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# Mean nuclei in F1-F2 space

Here we examine the locations of means of the measurements of F1 and F2 for each phonological vowel class. A particular mean location can be expressed with much greater precision than is justified given the data it is based on. Thus a mean might be calculated to four significant digits, while the standard error of the sample it was taken from has a spread of two significant digits, so that the actual precision of the estimate of the mean is much weaker than the 4-digit calculation would imply. For this reason the by-now-familiar bootstrap technique discussed in the Methods chapter is employed to show how much error is inherent in estimates of F1, F2 means. For a given vowel, a new sample of data is constructed by randomly selecting with uniform probability, n elements from the actual sample of n measurements, with replacement. The mean of this new sample is calculated. This procedure is repeated by a computer hundreds of times, and these re-estimated means are plotted. The re-estimated means are themselves in a bivariate normal distribution, which is a near-optimal estimate of the sampling distribution of the original sample mean. Thus the distribution of re-estimated means itself shows the area in which the true mean of the class is likely to fall, given the set of actual measurements. The chart in Figure  displays 200 re-estimated means per vowel class.

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The information presented in a chart like Figure  is extremely rich and informative, but requires considerable explication to see the patterns. The phonetic grammar of Jamaican Creole vowels (page ) is an excellent example of how the locations of vowel nuclei on this kind of chart can be predicted from quite general principles, applied in a partly language-particular way. Such perfection in a phonetic grammar may be difficult to attain in every analysis, but the goal at each point is the same: to see what the rules are that govern the relationships between the phonological structure and the phonetic forms.

Several general rules can be proposed to explain the relations among the distributions. The fundamental assumption in interpreting these data are that vowels with the same nuclei and different glides (or no glide) are underlyingly identical, and thus that the phonetic differences between corresponding nuclei must be accounted for by phonetic implementation rules, preferably general rules that apply to natural classes. The following section discusses the phonetic realizations of each of the vowel classes shown in Figure , while arguing for the phonetic implementation rules presented in Figure .

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The basic hypothesis of underlying identity for vowels with identical nuclei seems transparently born out by the /-/ vowels. In the phonological structure of both LA Chicano English and also of Reference American the low-back nuclei of the vowels /, w, y, r/ are identical. For Vince, /y/ is relatively raised and fronted, but /, w, r/ form a single, undifferentiated cloud, showing that their nuclei cannot statistically be distinguished in this data.

This is consistent with a view of phonetic grammar in which the phonological classes have a target phonetic realization determined entirely by their phonological content and general principles of phonetic form, plus some language-particular rules which modify the phonetic implementation of some classes according to phonological context. If the phonological content of the nuclei of two vowel classes is the same, and there are no language-particular and phoneme-particular rules modifying their realizations, then their phonetic nuclei will also be identical. This seems to describe the nuclei of these three /-/ vowels, /, w, r/, which are realized identically in phonetic vowel space.

The front-raised character of the /y/ class might be attributed to a phonetic rule governed by stress. /y/ is much more frequently unstressed (61%, n=193) than /, w, r/ (24%, n=104). (The chi-square significance of this difference is p19#190.001.) If nuclei assimilate toward their glides when unstressed, (as suggested, for example, for Alabama /w, w/ on page , or by the relative fronting of the effect of stress on this very vowel, /y/, in Vince's speech shown below in Figure , upper chart, page ), then the higher frequency of unstressed and thus glide-assimilated tokens for /y/ may account for its separation as well as the direction of its separation from the rest of the class of /-/ vowels. However, not all of the difference between /y/ and the other classes may be attributed to this effect. An examination of the differences between the stressed nuclei (the tails of the arrows) in Figure  below in Section  shows that the stressed-only means of the /y, , w, r/ classes retain much the same relations as they have in this chart which includes both stressed and unstressed tokens: stressed /y/ remains somewhat raised and to the front of the other (stressed) /-/ vowels. At the same time it lies to the back of the nucleus of the low-front vowel /æ/, so that one cannot, by analysing /ay/ as low-front instead of low-back, escape positing a phonetic rule to shift the nucleus of this phoneme. In either analysis, a phonetic rule is required. The contact of Chicanos with Anglos, who are somewhat influenced by the speech of (immigrating) Southerners (as are many Californians) who have a fronted, monophthongized /y/, might be responsible for the acquisition of a fronting rule for this phoneme, but this is mere speculation. Still, a phonetic fronting rule is necessary to reconcile the basic hypothesis that the nucleus of /y/ is phonologically identical with the nuclei of the other /-/ vowels. This is given above as rule 1.

The phonetic identity of the nuclei of the other /-/ vowels need not be stated in any phonetic rule; it follows from their phonological identity, and from the lack of rules to separate them phonetically.

Next, let's examine vowel length. The relationship of long and short vowels in this dialect is qualitatively quite similar to that found in Jamaican Creole: The short vowels are lower and more central than the nuclei of their corresponding long vowels. Thus /ɪ/ is backer and lower than /i:/; /ɛ/ is backer and lower than /e:/; /ʊ/ is fronter and lower than /u:/, and /⋀/ is fronter and lower than /o:/. A single phonetic implementation rule captures these differences, rule 2, above.

This same rule occurs in Jamaican Creole (page , rule 4), but there it applies to low vowels as well. The opposite formulation, that long vowels are raised and shifted to the periphery of vowel space relative to the corresponding short vowels, is equally valid; which direction the rule goes in is not yet clear. Long-vowel raising and short-vowel lowering are two sides of the same coin, in this dialect.

A redundancy rule was proposed in Phonological Preliminaries (page ) that adds to vowels the features [back] and/or [round]. The central and back vowels are underlyingly unspecified for the frontness feature, and this redundancy rule specifies some of them (/ɑ; ur, or, oy; u:, o:, :/) as phonetically [back]. The fronting of /u:, / may therefore be seen as undoing the results of this rule, or as preventing its application in the first place. In this chart the back-rounding rule's effects are only seen in the realizations of /o:, or/.9.19 The fronting itself follows Labov, et al's (1972) third rule of chain-shifting: Back vowels front. A synchronic analysis that minimizes the number of rule-applications required to derive the phonetic system shown here would prevent the application of the backing/rounding rule to high vowels. However, as seen in the discussion of the effects of consonants on vowels, there are back, rounded /u:, / tokens, so it seems preferable to make the synchronic analysis parallel to the historical analysis by stating that these back vowels are fronted in some (most) contexts. Rule 3 above reflects this conclusion.

Notice next that the nucleus of // is much more centralized than the corresponding non-front, mid, short vowel in Jamaican Creole (there written /o/, but consisting of the same class of words, Wells' STRUT class). While the corresponding vowel in Jamaican is truly back, on the back edge of the vowel space (see page ), this vowel in LA Chicano English (as in many other dialects) is central: it lies directly above the /-/ vowels and well to the front of /ow, or/.9.20

At the same time, the high-back vowels, /u:, / have fronted to some extent; their means lie directly above // and well to the front of /o:, or/, for example. The phonetic differences and similarities between California Anglos and Chicanos are largely unstudied, but this fronting may be related to the phonetic norms of the matrix Anglo community. Some early unpublished work of mine on the vowels of one Southern-California-raised Anglo9.21 found extreme fronting of the back vowels, so that F1-F2 measurements of nuclei of // and of // overlapped considerably; no phonetically back mid or high vowels occurred at all except before /r, l/. This evidence is only suggestive, however, and further work is called for to make clear the phonetic effects of ethnic diversity and (non-) contact in California.

There are important segmental conditioning factors in this fronting process, to be explored in future work (however, see Chapter 10 for the apparently retarding effect of following /l/).

One thing that seems clear about this fronting is that it applies to a natural class of vowels, not just to one phoneme. While many vocalic sound-shifts seem to operate on a single phoneme at a time, both high-back vowels /u:/, as well as //, are fronted in LACE (as compared with /u:, u/ in Jamaican or as compared with /u:, / in the Chicago speech of Jim C., to take two examples -- see pages  ,  ), as stated in rule 3 above (page ).

Next consider rule 4, which describes the backing of nuclei before /r/. Nuclei of Vr vowels are not always identical to the nuclei of correspoding short vowels in Figure . While / r, r/ are indistinguishable from /, /, respectively, /ir, or/ are both distinct from their corresponding short vowels, and fall below and to the back of the corresponding long vowels /i:, o:/. Similarly, // (symbolized ``R'' in Figure ) lies to the back of //. If one were to identify the phonetic target of /ir, or, / in F1,F2-space as phonologically related to the phonetic target of /i:, o:, /, then the effect of /r/ in the glide slot of the syllable would seem to be a uniform phonetic effect of backing the nucleus. This analysis could be generalized to the relationship between /e:, r/, since /r/ also lies to the back of /e:/. (This would suggest writing /r/ as /er/.) However, the phonetic difference is greater than in the other cases, and the example of /, r/ shows that nuclei with and without /-r/ can be phonetically identical, while /r, / lie directly on top of one another. Thus the target of /r/ would seem to be identical to that of //, and the rule of backing before /-r/-glides is restricted to /i:, o:, /. The fact that /r, r/ do not undergo the backing rule appears to be a rather unnatural (and presumably dialect-specific) condition which blocks the application of the rule, as represented in rule 4 above.

Next, consider the realization of the /æ/ phoneme. This phonologically low-front vowel is not as low as the /-/ vowels in Figure . Phonological Preliminaries claimed that [front] is the marked value while underlyingly unmarked vowels are central or back. Only one nucleus can be the lowest in the system. One may suppose that the lowest vowel should be unmarked except for [low]. Low nuclei that are phonologically unmarked for frontness or backness are in a sense purely low and nothing more, while the marked low nuclei, though low relative to other non-low vowels, are not purely or exclusively low, since other features are intrinsic to them. One may suppose that ``pure'' low vowels should be lower than low vowels that have other phonological features as well. This may explain why the nucleus of /æ/ is raised relative to the nuclei of the /-/ vowels. These suppositions are consistent both with this datum, and with the analysis of the back and central vowels of Reference American (and by extension, of LA Chicano) as unmarked.

However, it should be noted that /æ/ in this dialect is much lower (as [æ]) than it is in many other dialects, such as Chicago White English, where it may be realized as [e], higher than the realization of //. So the raising of /æ/ is relatively small in this dialect.

Consider finally the location of the syllabic /l/, which overlaps with //, to the back of // in the central, upper-mid region of F1-F2 space, as shown in Figure . // overlaps //, //, and /l/, which lie without mutual overlap in that order from front to back.

Since F1-F2 values directly reflect properties of the shape of the vocal tract, namely of the degree of mouth-opening and of tongue-body frontness and lip aperture, and since they very closely match fine impressionistic characterizations of phonetic vowel quality, these patterns of mean formant frequencies are not epiphenomenal. They are patterns of phonetic behavior that presumably reflect the phonetic intent of speakers. Thus the rules given discussed above may be inferred to have some psychological, as well as merely behavioral, reality; thus I refer to them as principles of phonetic grammar. The discussion above has thus given a complete (though qualitative) characterization of the phonetic grammar, through which the average nuclei of LA Chicano vowels are realized acoustically.

Next: Stress Reduction Up: Los Angeles Chicano English Previous: The Shape of Vowel
Thomas Veatch 2005-01-25