Contrast and the realization of
schwa vowels in English
Edward Flemming
Introduction
The project:
• To derive properties of phonetic and phonological
vowel reduction from general constraints related
to speech production and perception
Outline of the talk:
• Outline a model of vowel reduction.
• Explore its application to English vowel reduction
(‘reduction to schwa’).
2
Phonological vowel reduction
• Vowel contrasts are neutralized in unstressed syllables.
• E.g. Southern Italian (Mistretta dialect, Mazzola 1976)
Primary stressed:
Elsewhere:
i
u
i
u
e
o
a
a
[i]
[e]
[a]
[o]
[u]
stressed vowels
vi¤n˘i ‘he sells’
ve@ni ‘he comes’
a@vi ‘he has’
mo@ri ‘he dies’
u@Ô˘i ‘he boils’
unstressed vowels
vin˘i¤mu ‘we sell’
(vini¤mu ‘we come’)
avi¤ti
‘he has’
(muri¤mu ‘we die’)
uÔ˘i¤mu ‘we boil’
3
Phonological vowel reduction
• Common patterns of vowel reduction:
(a) i
u
(b) i
u
(c) i
u
e
o
e
o
a/´
E
ç
a
a
• (a) reduces to (b), e.g. Standard Italian, B. Portuguese, Slovene
• (b) reduces to (c), e.g. Standard Russian, S. Italian, Catalan
• (a) reduces to (c), e.g. E. Catalan
• Reduction to a single vowel, e.g. English, Dutch, Salish
• Primarily neutralization of height contrasts.
4
Outline of an analysis of vowel reduction
• Vowel reduction is fundamentally motivated by
undershoot in short unstressed syllables.
5
Phonetic vowel reduction - Undershoot
Lindblom's V Reduction Model - gVg
F2 (Hz)
2500
2000
1500
1000
500
300
i
u
350
400
e
100 ms
o
500
F1 (Hz)
450
550
125 ms
600
a
200ms
650
700
6
Outline of an analysis of vowel reduction
• Vowel reduction is fundamentally motivated by
undershoot in short unstressed syllables.
• Short duration of unstressed vowels increases the
effort required to achieve distinct vowel qualities,
particularly low vowels (Lindblom 1963).
• Contrasts are subject to distinctiveness constraints,
so neutralization occurs where phonetic reduction
would otherwise render contrasts insufficiently
distinct.
7
Undershoot as a consequence of effort minimization
• Faster movements are more effortful (Nelson 1983, Perkell
et al 2002).
• In a CVC sequence, the articulators have to move to and
from the position for the vowel.
• Undershoot results from avoiding fast movements.
F2C
F2V
F1V
F1C
8
Formant undershoot as a function of duration and
distance
Lindblom’s model:
1800
F2i
1600
if F1t  375 Hz:
F1V = F1t
F2t
1200
1000
800
F1t
600
F1v
400
if F1t > 375 Hz
F1V = k1(375
frequency (Hz)
F2V = k2(F2i –F2t)e-T+F2t
F2v
1400
F1i
200
–F1t)e-T+F1t
F2i is F2 at C release
F1t, F2t are V formant targets
k,  depend on consonant context
0
50
100
150
200
250
300
vowel duration (ms)
More undershoot where:
• Vowel is shorter
• Distance between C and V is greater
9
Formant undershoot as a function of duration and
distance
Lindblom’s model:
1800
F2i
1600
if F1t  375 Hz:
F1V = F1t
if F1t > 375 Hz
F1V = k1(375 –F1t)e-T+F1t
F2i is F2 at C release
F1t, F2t are V formant targets
k,  depend on consonant context
frequency (Hz)
F2V = k2(F2i –F2t)e-T+F2t
F2v
1400
F2t
1200
1000
800
600
400
F1t
F1i
F1v
200
0
50
100
150
200
250
300
vowel duration (ms)
More undershoot where:
• Vowel is shorter
• Distance between C and V is greater
10
Implementation of the model of vowel
reduction
• Stressed and unstressed inventories of contrasting
vowel categories are selected from a space of
possible vowels so as to best satisfy constraints on
contrasts:
 Maximize distinctiveness of contrasts.
 Maximize number of contrasts.
 Minimize articulatory effort.
• Effort minimization implies undershoot.
11
Model of vowel reduction
• The vowel space is modeled on Liljencrants and Lindblom
(1972).
F2(Bark)
14
12
10
8
6
2
i
u
3
5
F1(Bark)
4
6
a
7
8
12
i. Maximize the distinctiveness of contrasts
• Distinctiveness of the contrast between Vi and Vj is the
(weighted) distance between the vowels in formant space.
2
F2(Bark)
14
12
8
6
2
i
Where xn is F2 of Vn in Bark
yn is F1 of Vn in Bark
a<1
10
u
V1
d12
3
4
V2
5
6
a
7
8
13
F1(Bark)
dij  (a(x i  x j ))  (y i  y j )
2
i. Maximize the distinctiveness of contrasts
• Overall distinctiveness cost of a vowel system
depends on the minimum distance found in either
inventory.
1
Cost:
2
dmin
where
dmin  min dij
i j


14
ii. Maximize the number of contrasts
• maximize the number of vowels in the stressed and
unstressed vowel inventories.
Cost:

nstressed  nunstressed
where nave 
2
1
2
nave

15
iii. Articulatory effort
• The space of possible vowels contracts as vowel duration is
reduced, following the undershoot functions proposed by
Lindblom (1963)
• Consonants are assumed to assimilate partially to the vowel
target in F2, but not in F1.
F2(Bark)
12
10
8
6
2
2.5
3
3.5
4
100 ms
F1(Bark)
14
4.5
5
160 ms
5.5
6
16
Overall cost function
• The optimal vowel system is the one that best
satisfies these constraints:
1
wn2
minimize 2  2
V
dmin nave
(subject to vowel space constraint)

17
Optimal inventories
14
12
10
8
6
2
2.5
3
3.5
4
F1 (Bark)
a = 0.14,
k1 = 1.5,
1 = 0.008,
k2 =1.5,
1 = 0.01,
c = 0.27,
F2l = 1400 Hz,
wn = 6
F2 (Bark)
4.5
Durations:
stressed 160 ms
Unstressed 100 ms
5
5.5
6
stressed
unstressed
18
Italian vowels
F 2 (B ark)
14
12
10
8
6
2
i
2 .5
u
e
3
o
4
4 .5
E
ç
5
F1 (Bark)
3 .5
5 .5
6
6 .5
a
7
s tres s ed
Data from Albano Leoni et al 1995
uns tres s ed
19
Undershoot and vowel reduction
• Relating phonological vowel reduction to
undershoot helps to explain:
i. The tendency to neutralize vowel contrasts
in short unstressed syllables.
ii. The generalization that vowel reduction
primarily eliminates height contrasts.
iii. The generalization that neutralizing vowel
reduction is accompanied by phonetic
reduction.
20
English reduction to schwa
• English exhibits a pattern of vowel reduction
whereby vowel quality contrasts are neutralized in
unstressed syllables.
• The resulting vowel is usually transcribed as
schwa [´]
atom
»QR´m
atomic
´»tHAmIk
21
Reduction to ‘schwa’
Predictions of the undershoot model:
• Reduction to a single vowel should be most likely
where vowels are very short.
• Where there is a single vowel, distinctiveness of
vowel quality contrasts is irrelevant, so effort
minimization should dominate.
• So schwa should be a transitional vowel,
maximally assimilated to the surrounding context.
– ‘targetless schwa’
22
Minimum effort vowels
• Minimal deviation from the narrow constrictions
for surrounding consonants results in low F1 (a
high vowel) because any constriction above the
pharynx lowers F1.
• Minimal deviation from the tongue body and lip
positions for surrounding consonants and vowels
results in contextually variable F2.
• But schwa is often said to be a mid central vowel.
23
Experiment 1: English schwa vowels
( research with Stephanie Johnson)
• Materials
final
non-final
Rosa
Lisa
Russia
asia
rhapsody
suggest
suspend
prejudice
ninja
sofa
vodka
today
begin
report
soda
alpha
umbrella
compare
probable
suffocate
24
Experiment 1
• Also recorded full vowels for comparison.
heed [i], hid [I], head [E], had [Q], odd [A],
hood [U], who [u]
• Spoken in carrier phrase ‘Say ___ to me’.
• 9 female speakers of American English.
• Measured first two formants at the mid point of
the vowels.
• compare frequently lacked any voiced vowel in
the first syllable, so it was excluded from analysis.
25
Results
2500
2000
1500
1000
u
i
500
300
400
I
U
500
600
700
E
800
A
900
1000
Q
1100
non-final
full vowels (means)
26
F1 (Hz)
Non-final schwa:
• Low F1 (mean 425
Hz)
• F2 is contextually
variable.
F2 (Hz)
3000
Results
2500
2000
1500
1000
u
i
500
300
400
I
U
500
600
700
E
Final schwa:
• F1 shows wide range
(mean 665 Hz).
• Much of this is
between-speaker
variation.
• Central F2 (mean 1772
800
900
A
1000
Q
1100
non-final
full vowels (means)
final schwa
27
F1 (Hz)
Non-final schwa:
• Low F1 (mean 425
Hz)
• F2 is contextually
variable.
F2 (Hz)
3000
Results
Subject
0
2
4
6
8
10
0
200
mean F1 (Hz)
Final schwa:
• F1 shows wide range
(mean 665 Hz).
• Much of this is
between-speaker
variation.
 vocal tract size
 quality of final
schwa ([´] - [√])
400
600
final schwa
heed
800
had
1000
1200
1400
28
Two patterns of vowel reduction
• The difference between final and non-final schwa
vowels can interpreted in terms of the undershoot
model of vowel reduction.
• There are two degrees of unstressed vowel
reduction, depending on characteristic vowel
duration.
29
Two patterns of vowel reduction
• Final unstressed vowels are longer than non-final
unstressed vowels: 153 ms vs. 64 ms.
– Presumably a result of final lengthening.
• Allows for a lower schwa vowel, which in turns allows for
the maintenance of contrasts
• The vowels [i, ´, oU] and rhotic [´’] contrast in unstressed
syllables contrast in absolute word-final position.
pretty [»p®IRi]
letter [»lER´’]
beta [»beIŔ ]
motto [»mARoU]
• Non-final schwa does not minimally contrast with other
vowel qualities.
• Consequently it is assimilated to context.
30
The correlation between contrast and reduced
vowel quality
The same correlation between system of contrasts and
reduced vowel quality is observed across languages:
• Contextually variable high vowels only seems to be found
where all vowel quality contrasts are neutralized, e.g.
Dutch (van Bergem 1994), probably Montana Salish.
• Mid central [´] is found in contrast with higher vowels, e.g.
reduced vowel inventories of the form [i, ´, u] occur in
unstressed syllables in Russian (Padgett and Tabain 2003),
E. Bulgarian (Wood and Pettersson 1988), Catalan
(Herrick 2003), and in final unstressed syllables in
Brazilian Portuguese (Mattoso Camara 1972).
31
The correlation between contrast and reduced
vowel quality
• Central Catalan stressed and unstressed vowels (Herrick
2003).
i
u
e
o
´
E
ç
a
32
Experiment 2: Targetless schwa
• This analysis hypothesizes that the non-final
reduced vowel in English is a minimum effort
vowel.
• So far based on impressionistic evaluation of a
relatively unsystematic sample of medial schwa
vowels.
33
Experiment 2: Targetless schwa
• Systematically vary the preceding and following context of
medial schwa.
Questions:
• Does variability of schwa involve assimilation to the
surrounding context?
• Is there any evidence that schwa has a vowel quality
target?
Conclusions:
• Much of the variability of schwa can be attributed to
assimilation.
• Schwa lacks a vowel quality target, but it is not completely
targetless - its target is to be a vowel.
34
Materials
• Nonce words of the form: [»bV1C1´«C2V2t]
– All combinations of V1 from {i, œ, u}
Cn from {b, d, g}
V2 from {i, A, u}
(81 words)
– Subjects were instructed to model the stress
pattern on words like propagate and parakeet.
e.g. »bid´«gut, »bQg´«bit, etc.
35
Materials
• All words were read in the sentence frame:
‘X. Do you know what a X is?’
• Presented twice in random order (only second run
is analyzed here).
• Read by four native speakers of American English,
2 male, 2 female.
36
Analysis
Measured F1 and F2:
• at steady state, extreme values, or midpoint of V1 and
V2
• at the offset of V1, and at the onset of voicing in V2.
• in schwa: at the onset of voicing, at the offset of
schwa, and half way between these points.
5000
V1
S
0
26.1806
V2
37
26.6053
Time (s)
F2 (Hz)
F2 (Hz)
3000
2500
2000
1500
3000
1000
2500
2000
1500
1000
300
200
i
300
u
400
i
Results
u
400
500
600
700
800
900
1000
F2 (Hz)
2200
2000
1800
1600
1400
1200
1000
formants
at
midpoint
of schwa
700
Q
800
900
F2 (Hz)
2500
2000
1500
1000
200
200
300
i
u
i
300
u
400
400
500
500
600
600
700
Q
700
800
Q
38
800
900
F1 (Hz)
Q
600
F1 (Hz)
500
Results
• Medial schwa is highly variable in quality,
particularly in F2.
F2 (Hz)
F2 (Hz)
2500
2000
1500
1000
3000
2500
2000
1500
1000
300
200
i
u
300
i
u
400
400
500
500
600
600
700
700
800
Q
900
1000
Q
800
39
900
F1 (Hz)
3000
Is this variability the result of interpolation
between preceding and following context?
• F2 in schwa is correlated with F2 of surrounding
vowels
• But it is not the result of simple interpolation between
vowels.
2600
2400
F2 (Hz)
2200
i_i
u_a
i_a
u_i
2000
1800
1600
1400
1200
1000
V1mid
Smid
V2mid
40
Is schwa variability the result of interpolation?
2500
2500
2300
2300
2100
2100
1900
1900
F2 (Hz)
F2 (Hz)
• Unsurprisingly, the consonants also have a significant
influence on F2 of schwa.
1700
1500
1700
1500
1300
1300
1100
1100
900
900
V1mid
V1off
ud_da
Smid
ub_ba
V2ons
V2mid
ug_ga
V1mid
V1off
ib_bi
Smid
id_di
V2ons
V2mid
ig_gi
41
Is schwa variability the result of interpolation?
• The F2 trajectory of schwa is more likely to be an
interpolation between preceding and following
consonants.
• But F2 adjacent to a consonant depends in turn on F2
of the adjacent vowel.
42
Locus equations
• Typically consonant F2 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
bçd
5000
5000
0
1.96743
2.42708
Time (s)
0
11.3647
11.8142
Time (s)
43
Is schwa variability the result of interpolation?
• These considerations suggest the following model of
F2 at schwa midpoint:
F2Smid = aC1F2V1 + bC1 + cC2F2V2 + dC2
• The effect of the vowels on F2 of schwa is modulated
by the intervening consonants.
• This model is quite successful (r2 = 0.73-0.86 for
individual subjects)
– For comparison, a model based on F2 at the vowel
mid points alone yields r2 of 0.19-0.36
44
Summary for F2
• Medial schwas show wide variation in F2.
• This variation is systematically conditioned by
context.
• It is difficult to determine whether schwa F2 is the
result of simple interpolation.
45
Is F1 variability the result of interpolation?
• F1 at schwa midpoint also varies substantially
according to vowel context, but cannot be the result
of interpolation between preceding and following
vowels.
900
800
700
i_i
ae_a
i_a
ae_i
F1 (Hz)
600
500
400
300
200
100
0
V1mid
Smid
V2mid
46
Is F1 variability the result of interpolation?
• The consonants can account for the fact that schwa F1 tends to
be much lower than in adjacent vowels: forming a stop closure
lowers F1.
• But if F1 in schwa is governed by the adjacent consonantal
constrictions, then we would expect schwa vowels to have
very low F1.
900
800
700
i_i
ae_a
i_a
ae_i
F1 (Hz)
600
500
400
300
200
100
0
V1mid
Smid
V2mid
47
Is F1 variability the result of interpolation?
• In iC´Ci, F1 at schwa midpoint is higher than in preceding or
following vowels.
• Schwa appears to have an F1 (height) target.
900
900
800
800
700
700
F1 (Hz)
F1 (Hz)
• If there are no height contrasts, why is there a height target?
600
500
600
500
400
400
300
300
200
200
V1mid
V1off
aed_da
Smid
aeb_ba
V2ons
V2mid
aeg_ga
V1mid
V1off
ib_bi
Smid
id_di
V2ons
V2mid
48
ig_gi
Height target or ‘presence’ target?
• While non-final schwa does not contrast with other vowels
in quality, it is still important to distinguish presence vs.
absence of schwa.
• In some contexts presence vs. absence of schwa is
minimally contrastive.
about
[´baUt] vs.
bout
[baUt]
parade
[pH´®eId]
prayed
[pH®eId]
support [s´pHç®t]
sport
[spç®t]
• So schwa is expected to have targets related to signaling
the presence of a vowel, e.g.
 duration
 intensity peak
49
Height target or ‘presence’ target?
• Producing an intensity peak generally involves
increasing F1 (cf. Howitt 2000).
• So the apparent F1 target for non-final schwa may
be a byproduct of signaling the presence of a
vowel.
• This interpretation predicts that the ‘target’ for F1
is not a specific value, but a minimum value.
Accordingly, schwa should assimilate to its
context where this would result in high F1 - e.g.
adjacent to a low vowel.
50
• Preliminary evidence suggests that schwa fully assimilates to
the F1 of an adjacent low vowel. E.g. ‘Mrs Shah adressed the
audience’
• If schwa had a specific F1 target (e.g. ~400 Hz), then we
should observe movement towards this target.
5000
5000
0
0
0.309392
Time (s)
Mr Shah dressed...
0
5.13834
5.62427
Time (s)
Mrs Shah addressed...
51
Summary of experiment 2
• The quality of medial schwa vowels is highly variable.
• Variation in F2 is particularly extensive, and involves
assimilation to the surrounding context, suggesting that
medial schwa has no specific backness or rounding targets.
• F1 in schwa also covaries with F1 of surrounding vowels,
but systematically deviates from F1 of the context,
suggesting that schwa has an F1 target.
• This apparent F1 target may be a byproduct of realizing an
intensity peak to cue the presence of a vowel.
– it is important to consider contrasts with absence as
well as quality contrasts as sources of constraint on the
realization of segments.
52
Conclusion
• English shows two patterns of vowel reduction, both are consistent
with the undershoot model of vowel reduction.
• Non-final schwa vowels are short, which would tend to lead to
substantial undershoot.
• Vowel quality contrasts are neutralized.
• The resulting vowel is substantially assimilated to its context.
• But assimilation is limited by the need to provide clear cues to the
presence of a vowel, e.g. an intensity peak.
• Final unstressed position has longer vowels, allowing for vowel quality
contrasts.
• Schwa is realized as a mid central vowel, distinct from /i, oU/.
• The same correlation between system of contrasts and the quality of
reduced vowels is observed across languages
– contextually variable vowel ( high in most contexts) in the
absence of quality contrasts.
53
– mid central vowel in contrast with higher vowels.
End
54
Schwa presence vs. absence
5000
5000
0
0.0123687
0.291936
Time (s)
saw n(othing)
0
16.9501
17.2303
Time (s)
saw an(other)
55