseWare.
[h]
• The noise source generated at the glottis has lower intensity
at low frequencies, so F1 generally has low intensity in [h].
MAG (dB)
60
60
Periodic
source
50
40
20
[h]
0
40
20
60
Overall
noise source
30
0
1
2
3
4
5
Frequency (kHz)
Image by MIT OpenCourseWare.
MAG (dB)
SPL in 300 - Hz Bands
(dB re 0.0002 dyne/cm2)
70
[he]
[e]
[ho]
[o]
40
[h]
20
0
0
1
2
3
4
FREQ (kHz)
Image by MIT OpenCourseWare. Stevens, K. N. Acoustic Phonetics.
Cambridge, MA: MIT Press, 1999.
[h]
5000
5000
hoed
heed
0
13.686
5000
Time (s)
0
14.1873 17.5452
5000
18.0608
Time (s)
hoard
Hoyd
0
15.4067
0
15.9137 19.5239
Time (s)
20.0263
Time (s)
Filter characteristics
• As the place of articulation shifts forward, the cavity in front
of the noise source is progressively smaller.
• A smaller cavity has higher resonances, so other things
being equal, the concentration of energy in the fricative
spectrum is higher the closer the place of articulation is to
the lips.
4
Frequency (kHz)
40
s
Relative level (dB)
6
x
2
0
30
1.5
2.2
3.5
20
6
0
5.9
10
4
2
0
0
0-2 s
Image by MIT OpenCourseWare.
1
2
3
4
6
Frequency (kHz)
Image by MIT OpenCourseWare. Adapted from Stevens, K. N. "On the
Quantal Nature of Speech." Journal of Phonetics 17 (1989): 3-46.
Filter characteristics
• The front cavity of a labial is so short (first resonance ~10
kHz) that it has little effect on the fricative spectrum,
resulting in fricative noise spread over a wide range of
frequencies with a broad low-frequency peak.
• This picture can be complicated by acoustic coupling with
back cavity.
5000
20
0
–20
8000
0
Frequency (Hz)
0
12.0111
12.7989
Time (s)
Filter characteristics
• Lip rounding lowers the resonant frequencies of the front
cavity, just as in vowels.
• In coronals, the presence or absence of a sublingual cavity
has a significant effect on the size of the front cavity.
60
∫
S
40
20
dB
kHz
2
4
6
8
10
kHz
2
4
Image by MIT OpenCourseWare.
6
8
10
Source-filter analysis of stops
4000
b
d
3000
2000
1000
i
Image by MIT OpenCourseWare.
g
Stops
• Stops are complicated in that they involve a series of rapid
changes in acoustic properties, but each component can be
analyzed in similar terms to vowels and fricatives.
• A stop can consist of four phases: implosion (closure)
transitions - closure - burst - release transitions
Closure
• Only source of sound is voicing, propagated through the
walls of the vocal tract.
• The walls of the vocal tract resonate at low frequencies, so
only low-freqeuncy sound is transmitted (‘voice bar’).
Burst
• Consists of a transient, due to abrupt increase in pressure at
release, followed by a short period of frication as air flows at
high velocity through the narrow (but widening)
constriction.
• Transient source is an impulse (flat spectrum) filtered by the
front cavity.
• The frication is essentially the same as a fricative made at
the same place of articulation.
• Alveolars have high freqeuncy, high intensity bursts.
• Velar bursts are concentrated at the frequency of F2 and/or
F3 at release.
• Labial bursts are of low intensity, with energy over a wide
range of freqeuncies, with a broad, low-frequency peak.
Release transitions
• As the constriction becomes more open, frication ceases.
• The source at this time is at the glottis - either voicing or
aspiration noise. This source excites the entire vocal tract as
in a vowel (or [h]).
• The shape of the vocal tract, and thus the formants, during
this phase are basically determined by the location of the
stop constriction and the quality of adjacent vowels.
• The formants move rapidly as the articulators move from the
position of the stop to the position for the vowel. The
formant movements are usually called ‘formant transitions’.
d
b
4000
g
3000
2000
1000
i
4000
3000
2000
1000
4000
3000
2000
1000
4000
3000
2000
1000
a
4000
3000
2000
1000
u
ms 50
100
150
ms 50
100
150
ms 50
100 150
Image by MIT OpenCourseWare. Adapted from Ladefoged, Peter. Phonetic Data Analysis. Malden, MA: Blackwell, 2003.
Release transitions
• In alveolar stops the formant transitions due to the tongue tip
constriction are probably very rapid (Manuel and Stevens
1995), so the observed formant transitions appear to be due
to tongue body movements.
• The tongue body is generally relatively front to facilitate
placement of the tongue tip//blade, thus there is a relatively
high F2 at release (~1800-2000 Hz) and high F3.
• Labial stops involve a constriction at the lips. The tongue
position is determined by adjacent vowels, so the exact
formant frequencies at release depend on these vowel
qualities.
• The labial constriction always lowers formants, so F2 and
F3 are generally lower at release of a labial than in the
following vowel.
Release transitions
• Velar stops involve a dorsal constriction, but the exact
location of this constriction depends on the neighbouring
vowels.
• So the formant transitions of velars vary substantially,
approximately tracking F2 of the adjacent vowel.
• F2 and F3 are often said to converge at velar closure. Under
what conditions should this occur?
• Similar transitions are observed during the formation of a
stop closure.
• Similar transitions are observed into and out of any
consonant with a narrow constriction, e.g. fricatives, nasal
stops.
Locus equations
• Typically F2 at the release of a consonant is a linear
function of F2 at the midpoint of the adjacent vowel
(Lindblom 1963, Klatt 1987, etc).
• The slope and intercept of this function depend on the
consonant.
bid
5000
5000
0
1.96743
2.42708
Time (s)
bd
0
11.3647
11.8142
Time (s)
Locus equations
• The slope and intercept of this function depend
on the consonant.
y = 228.32 + 0.79963x R^2 = 0.968
2800
2600
2400
2200
2000
1800
1600
1400
1200
1000
1000 1400 1800 2200 2600 3000
/b/ F2 vowel (Hz)
/d/ F2 onset (Hz)
b.
c.
/b/ F2 onset (Hz)
/b/ F2 onset (Hz)
a.
y = 778.64 + 0.71259x R^2 = 0.930
2800
2600
2400
2200
2000
1800
1600
1400
1200
1000
1000 1400 1800 2200 2600 3000
/g/ F2 vowel (Hz)
y = 1099.2 + 0.47767x R^2 = 0.954
2800
2600
2400
2200
2000
1800
1600
1400
1200
1000
1000 1400 1800 2200 2600 3000
/d/ F2 vowel (Hz)
Image by MIT OpenCourseWare. Adpated from Fowler, C. A. “Invariants, Specifiers, Cues: An Investigation of Locus Equations as
Information for Place of Articulation.” Perception and Psychophysics 55, no. 6 (1994): 597-610.
Affricates
• The frication portion of the release of the stop is prolonged
to form a full-fledged fricative.
• The fricative portion of an affricate is distinguished from a
regular fricative by its shorter duration, and perhaps by the
rapid increase in intensity at its onset (short rise time).