Contrast and the realization of schwa vowels in English

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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).

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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 vin?i he
sells vin?imu we sell e ve_at_ni he
comes (vinimu we come) a a_at_vi he
has aviti he has o mo_at_ri he
dies (murimu we die) u u_at_Ô?i he
boils uÔ?imu we boil
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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.

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Outline of an analysis of vowel reduction

• Vowel reduction is fundamentally motivated by
  undershoot in short unstressed syllables.

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Phonetic vowel reduction - Undershoot
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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.

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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.

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Formant undershoot as a function of duration and
distance
Lindbloms model F2V k2(F2i F2t)e-?TF2t if
F1t ? 375 Hz F1V F1t if F1t gt 375 Hz
F1V k1(375 F1t)e-?TF1t F2i is F2 at C
release F1t, F2t are V formant targets k, ?
depend on consonant context

• More undershoot where
• Vowel is shorter
• Distance between C and V is greater

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Formant undershoot as a function of duration and
distance
Lindbloms model F2V k2(F2i F2t)e-?TF2t if
F1t ? 375 Hz F1V F1t if F1t gt 375 Hz
F1V k1(375 F1t)e-?TF1t F2i is F2 at C
release F1t, F2t are V formant targets k, ?
depend on consonant context

• More undershoot where
• Vowel is shorter
• Distance between C and V is greater

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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.

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Model of vowel reduction

• The vowel space is modeled on Liljencrants and
  Lindblom (1972).

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i. Maximize the distinctiveness of contrasts

• Distinctiveness of the contrast between Vi and Vj
  is the (weighted) distance between the vowels in
  formant space.

Where xn is F2 of Vn in Bark yn is F1 of Vn in
Bark a lt 1
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i. Maximize the distinctiveness of contrasts

• Overall distinctiveness cost of a vowel system
  depends on the minimum distance found in either
  inventory.

where
Cost
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ii. Maximize the number of contrasts

• maximize the number of vowels in the stressed and
  unstressed vowel inventories.

where
Cost
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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.

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Overall cost function

• The optimal vowel system is the one that best
  satisfies these constraints

(subject to vowel space constraint)
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Optimal inventories
a 0.14, k1 1.5, ?1 0.008, k2 1.5, ?1
0.01, c 0.27, F2l 1400 Hz, wn
6 Durations stressed 160 ms Unstressed 100 ms
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Italian vowels
Data from Albano Leoni et al 1995
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Undershoot and vowel reduction

• Relating phonological vowel reduction to
  undershoot helps to explain
• The tendency to neutralize vowel contrasts in
  short unstressed syllables.
• The generalization that vowel reduction primarily
  eliminates height contrasts.
• The generalization that neutralizing vowel
  reduction is accompanied by phonetic reduction.

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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 QRm
• atomic tHAmIk

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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

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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.

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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
alpha umbrella suffocate
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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.

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Results

• Non-final schwa
• Low F1 (mean 425 Hz)
• F2 is contextually variable.

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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)

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Results

• Final schwa
• F1 shows wide range (mean 665 Hz).
• Much of this is between-speaker variation.
• vocal tract size
• quality of final schwa ( - v)

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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.

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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.

• Non-final schwa does not minimally contrast with
  other vowel qualities.
• Consequently it is assimilated to context.

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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).

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The correlation between contrast and reduced
vowel quality

• Central Catalan stressed and unstressed vowels
  (Herrick 2003).

i
u
e
o

E
ç
a
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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.

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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.

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Materials

• Nonce words of the form bV1C1C2V2t
• 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. bidgut, bQgbit, etc.

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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.

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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.

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Results
formants at midpoint of schwa
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Results

• Medial schwa is highly variable in quality,
  particularly in F2.

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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.

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Is schwa variability the result of interpolation?

• Unsurprisingly, the consonants also have a
  significant influence on F2 of schwa.

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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.

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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.

bçd
bid
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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

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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.

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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.

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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.

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Is F1 variability the result of interpolation?

• In iCCi, 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?

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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 pHeId prayed pHeId
• support spHçt sport spçt
• So schwa is expected to have targets related to
  signaling the presence of a vowel, e.g.
• duration
• intensity peak

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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.

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• 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.

Mrs Shah addressed...
Mr Shah dressed...
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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.

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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.

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End
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Schwa presence vs. absence
saw an(other)
saw n(othing)