Spanish Perception of the English /i/-/I/ Distinction

Several studies have shown that Spanish speakers have problems perceiving certain English vowels. Fox, Flege, and Munro (1995) showed that Spanish listeners are not sensitive to durational information when categorizing vowels and therefore may have difficulty with English vowels that differ in both duration and quality (for the same claim, see Bradlow, 1995). For the English

distinction, Flege (1991) showed that monolingual Spanish listeners associate both English

and English

with Spanish /i/. According to Flege, this may explain why early Spanish learners of English use /i/ indiscriminately in their mental representations for English

, which again would explain why they do not differentiate the two vowels in L2 production. However, Bohn (1995) showed that some inexperienced Spanish learners of English were able to distinguish between

in an identification task (from which it seems to follow that they must have separate lexical representations for the vowels in bit and beat, given that they are capable of using these words as labels). Nevertheless, they made such a distinction by relying on auditory cues that are less important for English listeners. Specifically, the Spanish learners of English in Bohn's study paid as much attention to durational as to spectral differences when having to categorize English

(spectral cue reliance: 50% and duration: 44%), whereas the English listeners exhibited a strong preference for spectral cues (spectral cues: 88% and duration: 9%).

contrast (47% for the learners and 88% for the NSs). However, if a measured difference of 47% versus 88% is compatible with the absence of a true difference, the power of the statistical test must be so low that the measured difference is also compatible with a very large true difference (namely, 27% versus 97%), so that Flege et al.'s results must be considered inconclusive.

In sum, the literature seems to be inconclusive in two respects. First, it does not clearly answer the question as to whether Spanish learners of English can or cannot learn to perceive the English

contrast in a way that resembles NS perception. Second, it presents contradictory conclusions with respect to the auditory cue weighting in Spanish learners of English. Our experiment attempts to resolve these contradictory findings.

Optimal L1 English

In this section, we explain how Scottish and Southern English listeners implement an optimal categorization—that is, how they perceive the diamond in Figure 5 appropriately. The knowledge underlying a Scottish listener's perception of the auditory event [74 ms, 349 Hz] can be represented as a ranking of constraints. One possible ranking with the desired results is shown in Tableau 1. The top-left cell shows the auditory event, which is the input to the perception grammar. The cells below it show the relevant candidates for the output of the perception grammar. For reasons of space the tableau only shows the four relevant constraints. The highest ranked of these could be “349 Hz is not

,” perhaps because of the large distance between 349 Hz and the mean F1 for

(see Table 1). When the auditory event [74 ms, 349 Hz] arrives, the tableau will select the candidate /i/ as the winner (i.e., as the actually perceived category) because this candidate violates the least high-ranked constraints.

Tableau 1. The perception of the auditory event [74 ms, 349 Hz] by a Scottish listener.

The knowledge underlying the perception of the same auditory event for the Southerner can be shown with a ranking like the one in Tableau 2. If her two F1 constraints are ranked in the reverse order from those of the Scot, as in this example, she will choose to perceive

.

Tableau 2. The perception of the same auditory event [74 ms, 349 Hz] by a Southern English listener.

Optimal L1 Spanish

For NSs of Spanish, the most important constraints are those for the spectral features. For the three front vowels, we have three continuous constraint families for F1. Examples of such constraints are “an F1 of 200 Hz should not be perceived as /i/” “an F1 of 1000 Hz should not be perceived as /i/,” “an F1 of 200 Hz should not be perceived as /e/,” and “an F1 of 200 Hz should not be perceived as /a/.” Analogously, there are three constraint families for duration.

The constraints must be ranked in a way appropriate for the perception of Spanish—that is, they should result in an F1 boundary of 430 Hz between /i/ and /e/ (Bradlow, 1996) and in an F1 boundary of 630 Hz between /e/ and /a/ (from our own preliminary measurement). Figure 6 shows a possible continuous ranking of the constraints against perceiving /i/, /e/, and /a/ as functions of F1 (modeled analogously to Boersma, 1998, chapter 8).

The adult Spanish F1-to-front-vowel perception grammar. The solid curve is the continuous ranking of “do not perceive an F1 of x as /i/.” The dotted curve is “do not perceive an F1 of x as /e/.” The dashed curve is “do not perceive an F1 of x as /a/.”

The perception of Spanish front vowels on the basis of F1 can be derived from Figure 6. For an input of 350 Hz, the figure shows that the highest ranked constraint is “do not perceive an F1 of 350 Hz as /a/.” The constraint “do not perceive an F1 of 350 Hz as /e/” is ranked almost as high. The constraint “do not perceive an F1 of 350 Hz as /i/” is ranked lowest. As a result, the listener, when having to choose from the three candidates /i/, /e/, and /a/, will decide that /i/ violates the lowest ranked constraint and is therefore the best perception. The figure similarly shows that all F1 values below 430 Hz (one of the intersection points in the figure) are best perceived as /i/, F1 values between 430 and 630 Hz are best perceived as /e/, and F1 values above 630 Hz are best perceived as /a/.

Given that Spanish vowels do not exhibit large duration differences, the duration constraints cannot be ranked too high. If they are ranked at “middle” in the ranking scale of Figure 6, they are hardly capable of contributing to the determination of the winning candidate.

The Learning Algorithm

We have shown that OT listeners can handle several examples of vowel categorization. However, the number of constraints for the perception of continuous auditory dimensions is rather large, and the number of their possible rankings is extremely large. Our account, therefore, would be unsatisfactory if we did not supply a theory of how listeners arrive at these constraints and especially at optimal rankings of these constraints. Our answer is that listeners create categories (e.g.,

) on the basis of distributional information (Boersma, Escudero, & Hayes, 2003), then use these categories to create phonological forms in their lexicon (e.g.,

) and construction constraints in their perception grammar (e.g., “74 ms is not

), and finally optimize their constraint rankings by applying the Gradual Learning Algorithm (GLA; Boersma, 1998; Boersma & Hayes, 2001) to their perception grammar, driven by recognition in the lexicon.

The GLA, a learning algorithm for stochastic OT, was preceded by Error-Driven Constraint Demotion (Tesar, 1995; Tesar & Smolensky, 1998, 2000), a learning algorithm for nonstochastic OT. That learning algorithm would not have worked for our findings, because it is not capable of handling variable mapping—that is, the token [80 ms, 400 Hz] can sometimes represent

, sometimes /i/, and Error-Driven Constraint Demotion fails to work if such tokens are presented to it in sequence.

For L1 acquisition, we begin our modeling at the point where the infant has the lexicon in place. For example, an infant Scottish listener may at some point inadvertently entertain a grammar that would have been appropriate for a Southern English listener instead. As a consequence, she will perceive a token with a somewhat raised higher mid vowel with cues [74 ms, 349 Hz] as

, as shown with the pointing finger in Tableau 3. However, her environment is Scottish, so this auditory event could well have been related to

rather than to

. If so, the infant's recognition system detects the error, perhaps by noting that the semantic context (a fluffy animal rather than a floating means of transportation) requires that she should have perceived

because that matches the phonological part of her lexical representation of the English word sheep. Now that the child knows that

would have been correct (as depicted with a check mark in Tableau 3), the child's GLA changes her perception grammar by raising the rankings of all the constraints violated in her incorrect winner and by lowering the rankings of all the constraints violated in the form that she now considers correct (as depicted by the arrows in Tableau 3). This increases the probability that she will perceive

the next time she hears an F1 of 349 Hz or a duration of 74 ms. The rankings are changed by only a small step along the continuous ranking scale of stochastic OT (e.g., one-thousandth of the high-low distance in Figure 6), but after a large number of perception errors involving auditory events containing either an F1 of 349 Hz or a duration of 74 ms, the rankings of the constraints will have become similar to those of the adult Scottish listener in Tableau 1.

Tableau 3. Error-driven learning by the GLA in an OT perception grammar.

L1 English and Spanish Simulations

We illustrate the development of L1 acquisition with the behavior of a virtual Scottish listener, a virtual Southern English listener, and a virtual Spanish listener, who grow up in virtual Scottish, Southern English, and Spanish environments, respectively. We show how their behavior comes to be based on the relative reliability of the two cues in their virtual production environments.

In our L1 English simulations, we start at the stage in which the baby has just created different lexical representations for

. At that stage, distributional learning would have led to the creation of construction constraints like “an F1 of 260 Hz is not

,” together with a reasonably good initial ranking of these constraints (Boersma, Escudero, & Hayes, 2003). Because category emergence is beyond the scope of the present article, we assume instead, rather artificially, a worst-case initial state in which both virtual babies start with all constraints ranked at the same height, so that they are equally likely to perceive any auditory event as

. The virtual listeners are subsequently fed with input-output pairs drawn randomly from Gaussian distributions for the appropriate production environment. We assume that the distributions are centered about the mean F1 and duration values in Table 1. For both vowels and both English varieties, we chose fixed standard deviations of 0.2 octaves for F1 and 0.4 doublings for duration, which are large enough to ensure that a wide range of duration-F1 pairs occurs (these same distributions show up in Figure 5). For computational reasons, the duration continuum was divided into 21 values evenly spaced between 50 and 120 ms along a logarithmic scale, and the F1 continuum was divided up into 21 values evenly spaced between 260 and 500 Hz along a logarithmic scale. The number of relevant constraints, therefore, was 84 (= 21 steps × 2 continua × 2 categories).

Each virtual listener received 1,000 data per virtual month and changed some constraint rankings every time there was a mismatch between her perceived category and the correct category recognized by her lexicon. The size of the evaluation noise (the amount of fuzzy ranking associated with Stochastic OT, which is temporarily added to the ranking of each constraint at evaluation time) was held constant at 2.0, and the plasticity (the amount by which constraints are moved down or up along the ranking scale after the detection of an error) decreased with age: It was 1.0 during the first 10 months, 0.1 during the next 90 months, and 0.01 during the remaining 900 months (therefore, learning is fast at the beginning and slower but more accurate later on). Figure 7 shows the perceptual performance of the virtual Scot and the virtual Southerner in five stages. As in Figures 2, 3, and 4, black areas stand for /i/ perceptions, white areas for

perceptions, and the black curve is the 50% category boundary line; as before, the gray areas stand for variable perceptions, which are possible in Stochastic OT as a result of the evaluation noise (Boersma, 1998; Boersma & Hayes, 2001). These pictures were computed by running each of the 21 × 21 = 484 possible auditory events through the perception grammar 1,000 times, keeping the evaluation noise at the same level as during learning. For instance, the token in the center of the square (77 ms, 361 Hz) is perceived by a simulated Southern English listener more often as

than as /i/ because the constraint against perceiving 77 ms as

and the constraint against perceiving 361 Hz as

are both ranked slightly below the constraint against perceiving 77 ms as /i/.

Perceptual development of virtual Scottish (top) and Southern (bottom) listeners. Horizontal axes: duration from 50 ms (left) to 120 ms (right). Vertical axes: F1 from 500 Hz (bottom) to 260 Hz (top). Black = /i/, white = .

In our L1 Spanish simulations, the task of the virtual child was to develop an /i/-/e/ distinction. We started with all F1 and duration constraints ranked at the same height, then applied 1,000 inputs per virtual month and used the same evaluation noise and plasticity regime as for the L1 English. As seen in Figure 8, the listeners come to rely on the F1 cue only, with the duration constraints staying ranked approximately at their initial height (the resulting rankings for the F1-to-vowel mapping are very similar to those in Figure 6).

Development of Spanish L1 perception. Black = /i/, white = /e/.

The locations and slopes of the boundaries in the final stages in Figure 7 compare well with the optimal ones in Figure 5. We conclude that we are able to model the knowledge behind an optimal strategy for vowel categorization, as well as the acquisition of this knowledge.⁵

L1-like Boundary Shifts

Spanish learners of Scottish English would have to move their category boundary, perhaps from 430 to 400 Hz, as in Figure 10 (left), which also shows that the centers of the two reused categories have shifted. The availability of this boundary shift is an instance of access to L1-like learning mechanisms.

Further L2 perceptual optimization in the two environments. To the left: a shifted boundary in Scotland. To the right: a new length distinction in Southern England, presumably leading to the fourfold bit-beat-bet-bait contrast.

For Spanish speakers in Scotland, a small mismatch occurs in perception. F1 values around 420 Hz may have been intended as

in most of the Scottish utterances but perceived as /i/ by Spanish beginners most of the time. In such a situation, the GLA changes the perception grammar, as in Tableau 6. The learner perceives

but notes that the semantic context requires that she should have perceived

because that is the phonological part of her lexical representation of the English word ship.

Tableau 6. Acquisition of vowel categorization by a Spanish listener in Scotland.

L1-like Category Creation

The learning task for Spanish speakers in Southern England is to “notice” that their single /i/ category represents two different phonemes in the L2. This “noticing” (a mechanism for it is described in the next paragraph) could in principle either lead to splitting the /i/ category into two new vowels

or to forming a new feature contrast, perhaps a length distinction—that is, a new /short/-/long/ contrast that does not occur in the learners' L1. It seems that the latter is what we have seen L2 learners of Southern English actually do: The group of duration reliers does not distinguish the spectral properties of

, which suggests that their representations for these vowels are /i, long/ and /i, short/, respectively. Figure 10 (right) shows the results of applying this strategy.

It remains to be explained why the listeners choose the new length distinction rather than split their /i/ category. Bohn (1995) claimed that it has to do with a universal availability of duration as a source of lexical distinctions, which is called on if the L1 has insufficient spectral distinctions. Bohn tacitly assumed that Spanish speakers have a single duration category, and any explanation for their behavior would have to address the question as to why learners split this single duration category rather than the single high front vowel category. For Bohn, then, the explanation is that there is something universally special about duration. We claim, however, that duration is not special: These learners start not with one duration category but with no duration category at all, and they use the attested L1 acquisition strategy of distributional learning (Maye, Werker, & Gerken, 2002) to detect two peaks in the duration distribution, which allow them to divide the duration continuum into two categories. Thus, creating a length contrast is a case of category formation, which is a typical L1-like acquisition strategy, whereas creating a spectral contrast is a case of category split, which has, to our knowledge, not been proposed as a common L1 learning strategy. Thus, the simple hypothesis of Full Access is compatible with the availability to L2 learners of category formation in general and the formation of a duration contrast in this particular case and at the same time compatible with a general unavailability of category split to L2 learners. We predict that learners who implement a new length distinction will be able to cope with five short and five long vowels, thus extending their mastery of English from five vowels to 10. Tentatively, we can say that the resulting assimilation pattern will be as in (1).

This kind of suprasegmental length contrast (attested in our Spanish learners of English for the high front vowels and possibly existing for the other four vowels as well) is not found in the learners' L1, which has no length distinction at all, nor in the L2, in which nearly all vowels (and certainly high front vowels) are distinguished by spectral differences as well. This L2-specific phenomenon seems to be a big challenge for a formal theory that relies on a gradual learning algorithm, because at first sight one would think that such a theory predicts a learning path that interpolates linearly between the L1 and the L2. However, our theory also crucially relies on the L2 learners' access to the L1-like mechanism of category formation: We propose that the L2 learner starts with a virgin duration continuum (i.e., zero categories rather than one, with no duration-to-category mappings yet) as all infants do, and that she creates two categories as soon as she establishes that the distribution is bimodal (analogously to the explicit L1 OT modeling by Boersma et al., 2003). At that point, the learner adds a binary length contrast to her grammar, by introducing “phonetic” construction constraints such as: “a duration of 50 ms should not be perceived as /short/,” “a duration of 200 ms should not be perceived as /short/,” “a duration of 50 ms should not be perceived as /long/,” and “a duration of 200 ms should not be perceived as /long/.” Distributional learning not only introduces these constraints but also an initial ranking for them, so that the learner starts with a reasonable proficiency in mapping auditory duration to phonological length (as discussed at the end of this section, the learner introduces some more constraints later). After the creation of the /short/-/long/ contrast, the learners can start using the two length categories in their lexical representations. They represent Southern English

as /i, short/ and Southern English /i/ as /i, long/. Once the learners have a correct lexicalization of length, the appropriate mapping from continuous duration to the binary length contrast is achieved by the GLA. Tableau 7 shows what happens if an intended Southern English

“sheep,” which has the representation

for the learner, is pronounced appropriately with a duration of 104.6 ms, but the learner has a nonoptimal constraint ranking that leads her to perceive the vowel as /short/ rather than /long/. She perceives

and notices a mistake because the word that she should have recognized is

“sheep.” She takes action and reranks some constraints with the GLA, thus making it more likely that she will perceive 104.6 ms as /long/ on the next occasion.

Tableau 7. Acquisition of the categorization of length by a Spanish listener in Southern England.

L2 Simulations

We simulated developmental sequences of typical Spanish learners of English who have gone to two different English-speaking countries at an age of 200 months. The first listener lives in Scotland. She equates Scottish

with her Spanish /e/, and Scottish /i/ with her Spanish /i/ (Figure 9, left). We assumed that she already has correct lexical representations for ship and sheep. Every virtual month we fed this virtual L2 Scot with 1,000 vowels, drawn from the same Gaussian distribution used for the virtual L1 Scot. We continued this procedure for 800 virtual months, keeping the evaluation noise constant at 2.0 and the plasticity constant at the low (adult) value of 0.01. Figure 11 shows how the L2 Scot shifts her boundary from 430 to 400 Hz and then tilts it, thus becoming as proficient as the L1 Scot in Figure 7.

We did not discuss the representations for the Spanish learners of Scottish English in detail because the

contrast does not tell us much about the entire Scottish vowel length system (e.g., that presented in McClure, 1977), unlike in the Southern English case. If these learners have no constraints for mapping duration to vowel quality, they will only shift the boundary line and not tilt it toward a 10% duration reliance. The data of the real learners in Table 2 does not allow us to decide whether they use duration to this small extent or not at all.

The boundary shift of the simulated Spaniard in Scotland. Black = /i/, white = /e/ (= ).

The second listener lives in Southern England. She equates both Southern English

with her Spanish /i/ (Figure 9, right). Figure 12 shows how the L2 Southerner starts out at chance level (like the infants of Figures 7 and 8; i.e., we assumed correct lexical representations for ship and sheep but a very poor categorization) then learns how to map duration to the new length contrast, improving toward the performance of the simulated Southerner in Figure 7 although she continues to ignore the F1 cue.

The phonemic separation of the simulated Spaniard in Southern England. Black = /i, long/, white = /i, short/.

Comparison of Simulated and Real L2 Listeners and Comparison with L1 Learners

The simulated Spaniard in Scotland comes to rely primarily on F1, like most of the real Scottish-oriented L2 learners (e.g., subjects LG and MF in Figure 4 and Table 2). The simulated listener also shows a tiny boundary shift. We cannot detect such a shift between beginning and more advanced real L2 listeners (Figure 4), probably because the L1 Scottish boundary (Figure 2) is very close to the Spanish boundary to start with. This does not imply that developmental boundary shifts do not occur in L2 perception in general (because, in fact, they do occur, as described in the Discussion section). The simulated Spaniard in Southern England comes to rely on duration only, like most of the real Southern English–oriented L2 learners (e.g., subjects EF and OF in Figure 4 and Table 2). This is in stark contrast with the simulated and real native Southerners, who rely on both the spectral and the duration cues; this difference is due to the L2 learners' strategy of creating a length contrast, which leads to a problematic representation of the vowel contrast—namely, as /i, short/ versus /i, long/ rather than as the separate symbols

versus /i/ that would allow genuine cue integration. We conclude that our simulations reveal a formal explanation of the attested L2-specific behavior.

Later Developments

The L1 distributional learning model of Boersma et al. (2003) predicted that learners will initially use a single auditory cue for each phonological contrast in their language. In the case of our simulations for the Southern English–oriented L2 learners (Figure 12), the single cue for phonological length is duration; this is formally expressed as our exclusive use of “phonetic” constructions constraints such as “a duration of 110 ms is not /short/.” However, the same distributional learning model also predicts that learners will later on introduce less-phonetic construction constraints—in our case, constraints that relate the phonological length feature to the auditory continuum of F1, such as “an F1 of 300 Hz is not /short/.” As soon as such constraints become available, the categories /short/ and /long/ have become as abstract as the categories

, and learners can start to integrate spectral and duration cues for the length contrast. Indeed, at least two learners in Figure 4 seem to have reached such a stage. A computer simulation of such a scenario, however, would involve all 13 English vowels and all interlanguage vowels, given that all 5 × 2 interlanguage vowels contain one of the feature values /short/ or /long/. We can predict that, because all English high vowels are long, constraints for low F1 values, such as “an F1 of 260 Hz is not /short/,” will become high ranked and contribute to a good perception of the

contrast for highly advanced learners.