Figures , show more than merely the presence of differences between long and short vowels; it displays the acoustic structure of the vowel systems of these two speakers, insofar as this structure is shown by F1-F2 measurements at the phonetic nucleus of vowels.6.14 On this scale, the long vowels form a large inverted triangle, with the mid-long vowels raised along the front and back edges toward the upper corners. The short vowels form a much smaller pentagon, which is inside and in Juba's case near the bottom of the large triangle.
The relations between the long vowels (the triangle) and the short vowels (the pentagon) may be derived by four simple statements from a reasonable default distribution of vowels in this acoustic space, also characterized by four statements, which may themselves be derived from general facts of vowel phonetics. The first four statements are proposed universal phonetic implementation rules, as presented in Table .
(1) is a general fact about phonetic vowel space. (2) and (3) follow from the disputed claims of Liljencrantz and Lindblom (1972, also cf. Lindblom, 1978) on maximal dispersion of vowel phonemes.6.15 (4) is a general fact about the relation between peripherality and vowel length. These four statements of general phonetics, in combination with the phonological structure that distinguishes 5 nuclei and length, generate a picture of a 10-vowel acoustic vowel system like the first picture in Figure .
To generate the second picture from the first, four linguistic phonetic statements are needed, as in Table .
The procedure in Table generates the acoustic distribution of the long and short vowels seen in both the displayed schematic chart (Figure ) and Juba's actual chart of re-estimated means (Figure ). Roasta's pattern is only slightly different: the back long vowel is raised even less than Juba's; the short vowels are not apparently lowered (rule 7 is omitted), and /a/ is slightly to the front of /aa/.
Three of these four statements are closely related to the generalizations about historical chain shifts in Labov, Yaeger and Steiner (1972) discussed above: In chain shifts, peripheral (that is, long) vowels raise (as also in rule 5), non-peripheral (that is, short) vowels lower (as in rule 7), and back vowels move to the front (as in rule 8). Rules (5) and (6) may be related by a drag chain shift: When the long mid vowels are raised, the short mid vowels fall into the gap left behind, becoming peripheral vowels. These linguistic-phonetic rules are intended strictly as statements of synchronic relationships; they determine the locations within phonetic vowel space of the average nuclei of the short and long vowels in Jamaican Creole. LYS' rules of chain shifting, on the other hand, describe diachronic relationships. Since synchronic rules often recapitulate historical changes, it may be that these rules also describe actual historical changes in the development of this dialect. However, they are used here synchronically, as part of the derivation from phonological structure to aspects of phonetic implementation. The fact that the rules also govern whole classes of historical changes confirms their naturalness.
This derivation of the locations of the vowels in the acoustic vowel space is systematic and entirely plausible; further the number of statements it requires is significantly fewer than the number of statements required to simply list the mean first and second formant frequencies for each vowel class (2 formants * 5 vowels * 2 lengths = 20 specifications).
The two remaining vowels must also be located in this space, the raising diphthongs /ai, ou/, which are the only vowels peripheral to the long-vowel triangle. These follow a pattern opposite to that of the mid vowels, where the front vowel is higher than the back one: the front vowel, /ai/, is lower than the back vowel, /ou/.
The above statements characterize the locations of vowel nuclei in formant space, an important part of phonetic grammar. As argued in the Acoustics chapter, F1-F2 space directly reflects the continuous phonetic dimensions of height and backness, which are articulatorily realized by the degree of mouth opening and of tongue-body-frontness and lip-aperture. Thus this is not merely an acoustic description, but a phonetic description, which shows much of the structure of the phonetic grammar of the speaker. The rules relate phonological categories to mean locations of vowel nuclei in this phonetic space, accounting for rather complex details of phonetic distribution in a natural, simple, and general way. The rules largely refer to classes of vowels rather than single phonemes. Also, they are mostly independently motivated in previous general discussions of sound change, phonetic typology, etc.
The status of these rules in linguistic theory is of some interest. Statements (1-4) above appear to be consequences of universal principles of general phonetics6.16 that may not need to be stated in a purely linguistic description. These are similar to the phonetic implementation rules given for Reference American (Section ). Statements (5-8), on the other hand, must be included in the phonetic grammar, since counterexamples exist. Thus, long mid vowels need not be phonetically raised towards the long high vowels (statement 5). See, for example, /ey, ow/ in Alabama, page . The short mid vowels need not be peripheral (statement 6), and the short high-back vowel need not be fronted (statement 8). See for example, Jim from Chicago, page , where /, / are non-peripheral, and // is phonetically well to the back of //, as far back as /uw/. Since languages may or may not implement these statements, they should be specified in the gramar.
This phonetic grammar is incomplete: Further details must be specified to generate vowel trajectories from phonological specifications, including phonological and phonetic diphthongization, consonant-coarticulation effects, etc. Effects of F3, of formant amplitude, of temporal variation are not dealt with here. However, within the limits of single time-slice measurements of F1 and F2 in characterizing vowel quality -- limits within which much of what is linguistically significant about vowel quality can be characterized -- the 8-rule grammar presented above accurately describes the mapping from phonological to phonetic structure.