Note 10:

Semi-consonants and diphthongs

I chose not to use semi-consonants like j and w in the symbols for diphthongs, but i and u instead. A true diphthong is not two distinct vowels, but is a single vowel, the timbre of which varies in time, from one timbre to the other. The two symbols are used to indicate the starting point and the end point. The end point is often not fixed, but rather indicates the direction of sound change. Whether or not this end point is actually reached depends on the speed of talking, and on adjoinings sounds, but in many languages doesn't make any difference for the identity of the diphthong phoneme.
So the difference between j and i as the second element of a rising diphthong could be, at best, that if it's j the second element may be less prominent than the first, because a j is supposed to be shorter than an i. But in a speech sound with a continuously varying timbre, without any abrupt changes, this is hard to determine.
So although I transcribe "Coimbra" as /kwi~br3/, I wouldn't object to /kui~br3/ or /kuj~br3/. Likewise, where I transcribe /3~u~/ or /3i/, I would also accept /3~w~/ or /3j/.

On second thoughts (June 2001), I think the [ui] in Coimbra is not a true diphthong, because the [u] and [i] belong to separate syllables, and the i~ is stressed: /ku"i~br3/. True diphthongs also occur, as in "fui" and "contribuiu" /ko~tribu"iu/. This is one more argument against my /w/ as a separate phoneme: the second phoneme in Coimbra is more likely to be an unstressed o, which regularly sounds as a short /u/.
There is also a distinction between [3] and [i] forming a true diphthong, and those two vowels in separate syllables: Confer venho ©, tenho ©, tenha /t"3iJ3/ with rainha © /R\3"iJ3/. I could therefore have transcribed /t"3jJ3/ for /t"3iJ3/, but I don't.
Other such words are bainha, ainda, tainha, campainha, ladainha.