Paola Escudero, firstname.lastname@example.org|
Paul Boersma, email@example.com
|May 31, 2001, 20.00 GMT|
Note: This web page contains all the material from Paul & Paola's
but is in some respects preliminary.
Please do not cite. You can cite the available papers instead.
Our hypothesis, then, is that optimal cue reliance depends on cue reliability.
Boersma's (1998) three-grammar model of phonological acquisition, which implements a separate perception grammar within an Optimality-Theoretic framework, predicts exactly this hypothesised relation when a general Gradual Learning Algorithm (Boersma & Hayes 2001) is applied to the perception grammar (Boersma 1997). This grammar consists of a large number of constraints such as "an F1 of 350 Hz is not an /I/" and "a duration of 80 ms is not an /i/", for every value of F1 and duration, and for both vowels. Thus, if both the spectral and durational continua are divided into 100 discrete regions, the grammar contains 400 constraints.
We let this algorithm simulate the behaviour of two virtual babies, little Elspeth and little Liz, who are brought up in Scotland and Southern England, respectively. We will show how both of these listeners start with the same perception grammar, in which the constraints are ranked at the same level. The learners then repeatedly "hear" words with /I/ and /i/, appropriately distributed with respect to height and length according to their language environment. Every time little Elspeth or little Liz miscomprehends a word, she reranks some constraints in her perception grammar. Gradually, Elspeth comes to rely almost exclusively on height, whereas Liz comes to rely on both duration and height, thus achieving adult-like minimisation of perceptual confusion.
We also let the algorithm simulate the behaviour of two adult Spanish speakers, Isabel and Carmen, who move to Scotland and Southern England, respectively. We will show how these simulated listeners start with a copy of their Spanish perception grammar, in which the height and length reliances are zero since Spanish has no [I]-[i]-like height contrast and no length contrast (S0). With time, Isabel comes to rely on height almost exclusively (S3), whereas Carmen comes to rely on both length and height (S1, S2). The results show that a listener with an established perception grammar will also rerank the constraints and can ultimately attain native-like perception.
Finally, we let the algorithm simulate the behaviour of a virtual Spanish speaker who goes to live in Southern England and later moves to Scotland. In the South, she gradually comes to rely on both length and height (S1, S2) and achieves native-like comprehension. This comprehension deteriorates when she is subsequently exposed to Scottish English. With time, however, she comes to rely almost exclusively on height (S3) and returns to proficient comprehension.
Consequently, the formal three-grammar model of Functional Phonology,
together with the Gradual Learning Algorithm,
accounts for the acquisition of an effective perception of sound contrasts.
including the four attested,
possibly sequential, patterns or stages in the weighting of acoustic cues
in L2 phonological acquisition.
[i] [i:] [I] [I:]The stimuli in the bottom left and top right corners are the prototypes for /I/ and /i:/, respectively. The stimuli in the top left and bottom right corners have crossed acoustic cues. If in a forced-choice experiment [i] is perceived as /i:/, and [I:] as /I/, then we say that the spectral (height) cue is primary; if [i] is perceived as /I/, and [I:] as /i:/, then the duration (length) cue is primary. Note that we cannot determine in this way whether the other cue is secondary or whether it is not used at all (that has to be decided by a single-cue experiment, probably with neutralisation of all the other cues).
This method is suitable in many cases, especially if the synthesis method is restricted
to cutting and pasting.
For the place contrast in English initial plosives,
Schatz (1954) crossed the burst parts and the CV transitions,
and found that xx xx xx.
For the place contrast in English initial fricatives,
Harris (1958) crossed the noise parts and the CV transitions,
and found that the noise was the primary cue except
in the /f/-// comparison,
in which the CV transition was primary.
For the voicing contrast in English final fricatives,
Denes (1955) found that vowel duration outweighed fricative voicing,
i.e. [ju::s] and [ju:z] were recognized as /ju:z/ 'use-V' and /ju:s/ 'use-N', respectively,
if a third cue (consonant duration) was neutralised.
For the voicing contrast in English final plosives,
Eilers, Oller, Urbano & Moroff (1989) found that
the combined cues of vowel duration and periodicity burst (?)
led to better discrimination than either cue alone.
[i] . . . . . [i:] [I] . . . . . [I:]If the durational cue is primary, we will find a category boundary along the top edge and a category boundary along the bottom edge. The category boundary is defined as the point at which the fraction of /i:/ responses reached the 50 percent point. If the spectral cue is secondary but effective, the boundary points will be at different locations along the two edges:
[i] . | . . . [i:] [I] . . .|. . [I:]In this example, the category boundary along the bottom is at 4/7 = 57% (of the duration range), i.e. 4 of the 7 points lie to the left, 3 to the right of this boundary. Along the top, it is 2.5/7 = 29% (of the duration range). The difference (28% of the duration range) can be seen as the reliance on the secondary (spectral) cue, relative to the reliance on the primary (durational) cue, which we can assume is 100% (of the spectral range!). If we measure each of the 14 points 10 times (i.e. 140 stimuli per listener), a listener with a perfectly steep boundary will produce the following numbers of /i:/ responses:
0 0 5 10 10 10 10 0 0 0 0 10 10 10Another way, now, to compute the spectral reliance is to subtract the average /i:/ response probability for the bottom edge (30/70) from that for the top edge (45/70), i.e. (45-30)/70 = 28% (of the duration range). Redundantly, the durational reliance is computed by subtracting the average /i:/ response probability at the left ((0+0)/20) from that at the right ((10+20)/20), again giving 100% (of the spectral range). If the boundary is not perfect, we can still use this method:
4 6 6 7 9 10 10 1 0 0 6 9 10 9Rather than trying to find the boundary points by some fancy interpolation, we can directly compute the reliances from all the values along the top and bottom edges. The spectral reliance is ((4+6+6+7+9+10+10) - (1+0+0+6+9+10+9)) / 70 = 24% (of the duration range), and the durational reliance is (10+9-4-1)/20 = 70% (of the spectral range). The cue reliance ratio is then 70% / 24% = 2.9. This number depends on the sizes of the spectral and duration ranges. We could make it independent of that by multiplying numerator and denominator by the ranges, e.g. (70% * 140 Hz) / (24% * 90 ms) = 4.5 Hz / ms, which is a linear estimate of the slope of the category boundary.
The two-continuum method requires that the continously variable cue is the primary cue.
For the voicing contrast in New York English final plosives and fricatives, Raphael (1972) found with synthetic stimuli that the duration of the preceding vowel (which he varied continuously) was a stronger cue than all of the remaining cues (for plosives: formant cutback; for fricatives: formant cutback, friction duration, and voice bar) together [methodological problems: R. draws conclusions about plosives versus fricatives without controlling for the preceding vowel. Second, he mentions the //-// contrast as an exception, not realising that his minimal pair "cash"-"casual" has a phonemic tense-lax split for his New York listeners]. For plosives, the boundary was 42 ms longer for voiceless cues than for voiced cues. For fricatives, the difference was 34 ms. If the duration continuum runs from 150 to 350 ms in 10-ms steps (a range of 210 ms!), this means a reliance of 38/210 = 18% on the remaining cues, leading to a cue weighting of 85% for vowel duration, 15% for the remaining cues together. Some raw data (number of /p/ responses out of a total of 25 for each stimulus, duration going from 150 to 350 ms in 10-ms steps) were:
24 24 23 24 24 23 22 24 24 19 20 20 17 14 5 4 0 2 2 1 1 23 23 24 25 22 21 21 19 19 6 6 3 3 2 2 0 2 1 1 0 0From these data, we compute a duration reliance of (24+23-1-0)/25/2 = 92% and a formant cutback reliance of (1+1-1-1+2+2+1+5+5+13+14+17+14+12+3+4-2+1+1+1+1)/25/21 = 18%, giving weightings of 84% and 16%, respectively.
Hogan & Rozsypal (1980) used natural stimuli for the voicing contrast in Canadian (Alberta?) English, digitally shortening and lengthening the vowels. The duration cue for voicedness was overridden by the other cues for voicelessness in 21 of the 24 continua, and the duration cue for voicelessness was overridden by the other cues for voicedness in 15 of the 24 continua. The two-continuum method seems inappropriate for this result, though they present a factor analysis that suggests that voice bar duration is the primary cue for plosives.
Wardrip-Fruin (1982) also found that the duration cue was minor
(for speakers//listeners whose "speech was judged by two linguists//a linguist to be
without pronounced regional characteristics"). However,
she decided not to include the release burst in her stimuli, so that
the voiceless stimuli ended in silences, thus effectively removing the
consonant duration cue, and with it the consonant/vowel relative duration cue,
thus artificially diminishing the reliability of the vowel duration cue.
[i] . . . . . [i:] . . . . . . . . . . [I] . . . . . [I:]In a forced-choice experiment, there will be a category boundary that divides the rectangle into two parts. The reliance on the spectral cue can again be measured as the average probability of perceiving /i:/ along the top, minus the average probability of perceiving /i:/ along the bottom. Likewise, duration reliance is the average probability of perceiving /i:/ along the right edge, minus the average probability of perceiving /i:/ along the left edge.
The advantage of the four-continnum method is that it works even if the listeners have different primary cues.
This method has been used by Escudero (2000), who found that Scottish listeners rely for 90 percent on the spectral cue when identifying /I/ and /i:/.
The situation changes if we want to compare cue weighting strategies across languages. First suppose that we use language-particular rectangles. For instance, Scottish English /I/ and /i:/ are far apart spectrally, but do not differ much in duration in some positions; by contrast, Southern English /I/ is higher, while /i:/ is lower than in Scottish English, and /i:/ is longer than in Scottish English. In an approximated IPA transcription, the rectangles would be:
[j] . . . [j.] . . [i] . . . . . [i:] . . . . . . . . . . . . . . [I] . . . . . [I:] [e] . . . [e.] Scottish English Southern EnglishOne of our objectives is to show that perception depends on language and dialect. The null hypothesis that we try to reject, then, is that all listeners act in the same way, e.g., that all of them have equal category locations and cue weightings. Any listener will have a higher spectral reliance and a lower duration reliance when tested on the Scottish English rectangle than when tested on the Southern English rectangle. Thus, if we test Scottish English listeners on the Scottish English rectangle, and Southern English listeners on the Southern English rectangle, and we find that Scottish English listeners have a higher spectral reliance and a lower duration reliance than Southern English listeners, we have no proof of a difference in perception.
In order to prove that the cue weighting strategies of the groups are different, we have to test the groups with identical rectangles. This is what Escudero (2000) did for Spanish learners of English in Scotland: she tested them on the same rectangle that she had used for the native Scottish listeners. Unlike the Scots, many Spanish listeners of English turned out to rely mainly on duration. This proves that perception is language-dependent, not only with respect to the categories, but also with respect to the weighting of acoustic cues.
In an experiment that compares dialects, the rectangle that we should use is probably the union of the rectangles of the separate dialects. Thus, we need the following rectangle when comparing listeners of Scottish English and Southern English:
[j] . . . . . [j:] . . . . . . . . . . [e] . . . . . [e:]This is the rectangle that was used by Escudero (2000, reported below) for the Scottish and Spanish listeners: the heights were typical of Scottish, the lengths varied by more than a factor of two, which is more typical of Southern English. The use of the same rectangle for Southern English listeners (Escudero to appear b, also reported below) showed that they rely on durational and spectral cues equally.
[j] . . . . . [j:] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [e] . . . . . [e:]Instead of 24 points, we now measure 49 points, and are confident of finding an /I/-/i:/ boundary somewhere for every listener.
Finally, the computation of cue weighting now suddenly depends on the sizes of the edges of
the rectangle. It could be possible to normalise it, e.g. base it on a "square",
i.e. a rectangle with sides that represent a factor of two in duration and F1,
or with sides that are six just-noticeable difference long.
Non-native cue weighting by second-language learners has been observed in the following cases.
Flege, Bohn & Jang (1997)...
Escudero (2000, to appear a)...
Wardrip-Fruin & Peach (1984) showed that for the voicing distinction in English final plosives, 3-year-olds relied mainly on xx duration, 6-year-olds mainly on the spectral cue (first formant), and adults relied on both equally.
Nittrouer, Manning & Meyer (1993)...
Escudero's forthcoming longitudinal study?
Boersma & Escudero's forthcoming simulation?
For the voicing contrast in English final plosives and fricatives, Raphael (1972:1302) ascribes the low reliance on closure voicing to the unreliable absence of vocal pulsing in voiceless obstruents (Lisker, Abramson, Cooper & Schvey 1969: in not much more than 80% of the cases), and the low reliance on the plosive burst strength to its unreliable presence in American English (Rositzke 1943). The high reliance on vowel duration can be ascribed to the high reproducibility of that cue: the duration is 1.5 times larger before voiced than before voiceless consonants (Peterson & Lehiste 1960); However, Hogan & Rozsypal (1980) found that this factor was larger for "lax" (intrinsically short) vowels than for "tense" (intrinsically long) vowels, although the reliance was higher for the tense vowels.
For this reason, Wardrip-Fruin (1982:187) states that "it seems that the very well-established regularity of vowel duration differences in production may have effected an unwarranted confidence in their value for perceptual judgments".
Jusczyk (1997:215): "Information about the properties of sounds to which infants are exposed and their distribution in the input are likely to be critical factors in shaping the weighting scheme."
Jean Aitchison (1996:33) on flower perception by bees:
"The order of importance -- odour, then colour, then shape -- is probably
based on cue reliability."
[i] . . . . . [i:] . . . . . . . . . . . . . . . . . . . . . . . [I] . . . . . [I:]The six vertical steps were equal on the mel scale, ranging from 480 to 344 Hz for F1 and from 1893 to 2320 Hz for F2. The frequency in mels was computed as (1000/log 2) log (f/1000 + 1), and the inverse (mels to Hertz) was 1000 (10mels/(1000/log 2) - 1). The seven durations ranged from 83 ms to 176 ms in six equal fractional steps of 1.1335. Here are the sounds:
The PsyScope script is listeners/experiment/script.psyscope.
The experiment was a forced identification test. The subjects had to decide whether the vowel sound they heard was represented in the picture of a 'ship' or the picture of a 'sheep' by pressing one of the two buttons that had these pictures stuck onto them (or, if there is no button box, the space bar or the zero on the numeric keypad). They also had verbal and written instructions and were told to guess if not sure. They were told to take as much time as they thought convenient to make a decision and they knew that they would not have the next trial if they did not make a decision.
Before the identification test, all subjects were asked for the names
of the objects on the pictures ('sheep' and 'ship'), in order to to find out
whether they made a difference between the two objects or not.
The experimenter never produced the words for neither of the pictures nor did she tell
them that the words were different. For the L1 group, some of the subjects were not sure of
what the object in the red picture was. They thought it was a 'boat' or a 'yacht', and the
experimenter explained that it was something else until they produced the expected word ('ship').
All L1 subjects and 90% of the L2 subjects produced distinctive words for the two pictures.
The majority of the L2 subjects appeared to produce 'sheep' with a long [i] and 'ship'
with a short one. Likewise, the majority of these subjects, after producing the sounds,
referred to the difference as being one of length ('the long and the short', they said).
Of course, they could have thought that the vowels only differ in terms of length
but still perceived and produced a quality difference.
None of the L1 subjects made a similar judgement.
"Matrix" "cm" 1 7 7 1 1 1 7 7 1 1 1 0 1 1 4 2 4 0 0 0 2 0 0 6 0 0 0 2 0 0 6 6 4 7 6 7 9 7 9 0 0 9 9 0 9 10 0 0 10 0 10 10 9 10 10 10 10 10 10This depicts the following number of 'sheep' scores in the stimulus continuum:
9 10 10 10 10 10 10 10 . . 10 . 10 10 9 . . 9 9 . 9 6 4 7 6 7 9 7 0 . 0 2 . . 6 0 0 . 2 . . 6 1 0 1 1 4 2 4Thus, 10 of the 10 /i:/ tokens (upper right corner) were identified as 'sheep', while 9 of the 10 /I/ tokens (bottom left) were identified as 'ship'.
The Southern English listeners rely on both cues. The average F1 reliance is 65.2%, the average duration reliance 34.6%.
The Spanish listeners can be divided into five groups:
From the fact that Spanish learners of English tend to spirantise postvocalic voiced stops, Eckman concludes that their IL has a morphophonemic rule of Postvocalic Spirantisation, neutralising the /d/-// contrast. The NL, he argues, does not have this morphophonemic rule, since postvocalic spirantisation is an allophonic rule in Spanish. Since English obviously does not have Postvocalic Spirantisation either, the IL has a rule that it does not share with NL and TL. Hence, no full transfer.
It is clear that this conclusion is based on the structuralist distinction between morphophonemic and allophonic rules. Rule-based generative phonology (SPE: Chomsky & Halle 1968) does not have this distinction, so it would have to conclude that a rule of Postvocalic Spirantisation is transferred into the IL.
Then Eckman's second example. From the fact that Spanish learners of English tend to devoice final obstruents, Eckman argues that their IL has a rule of final devoicing that does not occur in either their NL or the TL. For a rule of final devoicing to exist in a grammar, the language has to have an obstruent voice contrast that is actively neutralised in final position. For instance, the German medial voice contrast in /ta:g/ 'days' versus /dk/ 'decks' is neutralised in /ta:k/ 'day' and /dk/ 'deck'. Eckman states that in order for there to be a rule, there should be alternation and neutralisation. In Spanish, however, there is no alternation, so Spanish does not have a final devoicing rule [how shall we account for ciudad?]. Since English obviously has no final devoicing either, we must conclude that only the IL has this rule. Hence, no full transfer.
But this conclusion is based on a theory of ordered rules. This is like Smith's (1973) account of a child who pronounces underlying |s| as : Smith describes this with a rule /s/ -> //, i.e., the child has a more complicated grammar than the adult. Constraint-based generative phonology (Optimality-Theory: Prince & Smolensky 1993), however, describes surface generalisations as high-ranked markedness constraints. Any language that does not allow final voiced obstruents has a ranking of *FINALVOICEDOBSTRUENT >> IDENT(voice) (the latter constraint means "any underlying voicing specification is realised in the output"). This ranking has not changed from the child's initial state, in which all markedness constraints outrank all faithfulness constraints (Smolensky 1996). The point is that the lexicon need not contain voiced final obstruents: the maxim of Richness of the Base (Prince & Smolensky 1993:191, Smolensky 1996) ensures that any underlying final voiced obstruents (even if they do not exist in the language) are devoiced. Thus, an OT account would state that the ranking *FINALVOICEDOBSTRUENT >> IDENT(voice) is transferred into the IL.
Then Eckman's third example. From the fact that Mandarin speakers of English tend to append a schwa after final voiced obstruents (tag, rob, is), Eckman argues that their IL has an optional rule of Schwa Paragoge. No such rule is needed for Mandarin, which has no underlying final obstruents, nor, obviously, for English. A generative OT account, with initial high-ranked *FINALOBSTRUENT, would predict either dropping of the final obstruent or schwa paragoge, depending on the ranking of the faithfulness constraints MAX(obs) ("any underlying obstruent is realised in the output") and DEP(schwa) ("do not insert a non-underlying schwa"). But according to the initial state hypothesis by Smolensky (1996) and the learning algorithm by Tesar & Smolensky (1998), all undominated faithfulness constraints should end up in the second stratum of the grammar, i.e. be ranked equally high, presumably with free L2 variation as a result. The choice for MAX(obs) >> DEP(schwa) in this IL, therefore, corresponds to nothing in the NL. Hence, no full transfer.
But this conclusion is based on an initial ranking of all markedness constraints above all faithfulness constraints, and on an ordinal learning algorithm. In Functional Phonology (Boersma 1998), however, articulatory constraints are ranked by articulatory effort, and faithfulness constraints are ranked by perceptual confusion. While the initial state can be regarded as a high ranking of articulatory constraints, analogously to the (seriously flawed...) markedness constraints of generative OT, the faithfulness constraints are still ranked by whether it is worse to delete an underlying obstruent or to insert a non-underlying schwa. The answer depends on the difference in amount of perceptual confusion that these deletions and insertions would cause, and this can be learned if the NL language environment is not perfect, as it never is, provided that we understand that a gradual learning algorithm is needed; it can also be learned rather swiftly during L2 contact, if, given the high ranking of *FINALOBSTRUENT, speakers notice more confusions when deleting the obstruent than when appending a schwa, which seems plausible.
(consult Silverman 1992 and Broselow et al. 1998; also Steriade 2000 and others, who state that this vowel epenthesis can never happen)
A paper that explicitly states that hidden rankings are transferred from L1 to L2 is Smolensky, Davidson & Jusczyk (2000).
We see that the four theories of phonology have different opinions on whether a certain phenomenon is transferred or not. The following table summarises the results, with plus signs where the theory in question proposes transfer:
Structuralist Rule-based Constraint-based Functional generative generative Postvoc. spir. - + + + Final Devoicing - - + + Schwa Paragoge - - - +Apparently, Functional Phonology is the only of the four theories that can regard all three rules as being transferred into the interlanguage. Thereby, it is the only of the four theories that can account for the behaviour of these L2 speakers without invoking extralinguistic explanations like those that Eckman provides. Eckman antipicated OT by invoking a "surface phonetic constraint" against final obstruents, the "maintenance of a canonical form of the intended TL word" (faithfulness), and "conflict resolution". He also anticipated functionalist OT with his "markedness differential hypothesis", which prohibits voicing more in final than in other positions.
Since the theory of Functional Phonology turns out to be able to formalise
many factors that used to be considered extralinguistic,
we will hypothesise that the L2 learner's initial IL perception grammar
is an identical copy of her NL perception grammar.
Until the facts prove us wrong!
Chapter 15 of Boersma (1998) contained a simulation of a one-dimensional continuum (simulation/categ1_learning.praat.txt). The basic idea is that for e.g. vowel height, the perceived category is determined on the basis of the ranking of constraints against mapping F1 values to each category, such as "350 Hz is not /i/", "350 Hz is not /e/", "350 Hz is not /a/", "370 Hz is not /i/", "370 Hz is not /e/", "370 Hz is not /a/", and so on for all F1 values and all categories.
There are two ways to extend the 1-dimensional model. The first is a high-level integration of cues. For the /I/-/i:/ contrast, this would mean that the listener first classifies F1 and duration into discrete height and length categories, then decides which is more important if the two are in conflict. The first step (cue categorization) would, for instance, map a certain first formant f to [+high] with the probability P (+high | F1=f), and a certain duration d to [+long] with the probability P (+long | duration=d). The second step (integration of binary cue values) would then be handled by constraints like "[+high] is not /I/", "[-high] is not /i:/", "[+long] is not /I/", and "[-long] is not /i:/". Suppose that these conflict, i.e. the cues have been constructed as [+high] and [-long], so that the result has to be determined by the relative ranking of the two constraints "[+high] is not /I/" and "[-long] is not /i:/". Saying that duration is the primary cue, is the same as saying that "[-long] is not /i:/" is ranked above "[+high] is not /I/". If the ranking difference is not large, then "[+high] is not /I/" may still outrank "[-long] is not /i:/" in a minority of cases, say 20% of the perceptions. The probability of an /i:/ response is then P (/i:/ | F1=f, duration=d) = 20% x P (+high | F1=f) + 80% x P (+long | duration=d). This causes the identification curve for the top row (the [i]-[i:] continuum) to lie exactly 20% above the identification curve for the bottom row (the [I]-[I:] continuum):
100% /i:/ * * * * * [i:] | * * | * o o o o o [I:] | * o o | * o | * o | * * o | [i] * * * * * o | o o 0% /i:/ [I] o o o o o duration ->Thus, the difference between the two curves is always 20%, giving a spectral reliance of 20%. However, the actual curves do not look like this. The /b/-/p/ curves discussed in section 2.1.2 do not seem to be vertically, but horizontally shifted:
100% /b/ * * * * * o o o o o | * * o o | * o | * o | * o | without F1 cutback * o with F1 cutback | * o | * o | * o | * * o o 0% /b/ * * * * * o o o o o vowel duration ->This suggests low-level cue integration. It corresponds to a straight boundary in the two-dimensional continuum, as if the criterium for deciding between /I/ and /i:/ is a function of a linear combination of F1 and duration values. In other words, the probability of an /i:/ response is P (/i:/ | F1=f, duration=d) = P (/i:/ | 20% x F1 + 80% x duration = x).
For our simulations, we simply use separate constraint families for the height and length
continua, i.e. constraints like "350 Hz is not /i:/" and "80 ms is not /I/",
for many values of F1 and duration.
The subject would sit at a table with a microphone, and the
carrier phrase was stuck to this table. The words were written on 500 cards
by the Praat script speakers/draw_cards.praat.
The experimenter was sitting beside the subject with a copy of the word list (speakers/stimuli.doc), on which s/he could mark any hesitations. If the subject hesitated at any words, these words were recorded again after the experiment.
Each subject was recorded on DAT tape.
After these preparations, both Paul and Paola take the TextGrid file and move the boundaries in such a way that they confine the vowel /I/ or /i:/ (select TextGrid plus LongSound, then choose Edit). Procedure:
The resulting (geometric) average duration/F1/F2 values were for the Scottish English speaker (in ms/Hz/Hz):
The standard deviations are expressed in duration doublings and octaves. For the Southern English speaker, the table is:
In all cases, the number of replications was N=50, except in the case of Scottish "feeling" and Southern "sheep", where N=49.
The following picture shows the averages of the Scottish English words (script speakers/drawScottish.praat); dark ellipses are /i/, light ellipses are /I/:
And here are the averages of the Southern English words (script speakers/drawSouthern.praat):
As far as the Scottish speaker is concerned, his height distinction (5 to 11 standard deviations) is much more reliable than his length distinction (0 to 2.5 standard deviations), whereas the Southern speaker's height distinction (0.5 to 3 standard deviations) is much less reliable than his length distinction (4 to 7 standard deviations).
Conversely, we see that the Scottish speaker uses duration for, in order of importance:
From both viewpoints, we can see that duration is a minor cue to the vowel category in Scottish English production. The regional variation in production thus correlates with the regional variation in perception.
Here are the averages:
The mean values in this table are geometrically averaged across consonantal context (i.e.
whether the following consonant is voiced or voiceless) and across number
of syllables (1 or 2). The total standard deviations in this table include the within-context variation
and the between-context variation.
This picture paints F1-duration pairs that are mainly perceived as /i/ in black,
and those that are mainly perceived as /I/ in white. The entire picture is grey, though,
meaning that every F1-duration pair is perceived as /i/ approximately 50 percent
of the time. The black contours depict the 50% category boundaries.
We see that the baby's reliance on both spectrum and duration is below one percent (as measured with
Rather simplifyingly, we will use these averaged values as the vowel prototypes for Elspeth and Liz.
With the script simulation/createEnvironment.praat, we created the Scottish English input-output distribution simulation/scot.PairDistribution and the Southern English input-output distribution simulation/seng.PairDistribution, representing the probability of occurrence of each of the 441 F1-duration values for /i/ and /I/ in the environment of the learner. The distributions were centred about the above mean F1 and duration values for the Scottish and Southern English speakers, and had standard deviations of 0.20 octaves and 0.40 duration doublings, as in the table. These standard deviations are different from those derived from the production experiment, since we can expect our listeners to partly normalize away the variation due to the consonant environment and the number of syllables (which would decrease the standard deviations), but there is also variation not taken into account in the production experiment (speaking rate, stress, vocal tract size). These standard deviations are the main unknown factor in our simulation, and influence the resulting cue reliances rather heavily.
The distributions can be drawn with the script
The learning regimes (falling plasticity) are described on page 10 of Escudero & Boersma (2001).
After 1, 2, 4, 10, 100, and 1000 months we measured the resulting grammars, again with the script simulation/measureListener.praat. For Elspeth, the perceptual development is seen in the following matrices:
For Liz, the perceptual development is seen in the following matrices and pictures:
|Isabel||age||environment||plasticity||data per month|
|0-10 months||Peruvian Spanish||1||1000|
|10-100 months||Peruvian Spanish||0.1||1000|
|100-200 months||Peruvian Spanish||0.01||1000|
|200-300 months||Scottish English||0.01||1000|
|300-400 months||Southern English||0.01||1000|
The Spanish environment was:
After 10, 100, and 200 months, Isabel had the following perceptual fields:
Isabel has become a fluent listener of Spanish. She then goes to Edinburgh and copies her L1 grammar (all the constraints and their rankings) to the grammar of her interlanguage (full transfer). She will identify Scottish English /i/ with her existing /i/, and Southern English /I/ with her existing /e/ (two-category assimilation). After 100 months, she is a fluent listener of Scottish English:
Isabel then moves to London and in 10 years changes the weighting of the two cues:
She has become a native-like listener of Southern English.
Real Spanish learners of English often act differently: Spanish learners of Scottish English
tend to rely on spectrum only, and Spanish learners of Southern English tend to rely on duration only.
Apparently, these learners have a different constraint set, with thing like
"350 is not /high/", "350 is not /mid/", "80 ms is not /short/", "80 ms is not /long/",
i.e. they do not integrate the cues to segments but they classify each continuum separately.
This suggests that native speakers of English have separate /I/ and /i/ symbols,
whereas Spanish learners of English have /mid,front/ and /high,front/ (in Scotland)
or /high,short/ and /high,long/ (in Southern England).
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