Canonically, English is not a tonal language, and there are a number of posts on this site discussing why the use of rising tone in asking a question does not qualify (the reason being that it doesn't actually change the definitions of words).
This question is about something different. There is a well-known phenomenon called the "cot-caught merger" that concisely describes the pattern of sound changes that results in those two words being pronounced exactly the same. In general, a sound change pattern which results in different words becoming homophones is a merger, and a change which makes former homophones become differentiable is a split. What I'm asking about here is very similar to both these kinds of patterns, but involves a change in tone instead of (or maybe accompanying) a change in pronunciation.
"Cot" (and of course also "caught") don't actually always (to the best of my ability to assess) end the same way as do other similar words like "sit," "set," "note," etc.
'Sit,' 'set,' 'note' etc. all end in the unreleased 't' sound (IPA symbol is t with a 90 degree angle afterwards), but in certain contexts* 'cot' and 'caught' don't end in a consonant at all, but instead in a kind of upwardly pitched vowel sound. The vowel starts out with the "a" sound as in the words 'father' and 'bother,' which has the IPA symbol ɑ.
(Initially I had thought it then transitioned into a dipthong with some other vowel (possibly a shwa, the 'set' vowel or a short 'i' sound), but playing the audio from the interactive IPA chart for each of them sequentially, none of these really fits. So, this leads me to think that it is just the sharp rise in pitch which I was incorrectly perceiving as a dipthong.)
I'm not sure how one would accurately transcribe the word "cot" pronounced with the result of these changes, but here is an attempt:
kʰɑ with sudden upward pitch movement
This means that although the word effectively ends in a vowel, it is not pronounced the same as "caw," like the sound a crow makes. They have the same final dipthong (I believe) a very similar vowel sound, but while "caw" has a level tone, "cot" has a rising tone. So, I wouldn't confuse one for the other.
Is there a name for this phenomenon? It really seems like tone being the sole differentiator in a minimal pair.
EDIT: @tchrist has pointed out to me that the sound in "caw" is actually transcribed ɔ, which is different from the ɑ sound in "cot." I would have thought that "caw" would be kʰɑw, but I'm not very familiar with the IPA alphabet and may be making the kind of mistake which someone more experienced would not. If this is the case, I may have been mistaken about the rise in pitch being the only differentiator between the two words. But, it is the pitch change that distinguishes the pair in my ears, which may not be 100% accurate!
*I'll add a clarification of "some contexts" here, following from the discussion in the comments:
"Caught a fish" --> flapped 't' because the next word is a vowel
"There's a fish in my cot" --> has that rising pitch, where 'cot' is the last thing in the sentence
"Network" --> the 't' is dropped completely from the middle of the word
"Set square" --> I'm pretty sure the 't' is getting dropped because of the 's' after it, but the vowel in 'set' does not rise suddenly in pitch as a result of that
"This is a set." --> Unreleased 't' in 'set,' because nothing comes after it in the sentence. (also, level pitch)
"Caught" --> All on its own (no context): rising tone
"Caw," "Set" --> All on their own (no context): level tone
For the sake of avoiding confusion, I'll add that I don't put a rising pitch at the end of every sentence, as is done in some parts of California. This didn't seem relevant at the time I posted the question, since it was intended to be entirely about nomenclature, but I believe I pronounce things in a fairly standard GE (General American) or North Midlands accent but may also be influenced by more West Coast variants (like saying "soda" instead of "pop" or any of the alternatives).
