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Contrast and the realization of schwa vowels in English

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  1. 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

  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.

  9. 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 F2iisF2 at C release F1t, F2tare V formant targets k,  depend on consonant context • 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-T+F2t if F1t 375 Hz: F1V = F1t if F1t > 375 Hz F1V = k1(375–F1t)e-T+F1t F2iisF2 at C release F1t, F2tare V formant targets k,  depend on consonant context • More undershoot where: • Vowel is shorter • Distance between C and V is greater

  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).

  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. Where xn is F2 of Vn in Bark ynis F1 of Vn in Bark a < 1

  14. i. Maximize the distinctiveness of contrasts • Overall distinctiveness cost of a vowel system depends on the minimum distance found in either inventory. where Cost:

  15. ii. Maximize the number of contrasts • maximize the number of vowels in the stressed and unstressed vowel inventories. Cost: where

  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.

  17. Overall cost function • The optimal vowel system is the one that best satisfies these constraints: (subject to vowel space constraint)

  18. 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

  19. Italian vowels Data from Albano Leoni et al 1995

  20. 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.

  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

  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.

  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)

  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 ([´] - [√])

  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. • 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 u e o ´ E ç a

  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 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.

  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.

  38. Results formants at midpoint of schwa

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

  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.

  41. Is schwa variability the result of interpolation? • Unsurprisingly, the consonants also have a significant influence on F2 of schwa.

  42. 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.

  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. bçd bid

  44. 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

  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.

  47. 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.

  48. 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?

  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.