Schwa

Contrast and the realization of
schwa vowels in English
Edward Flemming

2
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’).

3
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
stressed vowels unstressed vowels
[i] vi¤n˘i ‘he sells’ vin˘i¤mu ‘we sell’
[e] ve@ni ‘he comes’ (vini¤mu ‘we come’)
[a] a@vi ‘he has’ avi¤ti ‘he has’
[o] mo@ri ‘he dies’ (muri¤mu ‘we die’)
[u] u@Ô˘i ‘he boils’ uÔ˘i¤mu ‘we boil’

4
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.

5
Outline of an analysis of vowel reduction
• Vowel reduction is fundamentally motivated by
undershoot in short unstressed syllables.

6
Phonetic vowel reduction - Undershoot
Lindblom's V Reduction Model - gVg
300
350
400
450
500
550
600
650
700
5001000150020002500
F2 (Hz)
F1 (Hz)
200ms
125 ms
100 ms
i
e
a
o
u

7
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.

8
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.
F2V
F2C
F1C
F1V

9
Formant undershoot as a function of duration and
distance
Lindblom’s model:
F2V = k2(F2i –F2t)e-βT
+F2t
if F1t ≤ 375 Hz:
F1V = F1t
if F1t > 375 Hz
F1V = k1(375 –F1t)e-βT
+F1t
F2i is F2 at C release
0
200
400
600
800
1000
1200
1400
1600
1800
50 100 150 200 250 300
vowel duration (ms)
frequency (Hz)
F1i
F2i
F2t
F1t
F2v
F1v
More undershoot where:
• Vowel is shorter
• Distance between C and V is greater

10
Formant undershoot as a function of duration and
distance
Lindblom’s model:
F2V = k2(F2i –F2t)e-βT
+F2t
if F1t ≤ 375 Hz:
F1V = F1t
if F1t > 375 Hz
F1V = k1(375 –F1t)e-βT
+F1t
F2i is F2 at C release
More undershoot where:
• Vowel is shorter
• Distance between C and V is greater
0
200
400
600
800
1000
1200
1400
1600
1800
50 100 150 200 250 300
vowel duration (ms)
frequency (Hz)
F1i
F2i
F2t
F1t
F2v
F1v

11
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.

12
Model of vowel reduction
• The vowel space is modeled on Liljencrants and Lindblom
(1972).
2
3
4
5
6
7
8
68101214
F2(Bark)
F1(Bark)
i u
a

13
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
3
4
5
6
7
8
68101214
F2(Bark)
F1(Bark)
i u
a
V1
V2
d12
dij = (a(xi − x j ))2
+ (yi − y j )2
Where xn is F2 of Vn in Bark
yn is F1 of Vn in Bark
a < 1

14
i. Maximize the distinctiveness of contrasts
where
• Overall distinctiveness cost of a vowel system
depends on the minimum distance found in either
inventory.
1
dmin
2
dmin = min
i ≠j
dijCost:

15
ii. Maximize the number of contrasts
• maximize the number of vowels in the stressed and
unstressed vowel inventories.
where
1
nave
2
nave =
nstressed + nunstressed
2
Cost:

16
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.
2
2.5
3
3.5
4
4.5
5
5.5
6
68101214
F2(Bark)
F1(Bark)
100 ms
160 ms

17
Overall cost function
• The optimal vowel system is the one that best
satisfies these constraints:
minimize
V
1
dmin
2
+
wn
2
nave
2
(subject to vowel space constraint)

18
Optimal inventories
a = 0.14,
k1 = 1.5,
β1 = 0.008,
k2 =1.5,
β1 = 0.01,
c = 0.27,
F2l = 1400 Hz,
wn = 6
Durations:
stressed 160 ms
Unstressed 100 ms
2
2.5
3
3.5
4
4.5
5
5.5
6
68101214
F2 (Bark)
F1 (Bark)
stressed unstressed

19
Italian vowels
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
68101214
F2 (Bark)
F1 (Bark)
stressed unstressed
e
E
a
ç
o
u
i
Data from Albano Leoni et al 1995

20
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.

21
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

22
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’

23
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.

24
Experiment 1: English schwa vowels
( research with Stephanie Johnson)
• Materials final non-final
Rosa rhapsody
Lisa suggest
Russia suspend
asia prejudice
ninja today
sofa begin
vodka report
soda compare
alpha
umbrella
probable
suffocate

25
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.

26
Results
Non-final schwa:
• Low F1 (mean 425 Hz)
• F2 is contextually
variable.
300
400
500
600
700
800
900
1000
1100
50010001500200025003000
F2 (Hz)
F1 (Hz
non-final full vowels (means)
i
I
E
Q
A
U
u

27
Results
Non-final schwa:
• Low F1 (mean 425 Hz)
• F2 is contextually
variable.
Final schwa:
• F1 shows wide range
(mean 665 Hz).
• Much of this is
between-speaker
variation.
• Central F2 (mean 1772
Hz)
300
400
500
600
700
800
900
1000
1100
50010001500200025003000
F2 (Hz)
F1 (Hz
non-final full vowels (means) final schwa
i
I
E
Q
A
U
u

28
Results
Final schwa:
• F1 shows wide range
(mean 665 Hz).
• Much of this is
between-speaker
variation.
 vocal tract size
 quality of final
schwa ([´] - [√])
0
200
400
600
800
1000
1200
1400
0 2 4 6 8 10
Subject
mean F1 (Hz)
final schwa
heed
had

29
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.

30
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 [»beIR´]
motto [»mARoU]
• Non-final schwa does not minimally contrast with other vowel
qualities.
• Consequently it is assimilated to context.

31
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).

32
The correlation between contrast and reduced
vowel quality
• Central Catalan stressed and unstressed vowels (Herrick
2003).
i
e
E
a
ç
o
u
´

33
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.

34
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.

35
Materials
• Nonce words of the form: [»bV1C1´«C2V2t]
– All combinations of V1from {i, œ, u}
Cn from {b, d, g}
V2from {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.

36
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.

37
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.
Time (s)
26.1806 26.60530
5000
V1 S V2

38
Results
200
300
400
500
600
700
800
1000120014001600180020002200
F2 (Hz)
i
u
Q
200
300
400
500
600
700
800
900
1000150020002500
F2 (Hz)
F1
i
u
Q
200
300
400
500
600
700
800
900
1000
10001500200025003000
F2 (Hz)
i
Q
u
300
400
500
600
700
800
900
10001500200025003000
F2 (Hz)
F1
u
i
Q
formants
at
midpoint
of schwa

39
Results
• Medial schwa is highly variable in quality,
particularly in F2.
200
300
400
500
600
700
800
900
1000
10001500200025003000
F2 (Hz)
i
Q
u
300
400
500
600
700
800
900
10001500200025003000
F2 (Hz)
F1
u
i
Q

40
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.
1000
1200
1400
1600
1800
2000
2200
2400
2600
V1mid Smid V2mid
F2 (Hz)
i_i
u_a
i_a
u_i

41
Is schwa variability the result of
interpolation?
• Unsurprisingly, the consonants also have a significant
influence on F2 of schwa.
900
1100
1300
1500
1700
1900
2100
2300
2500
V1mid V1off Smid V2ons V2mid
F2 (Hz)
ib_bi id_di ig_gi
900
1100
1300
1500
1700
1900
2100
2300
2500
F2 (Hz)
ud_da ub_ba ug_ga

42
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.

43
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.
Time (s)
1.96743 2.42708
0
5000
Time (s)
11.3647 11.8142
0
5000
bid bçd

44
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

45
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.

46
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.
0
100
200
300
400
500
600
700
800
900
V1mid Smid V2mid
F1 (Hz)
i_i
ae_a
i_a
ae_i

47
• 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.
0
100
200
300
400
500
600
700
800
900
V1mid Smid V2mid
F1 (Hz)
i_i
ae_a
i_a
ae_i

48
• In iC´Ci, F1 at schwa midpoint is higher than in preceding or
following vowels.
• Schwa appears to have an F1 (height) target.
• If there are no height contrasts, why is there a height target?
200
300
400
500
600
700
800
900
F1 (Hz)
ib_bi id_di ig_gi
200
300
400
500
600
700
800
900
F1 (Hz)
aed_da aeb_ba aeg_ga

49
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

50
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.

51
• 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.
Time (s)
0 0.309392
0
5000
Time (s)
5.13834 5.62427
0
5000
Mr Shah dressed... Mrs Shah addressed...

52
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.

53
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.
– mid central vowel in contrast with higher vowels.

55
Schwa presence vs. absence
Time (s)
0.0123687 0.291936
0
5000
Time (s)
16.9501 17.2303
0
5000
saw n(othing) saw an(other)

Schwa

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