Static vowel structure in English must distinguish three levels of height, and two levels in the front-back dimension. This section discusses various approaches to the formal representation of this three-by-two grid, which has exercised phonologists for many years.
I discuss several types of featural analyses for vowel height. The first, as in SPE, describes vowel qualities in terms of their opposition to a language-particular ``neutral position''. Taking its language-particularity seriously suggests that the neutral position for each dialect determines its particular feature system. In the standard generativist treatment, vowel height is considered to be multi-dimensional (that is, more than one feature is used to distinguish among heights). This type of treatment is also characteristic of some provocative recent work by Petterson and Wood (1987a,b; also Wood and Petterson 1988). In the second type of treatment, vowel height is a multiply-valued single dimension, and various sub-theories (tacitly, theories of counting or numbers) are proposed in order to deal with the multiple values of the dimension. In a third type of analysis, proposed here, privative height features [high] and [low] are used in order to avoid both the combinatorical problems of the standard treatment, and the admission of many-valued dimensions into phonological structure. Finally, the feature [front] is proposed to replace the feature [back].