Summarizing work descending from SPE, Keating (1988:23) provides a ``consensus set of segmental features'' which, she believes, ``in most respects represents current practice''. Binary features in this set which are used to describe vowels include those in (8).
(8) [round], [high], [low], [back], [tense], [ATR].
These binary features may have values + and -. The grammar for static vowel structure is the free combination of independent features. This grammar, applied to the height features [15#15high], [15#15low] generates four distinct phonological heights, [+high,-low] (which is interpreted as high), [-high,-low] (interpreted as mid), and [-high,+low] (interpreted as low), and a fourth combination, [+high, +low]. This fourth combination is ruled out in SPE by the physical impossibility of the tongue body being both raised and lowered at the same time.3.40 The form of this argument is typical in modularist argumentation: principles from one module or level of structure are used to rule out structures that are entirely acceptable to other modules. In this way, structure at one level (the combination of [+high] and [+low]) is ruled out due to constraints at another level (here, physical constraints on the tongue).
Phonetics and phonology are the most isomorphic parts of grammar. (Surface) phonological structures map directly onto phonetic form, and those features which occur at both levels are argued to have essentially similar content. In no other area of grammar are modules so closely matched. The phonetic impossibility of the phonologically possible combination [+high,+low] is an example of a mismatch between the two modules: one module accepts a structure, another rejects it. If we prefer linguistic modules to be orthogonal, that is, to be maximally different from each other, then this mismatch is not a problem. If on the other hand isomorphism is preferable between phonological and phonetic structure, it is undesirable. I take the latter view. Phonology is the category-based, abstract mental representation of phonetic form in language, and the isomorphism of the two levels is one of phonology's fundamental properties.
I therefore assume that if phonological features have mutually exclusive values, and thus if a grammar in principle overgenerates, then it is flawed.3.41 A number of other theorists have been motivated by this view of the problem of vowel height to develop static theories of vowel features which do not have the problems of overgeneration and non-independence of dimensions that the standard view suffers from. Three classes of solutions are given, those of Wood and his coworkers, and various numbering systems, and a solution I propose that combines privative features and autosegmental tiers. The superiority of any one of these systems over the others in the analysis of English is not clear.
The standard model of vowel quality as defined by the dimensions of height and frontness originated with Alexander Melville Bell's3.42 Visible Speech (1867).3.43 Work over the last decade or so by Wood and his coworkers has challenged this classical model on both phonetic and phonological grounds.
In a treatment of the phonology of vowel raising in Bulgarian, Pettersson and Wood (1987) argue that the rule of vowel reduction, in which the vowels /e, a, o/ are raised to /i, , u/, respectively, cannot be treated elegantly in a standard binary feature treatment of vowel heights. /e, o/ are mid vowels, and undergo raising to high, while /a/ is a low vowel, and raises to mid. They argue that the standard feature systems are unable to state the raising process in a single rule, since raising must separately change [+low] to [-low], and [-high] to [+high]. They then use articulatory data to argue for the separation of the feature of jaw-opening from the feature of lingual constriction. /e, a, o/ are [+open], while /i, ⋀, u/ are [-open], so that the reduction rule can be stated simply as: [+open] 14#14 [-open] /[ 16#16 ]. ``This is not the same as saying nonhigh becomes high, since /⋀/ has the same low pharyngeal tongue posture as /a/. The combination of low pharyngeal tongue posture with close jaw position cannot be expressed by Bell's features, since a vowel cannot be simultaneously be [+high] and [+low]. It is necessary to distinguish between mandibular and lingual maneuvers. ...''(p. 242)
We may infer that Wood's analysis resolves vowel height into two articulatory features, such as [open] for the jaw, and [raised] for the tongue, where /i, u/ are [-open,+raised]; /a/ is [+open,-raised]; /e, o/ are [+open,+raised], and /⋀/ is [-open,-raised]. [Mid] might be defined as a cover feature for [17#17 open, 17#17 raised]. Thus all four combinations of two height features do occur, and so Wood has avoided the impossible-combination problem, using a truly multi-dimensional treatment of vowel height. In common practice vowel height is inconsistently held to be both two dimensions (in the formal structure) and one dimension (in phonetic reality). Wood has commendably gotten beyond this inconsistency, since in his view the two dimensions of vowel height are two separate dimensions in articulatory phonetics as well as in the abstract phonology.