1 / 34

Predicting Vowel Inventories: The Dispersion-Focalization Theory Revisited

Predicting Vowel Inventories: The Dispersion-Focalization Theory Revisited. Roy Becker Department of Linguistics University of California Los Angeles. Main Theme. The predominant factor in the organization of vowel inventories is perceptual dispersion .

kynton
Télécharger la présentation

Predicting Vowel Inventories: The Dispersion-Focalization Theory Revisited

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Predicting Vowel Inventories:TheDispersion-Focalization TheoryRevisited Roy Becker Department of Linguistics University of California Los Angeles

  2. Main Theme • The predominant factor in the organization of vowel inventories is perceptual dispersion. • Perceptual dispersion is not determined only by distance, but also by reliability, of the components of the auditory image of the vowel (the perceptual formants F1’ & F2’). Two close reliable vowels may be as perceptually-dispersed as two remote unreliable vowels. • The 3.5Bark Center of Gravity Effect (CoGE) both shifts the values of the perceptual formants and enhances their reliability. • The CoGE is gradual and continuous: The 3.5Bark inter-formant distance is merely a landmark, below which the CoGE accelerates and becomes significant. • This interpretation of dispersion and the role of the CoGE predict more realistic inventories than other models, as well as the emergence of a series offront-rounded vowels as an optional organizational feature in larger inventories (n8).

  3. Lindblom’s Dispersion Theory (DT) • Vowel inventories are organized according to maximization of perceptual contrast within the system. • Perceptual contrast between vowels is quantifiable, using acoustic formants, perceptual formants or the (quantized) whole spectrum, as coordinates in dimensions in a perceptual space. The contrast between two vowels is the Euclidean distance between their coordinates. • The level of systemic dispersion within a given inventory is quantifiable, using a function that takes into account the distances within all of the vowel-pairs in the inventory. • For any given inventory size, the optimal inventory is the one with the highest level of systemic dispersion. A computational optimization algorithm can find the predicted optimal inventory. • By comparing the predicted optimal inventories to the vowel inventories found in the world’s languages it is possible to evaluate the explanatory adequacy of the theory and of its formal implementation.

  4. Previous Implementations of DT • Liljencrants & Lindblom (1972): F1&F2’ in Mels. F2’ represents F2 corrected for F3. Equal weights for F1 & F2’. Predictions are fine for n=3,4,6, but poor for n=5 (), n>6 (too many high vowels). • Lindblom (1986): Whole-spectrum distances, based on excitation per frequency (Sone/Bark). Predictions arefine for n=3,5,6, but poor for n=4, n>6 (same problem). • ten Bosch et al. (1987), Bonder & ten Bosch (1991):F1& F2 in log(Hz). Acoustic distance is reinterpreted as confusion probability. Articulatory effort is added to the energy function. Predictions are not given in detail, seems to work well for n= 3~6, but poor for n>6 (same problem). • Roark (2001):F1& F2 (or F1 & F2-F1) in log(Hz). Equal weights for F1 & F2. Predictions are provided only in terms of vowel population within coarse areas (front, back, low, non-peripheral). Seems to improve Lindblom (1986). • Diehl et al. (2003):Distances based on whole-spectra in noise (reducing the contribution of spectral valleys) or whole-spectra excitation-pattern as a function of time (boosting spectral peaks as their excitation lasts longer).Predictions: Given only for n=7. Significantly improves Lindblom(1986).

  5. Implementations of DT - drawbacks • All models predict very peripheral /u/ (F2600Hz), which is rare in languages lacking a {u vs. y~} contrast (e.g. English, Greek, Hebrew, Maori). • All models predict a high-back-unrounded vowel // (F2<1400Hz) as the first vowel to appear between /i/ and /u/. In real inventories such a vowel is typically // or /y/, both with a significantly higher second formant. • No model can predict the emergence of a series of front-rounded vowels as a ‘legitimate’ strategy for inventories with more than 7 vowels. • The predicted vowel qualities are reinterpreted using best matches out of a small set of (typically 19) more common vowel prototypes. Such brute-force mapping might be disguising inaccurate predictions that would have emerged if a more representative set of prototypes were used. • Models based on whole spectra (or temporal resolution of excitation patterns) are almost impossible to evaluate, as their presuppositions and predictions rely on the availability and uniformity of whole-spectral data for vowels (which are hardly ever reported in acoustic descriptions of vowel inventories). • Models are evaluated against typological-phonological databases, and not against detailed phonetic studies.

  6. The Center of Gravity Effect (CoGE)Chistovich&Lublinskaya(1979) • Finding: A vowel containing two formants less than a critical distance of 3.5Bark apart from one another can be perceptually matched by a vowel containing one formant somewhere between them. The single formant match lies closer to the louder of the two formants. • Interpretation: Two formants less than 3~3.5Bark apart undergo spectral integration at their center of gravity. • Theoretical implications: Formant integration is both a distinct perceptual phonetic feature and a ‘quantizer’ of auditory quality for a range of acoustic spectra (with the same CoG). Stevens (1989) advocates the CoGE as an acoustic-to-auditory extension of the articulatory-to-acoustic quantal property of vowels with converging formants, as part of his Quantal Theory (QT). • Applications: Vowel inventories reanalyzed in terms of this perceptual feature, e.g.: [+back] in Swedish = F2’-F1<3.5Bark; [-back] in English = F3-F2<3.5Bark; [+high] in English = F1-f0<3.5Bark (Fant 1983, Syrdal&Gopal 1986, Hoemeke&Diehl 1994). • Implementations: Bias towards CoGE-involving (‘focal’) vowels is integrated in the inventory prediction algorithm of the Dispersion-Focalization Theory.

  7. Dispersion-Focalization Theory (DFT)Abry et al. (1989), Boë et al. (1994), Schwartz et al. (1997b) • Focal vowels are a perceptual goal, as the CoGE enhances their percept, like “saturated colors” in vision. Vowel inventories combine a general bias towards systemic dispersion with particular bias towards focal vowels. • Special concern about /y/, which is too close to /i/, but involves F2~F3 convergence. /i y u/ is a common strategy in larger inventories. An adequate theory must predict its ‘legitimacy’ (unachievable in DT implementations). Implementation Principles (Schwartz et al. 1997b): • Vowels are represented by F1 and F2’ values. F2’ has a weight λ relative to F1. • The CoGE is used in F2’ calculation based on F2, F3& F4. • An inventory’s dispersion energy(ED) is calculated as in previous models. • The first three overlapping formant pairs for each vowel compose ‘focalization components’ for the vowel. • The focalization components of all vowels are summed to yield an inventory’s focalization energy (EF), which has a weight α) relative to ED. • Summing the weighted energy components yields the inventory’s total energy.

  8. Implementation of DFT: algorithmSchwartz et al. (1997b) Vowel Space Coverage: Quantized using 33 prototypical qualities fully specified for F1~F4 (in Hz). For any inventory size, full enumeration over all quality combination is performed. Calculation of F2’ (in Bark units):if F3-F2>3.5 then c2=1,c3=0,c4=0 elseif F3-F2>2.5 then c2=1,c3=(F3-F2)/2,c4=0 elseif F4-F2>3.5 or F4-F3>F3-F2 then c2=1,c3=0.5,c4=0 elsec2=0,c3=1,c4=0.5 F2’ = (c2F2+c3F3+c4F4)/(c2+c3+c4) Calculation of ED: Calculation of EF: Calculation of E: E = ED + αEF

  9. Implementation of DFT: resultsSchwartz et al. (1997b) • Simulations for inventories of size3≤n≤7 are presented in terms of the optimal inventory as a function of the F2’ weight parameter (λ) and the focalization weight parameter (α). Fig. 1 presents simulations for inventories with 5≤n≤7 Fig. 1: Prediction simulations for inventories with 5,6 and 7 vowels in Schwartz et al. (1997b) • For 0.20≤λ≤0.22, α0, n≤7, the model predicts the most common inventories. • The results imply that focalization plays no role in optimal inventories. • The vowel /y/ emerges in calculations of stable sub-optimal 7-vowel inventories for 0.3≤α≤0.4.

  10. Implementation of DFT: drawbacksSchwartz et al. (1997b) Universal Typology: • The model keeps predicting very peripheral /u/ in small inventories. • Results for inventories with more than 7 vowels are not presented, although the authors themselves show that 8- and 9-vowel inventories are universally stable and viable as well (Schwartz et al. 1997a). • While /y/ emerges as a stable sub-optimal inventory for a particular range of λ and α, other front-rounded vowels do not. Front rounded vowels typically appear in series (e.g. Germanic, Finno-Ugric, Turkic, French). Manifestation of the Center of Gravity Effect: • While the authors recognize the CoGE as a crucial factor in focalization, the CoGE and the 3.5Bark critical band has no role the calculation of EF. • Potential CoGEs of F1~F2 (back rounded vowels) and f0~F1 (high vowels) are ignored altogether.

  11. Implementation of DFT: drawbacksSchwartz et al. (1997b) Relevance to cognitive theory: • Unless the ranges of the weighting parameters λ and α are significantly restricted and interpreted as ‘exemplar-based adaptive components’ of vowel perception, they have little relevance to cognition and are difficult to integrate into a grammatical theory. • The ranges of F2’ values as a function F2 or F3 continua are ‘jumping around’ (Fig. 2). Such discontinuous acoustic-to-auditory mapping is very unlikely. Fig. 2: Discontinuities in the value of F2’ as a function of (a) F2, and (b) F3, given the F2’ calculation formula in Schwartz et al. (1997b).

  12. Towards a revision of the DFTThe CoGE Paradox • The CoGE hypothesis was tested experimentally, with mixed results: Some experiments (Chistovich&Lublinskaya 1979, Schwartz&Escudier 1989, Hoemeke&Diehl 1994) corroborated the notion of spectral integration and categorical shift in auditory perception at 3.5Bark between-formant interval. Other experiments indicate that the CoGE does not eliminate the role of distinct formants in the vowel percept (Beddor&Hawkins 1990, Johnson et al. 1993), and that the alleged 3.5Bark interval has no categorical effect on perceptual behaviour (Fahey et al. 1996). • While the notion of spectral integration is well-established for smaller frequency intervals, it is unlikely that its domain would span 3 times the bandwidth of the acoustic peaks or 1/7 of the auditory frequency scale. • The fact that the best single-formant match for 2-formants stimuli is near their CoG only implies sufficient perceptual resemblance, rather than perceptual identity, between the 2-formant stimulus and the 1-formant match. Whatever underlies such perceptual resemblance is somehow significantly boosted at between-formant interval of less than 3~3.5Bark. • Thus, the ‘strong CoGE hypothesis’ must be revised.

  13. Towards a revision of the DFTReinterpreting the CoGE (and solving the paradox) • The CoGE is a continuous,non-linear function: CoGE({Fn,Fn+1}) = {Fn’,Fn+1’} • The 3~3.5Bk landmark demarcates the ‘domain of acceleration towards formant integration’ (see fig. 3). • At longer distances (Fn+1–Fn>3.5Bk), the CoGE is negligible. • Within the ‘domain of acceleration’ (2<Fn+1–Fn<3.5Bk), both formants are perturbed towards their CoG. The perceptual distance between them shrinks rapidly, but they remain distinct. • Formant integration is limited to a much shorter interval (Fn+1–Fn<1.5~2Bk). • This reinterpretation of the CoGE is consistent with Johnson et al. (1993). negligible accelerated integrated Fig. 3: The CoGE as a function from two acoustic formants to two auditory formants, with three distinct ranges.

  14. Towards a revision of the DFTThe CoGE, perceptual enhancement and formant reliability • In auditory transmission, an acoustic formant (spectral peak) enhances neural response throughout the closer vicinity of its frequency range. • The CoGE emerges when formants are close enough such that points in the valley between them get more prominent than the ‘original’ peaks. • As both perceptual peaks are amplified, both get ‘louder’ and hence more reliable. This is the essence of the CoGE asa perceptual goal. • Following CoG principles, a ‘lighter’ peak is both perturbed more and amplified more than a ‘heavier’ peak. Fig. 4: Schematic representation of (a) the auditory response to an acoustic formant, (b) the mutual auditory enhancement between two ‘equal’ formants and the emergence of a CoGE, and (c) the mutual enhancement and CoGE between two ‘unequal’ formants’.

  15. Towards a revision of the DFTA tentative model of vowel perception • A ‘vowel envelope’ is projected with the perception of f0, which serves as a normalization anchor. The ‘envelope’ is delimited by the speaker’s formant (SF) integrating the back cavity formant (BF = F3, or F2 in high-front vowels) and F4 (Syrdal 1985, Nawka et al. 1997, Halberstam&Raphael 2004). • Within the ‘vowel envelope’, the aperture formant (AF = F1) and the front cavity formant (FF = F2, or F3 in high-front vowels - Ladefoged&Bladon 1982), are the basis for the perceptual coordinates of the vowel, AP & FP. The F2’-to-FF correspondence, regardless of whether FF is F2 or F3, is consistent with Carlson et al.’s (1970) results regarding F2’. Fig. 5: Deriving the percept of schwa according to the tentative model suggested.

  16. Towards a revision of the DFTThe model of vowel perception and the CoGE • AF may undergo a CoGE with f0 (higher vowels), lowering and enhancing AP (fig. 6a). • FF may undergo a CoGE with SF (front vowels, both rounded and unrounded), raising and enhancing FP (fig. 6b). • AF and FF may undergo a CoGE with each other (rounded/low back vowels), raising AP, lowering FP, and enhancing them both (fig. 6c). • A vowel’s percept comprises of AP and FP, each with its value and its reliability weight. Fig. 6: Illustrations of vowel percepts according to the current model, as a result of CoGEs on (a) AF & f0 in the high vowel [], (b) FF & SF in the front vowel [], and (c) AF & FF in the low back vowel []. Notice that CoGEs are substantially more effective on FP than on AP.

  17. Towards a revision of the DFTInventory evaluation • A vowel percept is calculable given: a) f0, AF, FF, BF & F4 (it is assumed that formant-cavity affiliations are known).b) the magnitude of formant-percept perturbation of the CoGE function.c) the default and dynamic range of the reliability weights of AP and FP. • The space of possible vowels may be constrained by rigid requirements on tongue-body and jaw displacement. • The perceptual dispersion between two given vowels is the weighted Euclidean distance between their calculated percepts. • The criterion for an inventory’s dispersion is its least dispersed vowel-pair (the inventory is ‘as bad as its worst pair’ – see ten Bosch 1991, Flemming 2005). • All other vowel-pairs contribute negligibly. They can make a difference between two ‘equally bad’ inventories, but cannot promote a worse inventory over a better one. • Learning is an adaptive search compromising perfection and stability. An inventory is learnable if it near-perfect and near-stable, i.e. if it is better than all other inventories in its greater neighbourhood (major local extremum).

  18. The DFT revised – MatLab simulationSystem tools • A realistic male acoustic vowel space, with 230<AF<830Hz and FF-range depending on AF. Range of BF determined by AF&FF. F4 value determined by FF&BF. • F2 & F3 exchange cavity affiliation for high-front vowels (FF>BF) in accordance with Ladefoged & Bladon’s (1982) nomograms. • Boundaries for the articulatory constraints banning extreme dorsum displacementand extreme and moderate jaw lowering. • 66 vowel prototypes (9 height degrees, 3~12 backness/rounding degrees per height degree), specified for all 4 formants. Fig. 8: The AF~FF vowel space used in the simulation (solid black). The solid blueline denotes the are where FF switches affiliation between F2 and F3. The solid red line delineates the space for vowels with non-extreme dorsum displacement. The dotted red lines mark the highest AF for vowels with no/moderate jaw lowering.

  19. The DFT revised – MatLab simulationMathematical implementation of principles • For every vowel: f0 = 125Hz; AF, FF and BF determined by variables; F4 determined by FF & BF; ‘Pinched’ FF & BF forbidden (due to cavity coupling), resolved in accordance with Stevens(1989); Hz values transformed to Barks. • SF is calculated ¼ the way from BF to F4 (BF is more prominent than F4). • The CoGE function is applied to {f0,AF}, {AF,FF} or {FF,SF}. Assuming relative prominence AF>f0, AF>FF>SF, the CoG-approximations are calculated ¼ the way from AF to f0 or FF, and ¼ the way from FF to SF. • The perturbed AF & FF are the values of AP and FP (APV, FPV), respectively. • The default weight of AP (APW) is 0.7. CoGEs raise it gradually up to 1.0.* • The default weight of FP (FPW) is 0.11. CoGEs raise it gradually up to 0.83.* • The distance between two vowels: di,j = [APWi*APWj*(APVi-APVj)² + FPWi*FPWj*(FPVi-FPVj)²]½ * The reliability weights are semi-arbitrary, but they express the underlying hypotheses, and they are not parameterized unlike Schwartz et al. (1997). Moreover, for average APWs & FPWs (0.85 & 0.47 respectively), the contribution ratio of FP/AP is (0.47/0.85)² = 0.3, identical to de Boer’s (2001).

  20. The DFT revised – MatLab simulationInventory stabilization algorithm For an inventory size s and a set of jaw, tongue-body and tongue-root constraints: • s*3 inventories are created, each with s randomly-generated vowels. • These inventories undergo the following Simulated annealing procedure: a) At each cycle, the least dispersed vowel-pair is perturbed. b) If the perturbation improves the inventory, or if a low-probability game is successful, the new inventory replaces the old one. c) The probability to approve a degraded inventory decreases gradually. d) The annealing procedure terminates after 42+4*s successive cycles with no significant improvement or after 3200+400*s cycles in total. • The ‘annealed’ inventory is categorized using the 66 prototypes. Each vowel is assigned a best-matching prototype using a distance function over the formant values in Hz. The vowels are ‘labeled’, but retain their own formant values. • Inventories of the same type (exactly the same categorical composition) are counted and grouped under the best inventory among them. • A report is printed, listing all inventory types found, each with its count and the category and formant values for each vowel. AF~FF plots are created as well.

  21. The DFT revised: results (3 vowels) • Strategy: {~~ }. • The pair {,} offers better dispersion but less symmetry than {,}. • Both patterns are universally common, as is the variation in the low vowel.

  22. The DFT revised: results (4 vowels) • Strategy: {~  }. • Relatively low //, retracted // and variation between // and // are indeed the universally common strategies. • The strategy {}, which is also known but far less common, was predicted only marginally.

  23. The DFT revised: results (5 vowels) • Strategy: {~ ~~ }. • The symmetrical {} is by the most common inventory in the world, but the less symmetrical {} is also attested. • The slightly fronted // (F2≈800Hz), which emerged in all settings, and the marginal appearance of //, are real ‘goodies’ predicted nowhere else. • The predicted strategy {}, which is highly dispersed but very asymmetrical, is very rare (probably exists in Wari’).

  24. The DFT revised: results (6 vowels) • Strategies: {     } / {   ~~ i}. • The strategy competition mimics universally common patterns. • The first strategy is accurate (cf. Russian). • In the second strategy, the preference of // and the marginality of // are a drawback, but // makes a reasonable compromise.

  25. The DFT revised: results (7 vowels) • Strategies: {      ~} / {~    ~ }. • Both are attested (the latter is common, cf. Italian). • The emerging third strategy ({} cf. Hungarian) illustrates a series of front rounded vowels. • The aperture contrast between non-high rounded vs. unrounded front vowels exaggerates a true phonetic universal, and is therefore only a minor drawback.

  26. The DFT revised: results (8 vowels) • Strategy: {       ~}. • The fully peripheral strategy disappears (a drawback). • Further emergence of universally attested internal series (front-rounded, c.f. Finnish, and, marginally, central-unrounded). • Emergence of a ‘Turkic’ strategy for extreme-tongue/no-jaw-displacement (realistic for Turkish).

  27. The DFT revised: results (9 vowels) • Strategies: 6~8-peripheral/3~1-central. • The front-rounded series is ‘fully-established’. • Many other, less symmetrical, internal strategies.

  28. The DFT revised: results (10 vowels) • Strategies: more ‘mess’ in the internal area. • A French-like pattern emerges (the lower front-rounded vowel is indeed centralized in French).

  29. The DFT revised: results(selected plots)

  30. The DFT revised: results(selected plots)

  31. The DFT revised: results(selected plots)

  32. The DFT revised: summary of ‘goodies’ • /~/ variation in 3- and 4-vowel inventories. • Slightly fronted // in 5-vowel inventories. • 2-2-2 vs. 3-2-1 strategy competition in 6-vowel inventories. • The extreme displacement 7-vowel inventory /u/ and the moderate displacement 5-vowel inventory // have exactly the samedispersion score (see Flemming 2004). • The emergence of a series of front-rounded vowels in larger inventories (s>6), and the aperture contrast between the non-high unrounded and rounded front vowels. • 8-vowel results (extreme conditions) imply that the /u~a/ & /~a/ ranges are 3/2 the /u~/ range (Boersma1998:109). • The average PF/AF contribution ratio of 0.3 used elsewhere emerges as an artifact of the dynamic weighting as determined by CoGEs.

  33. The DFT Revised: Conclusions The model and algorithm suggested here: • Make more accurate and realistic predictions than previous models despite greater detail in prototype-matching. • Render series of front-rounded vowels as a legitimate strategy in inventories with more than 6 vowels. • Generate almost all common strategies for all inventory sizes, including competitions mimicking universal typology. • Generate ‘phonetically learnable’ inventories. • Have no continuant parameters. • Are compatible with a model of phonology like Optimality Theory. Rigid phonological symmetry constraints can passively filter out most of the over-generated inventories. • Unlike whole-spectrum based models, they are easily testable against (normalized) acoustic-phonetic descriptive studies of vowel inventories.

  34. References Abry, C., Boë, L.J. and Schwartz, J.L. (1989): Plateaus, catastrophes and the structuring of vowel systems. J.Phon. 17:47-54. Badin, P., Perrier, P., Boë, L.J. and Abry, C. (1990): Vocalic nomograms: acoustic and articulatory considerations upon formant convergences. JASA 87(3):1290-1300. Beddor, P.S. and Hawkins, S. (1990): The influence of spectral prominence on perceived vowel quality. JASA 87(6):2684-2704. Boë, L.J., Schwartz, J.L. and Vallée, N. (1994): The prediction of vowel systems: perceptual contrast and stability. InE. Keller (ed.), Fundamentals of Speech Synthesis and Speech Recognition (185-213). Chichester, England: Wiley & Sons. de Boer, B. (2001): Self organization in vowel systems. J.Phon. 28(4):441-466. Boersma, P. (1998): Functional Phonology. PhD thesis, University of Amsterdam. Bonder, L.J. and ten Bosch, L.F.M. (1991): Recent developments in the research of the structure of vowel systems. Proceedings of the 12th ICPhS, 1:160-165. Aix-en-Provence: Université de Provence Bladdon, A. (1983): Two-formant models of vowel perception: shortcomings and enhancements. Speech Communication 2:305-313. ten Bosch, L.F.M. (1991): Modeling vowel systems by effort and contast. Proceedings of the 12th ICPhS, 4:406-409. Aix-en-Provence: Université de Provence. ten Bosch, L.F.M., Bonder, L.J. and Pols, L.C.W. (1987): Static and dynamic structure of vowel systems. Proceedings of the 11th ICPhS, 1:235-238. Tallinn: Academy of Sciences of the Estonian S.S.R. Carlson, R., Granström, B. and Fant, G. (1970): Some studies concerning the perception of isolated vowels. STL-QSPR 2-3:19-35. Chistovich, L.A. and Lublinskaya, V.V. (1979): The ‘center of gravity’ effect in vowel spectra and critical distance between the formants: psychoacoustical study of the perception of vowel-like stimuli. Hearing Research 1:185-195. Diehl, R.L., Lindblom, B. and Creeger, C.P. (2003): Increasing realism of auditory representations yields further insights into vowel phonetics. Proceedings of the 15th ICPhs, 2:1381-1384. Adelaide: Causal Publications. Fahey, R.P., Diehl, R.L. and Traunmüller, H. (1996): Perception of back vowels: effects of varying F1-F0 distance. JASA 99:2350-2357. Fant, G. (1983): Feature analysis of Swedish vowels – a revisit. STL-QSPR 2-3/1983:1-19. Flemming, E. (2004): ‘Contrast and perceptual distinctiveness’, In Hayes, B., Kirchner, R. and Steriade, D. (eds.) Phonetically-Based Phonology (232-276). Cambridge University Press. Flemming, E. (2005): A phonetically-based model of vowel reduction. Submitted manuscript. Halberstam, B. and Raphael, L.J. (2004): Vowel normalization: the role of fundamental frequency and upper formants. J.Phon. 32:423-434. Johnson, K., Fernandez, M,m Henninger, M. and Sandstrum, J. (1993): Spectral integration in vowel perceptiion: matching and discrimination studies. UCLA-WPP 83:47-54 Ladefoged, P. and Bladon, A. (1982): Attempts by human speakers to reproduce Fant’s nomograms. Speech Communication 1:185-198. Liljencrants, J. and Lindblom, B. (1972): Numerical simulation of vowel quality systems: the role of perceptual contrast. Language 48(4):839-862. Lindblom, B. (1986): Phonetic universals in vowel systems. In Ohala, J. and Jaeger, J. (eds.) Experimental Phonology (13-44). Orlando: Academic Press. Nawka, T., Anders, L.C.,Cebulla, M. and Zurakowski, D. (1997): The speaker’s formant in male voices. Journal of Voice, 11(4):422-428. Roark, B. (2001): Explaining vowel inventory tendencies via simulation: finding a role for quantal locations and formant normalization. In Proceedings of the 31st Conference of the North East Linguistics Society (NELS 31). Schwartz, J.L., Boë, L.J., Vallée, N. and Abry, C. (1997a): Major trends in vowel system inventories. J.Phon 25:233-253. Schwartz, J.L., Boë, L.J., Vallée, N. and Abry, C. (1997b): The Dispersion-Focalization Theory of vowel systems. J.Phon 25:255-286. Schwartz, J.L. and Escudier, P. (1989): A strong evidence for the existence of a large-scale integrated spectral representation in vowel perception. Speech Communication 8:235-259. Stevens, K.N. (1989): On the quantal nature of speech. J.Phon. 17:3-45. Syrdal, A.K. (1985): Aspects of a model of the auditory representation of American English vowels. Speech Communication 4:121-135. Syrdal, A.K. and Gopal, H.S. (1986): A perceptual model of vowel recognition based on the auditory representation of American English vowels. JASA 79(4):1086-1100. Traunmüller, H. and Lacerda, F. (1987): Perceptual relativity in identification of two-formant vowels. Speech Communication 6:143-157. I am indebted to Prof. Bruce Hayes for accompanying me, for his criticism and his insistence on the broader linguistic picture and on formal modeling.

More Related