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.

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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

Lindblom's V Reduction Model - gVg

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F2 (Hz)

F1 (Hz)

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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.

F2V

F2C

F1C

F1V

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Formant undershoot as a function of duration and distance

Lindblom’s model:

F2V = k2(F2i –F2t)e-T+F2t

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

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vowel duration (ms)

frequency (Hz)

F1i

F2i

F2t

F1t

F2v

F1v

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

Lindblom’s model:

F2V = k2(F2i –F2t)e-T+F2t

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

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

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vowel duration (ms)

frequency (Hz)

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F2v

F1v

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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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68101214

F2(Bark)

F1(Bark)

i u

a

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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.

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F2(Bark)

F1(Bark)

i u

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V1

V2

d12

€

dij = (a(x i − x j ))2 + (y i − y j )

2

Where xn is F2 of Vn in Barkyn is F1 of Vn in Barka < 1

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i. Maximize the distinctiveness of contrasts

where

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

€

1

dmin2

€

dmin = mini ≠j

dijCost:

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ii. Maximize the number of contrasts

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

where

€

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nave2

€

nave =nstressed + nunstressed

2Cost:

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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:

€

minimizeV

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dmin2

+wn

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nave2

(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 msUnstressed 100 ms

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F2 (Bark)

F1 (Bark)

stressed unstressed

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Italian vowels

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68101214F2 (Bark)

F1 (Bark)

stressed unstressed

e

E

a

ç

o

ui

Data from Albano Leoni et al 1995

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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.

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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 »QR´matomic ´»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

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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F1 (Hz)

non-final full vowels (means)

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I

E

Q

A

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u

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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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F1 (Hz)

non-final full vowels (means) final schwa

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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 ([´] - [√])

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mean F1 (Hz)

final schwa

heed

had

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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.

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.

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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).

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´

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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: [»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.

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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.

Time (s)26.1806 26.60530

5000

V1 S V2

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Results

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F2 (Hz)

iu

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F2 (Hz)

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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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V1mid Smid V2mid

F2 (Hz)

i_iu_ai_au_i

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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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ib_bi id_di ig_gi

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V1mid V1off Smid V2ons V2mid

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ud_da ub_ba ug_ga

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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.

Time (s)1.96743 2.42708

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Time (s)11.3647 11.8142

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5000bid bçd

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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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i_iae_ai_aae_i

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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 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?

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V1mid V1off Smid V2ons V2mid

F1 (Hz)

ib_bi id_di ig_gi

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V1mid V1off Smid V2ons V2mid

F1 (Hz)

aed_da aeb_ba aeg_ga

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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 [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

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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.

Time (s)0 0.309392

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Time (s)5.13834 5.62427

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

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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

Time (s)0.0123687 0.291936

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Time (s)16.9501 17.2303

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saw n(othing) saw an(other)