English phonology
A radically different approach to the English vowel system was proposed by Chomsky and Halle. Their Sound Pattern of English  proposed that English has lax and tense vowel phonemes which are operated on by a complex set of phonological rules to transform underlying phonological forms into surface phonetic representations. This generative analysis is not easily comparable with conventional analyses, but the total number of vowel phonemes proposed falls well short of the figure of 20 often claimed as the number of English vowel phonemes.