I will argue that the glide slot need not be kept separate from the slot for /r/. Let us reconsider Trager and Bloch's chart, Table above. The last three columns of this chart constitute a catalog of counterexamples to the claim that /r/ occurs in glide position, since they each contain a glide preceding /r/. Three observations will suffice to eliminate these counterexamples.
First, note that the /r/ in the disyllables eyrie, Irish, Moira, and cowrie may be analysed as syllabified with the following syllable. Indeed if the observations about /ɑy, ɑw, oy/ above is taken seriously, this step is required, since /r/ cannot occur in the same syllable with just these vowels. This step eliminates several phoneme-classes.
Second, notice that once these words are excluded, Columns F and G (Vyr, Vwr) have only a single member each, and perhaps coincidentally both of them correspond to gaps in column H (Vhr). If this complementary distribution is not a coincidence, then columns F and G should be collapsed with column H, resulting in a pleasantly gap-less column. Gaps in a paradigm are often suggestive of missing generalizations; this generalization eliminates twelve.
Thus the separation of the ({y, w, h}) slot from the (r) slot has been deprived of two-thirds of its justification. If the Vhr class of vowels in column H can somehow be removed, then T&B's justification for the separation of glides from /r/ will be completely destroyed. This leads to the third observation.
Notice that the Vr class of vowels all occur before unstressed syllables, where the /r/ may be ambisyllabic. None of the Vhr class occurs in this environment; the /r/ in this class is tautosyllabic. This is yet another case of complementary distribution of classes within the structure; it allows us to collapse the two classes into one. The fact that the Vhr class is phonetically more tense or peripheral than the Vr class must then be accounted for by a phonetic rule which tenses these vowels before /r/ in the same syllable. The rule is familiar from previous studies of English vowels:3.27 the independently motivated vowel-before-vowel raising rule (which converts the vowel following /d/ in idea into a peripheral vowel, for example).
Thus we have been able to eliminate all 18 of T&B's catalog of counterexamples to the theory that /r/ occurs in glide position.
In a later work, Trager & Smith (1951) attempt to provide a pan-English vowel structure. By this time their greater knowledge of phonetic differences among English dialects, combined with the American structuralist principle of bi-uniqueness, resulted in an even greater proliferation of unnecessary phonemes. The 1951 system contains three heights and three front/back levels, making nine base vowels, each occurring in eight sub-systems (V, Vy, Vw, Vh, VrV, VrC, Vhr, VhrV). Because the analysis is pan-English and bi-unique, vowels with following /r/ in ``r-ful'' dialects are analysed as occurring in different locations in the structure as phonetically different ``r-less'' phonemes, thus accomodating the ``r-less'' dialects at the same time, in the same system. Nine phonemes in their analysis are vowels before /r/ in dialects where /r/ is lost -- but they are considered to be in the same system, rather than in the new and separate systems of the r-less dialects. A result of this approach is that the basic correspondence between sound class and lexical set or word class is lost: some word classes correspond at the same time to multiple sound classes, since in different dialects they are pronounced in different ways. Further, a number of evidently allophonic differences are analysed as phonemic, as between jury and boorish, story and pouring (where a preceding labial and following word boundary may for some speakers make the vowel in the boorish and pouring phonetically longer and backer than the vowel in the other contexts). Their VrC and Vhr sub-systems contain the identical word-classes. Though their considerable knowledge of English dialects and their sensitivity to subtle differences of sound makes Trager and Smith (1951) a very useful source of information about sound patterns in English, their theoretical assumptions lead them away from, rather than towards, the kind of system argued for in this chapter.