Half-Syllables in English?

Has any authority recognized what we could call "half-syllables"? I.e., "Air" being pronounced /ay-r or /eh-r; not quite two whole syllables, but more than one. Or "I" pronounced /ah-e {except in the U.S. South, where it's just /ah.}

In a way...'sesquisyllabic' describes one-and-a-half syllable words, and they are recognized at least theoretically, by some authorities, in English. See, for example, "SESQUISYLLABLES OF ENGLISH: THE STRUCTURE OF VOWEL-LIQUID SYLLABLES", by Lisa M. Lavoie and Abigail C. Cohn, Cornell Univ.

By their account, the juxtaposition of a liquid consonant and a dipthong can produce a 'half-syllable' pronunciation. The account applies to 'air', but not 'I'.