zompist bboard

... in English. This is somewhat contrived, but I've been thinking about it, and I think there's a situation where [t] and [t^h] form a minimal pair. Consider the following words: bank stop (a phrase I made up to refer to, I don't know, a stop sign by a bank, which becomes known as the bank stop) and the bank's top (i.e., the roof of the bank.) In normal spoken English, these would be differentiated by [t^h] beginning the second word in the second phrase, but not the first.

I realize this is contrived, but there are words in english that end in either stop ('backstop') or top ('bigtop') and it's not impossible that there might be two that have the same initial morpheme, differing only in the stop/top distinction. I want to be clear - this is not some bizarre argument that [t] and [t^h] are different phonemes, just that it's possible to contrive a situation where they are distinctive.

So you're saying they could be distinctive but are still the same phoneme. wut

As for "bank stop" and "bank's top", it's just a syllabification problem...

I'm sure there's a stress difference between the two; at least there is when I say them.

As Canepari suggests, this is because of syllabification.

Indeed - and syllabification in English is dependent on morpheme boundaries: whenever possible a sound syllabifies with the remainder of the morpheme it belongs to. That is why minimal pairs need to be monomorphemic - or, at least, the morpheme boundary should be distant from the sound in question.

For me:
bank stop [ˈbeŋkstɑp]
bank's top [ˌbẽŋksˈtʰɑp]

The latter has primary stress on the second syllable, the former is on the first.

It appears that stress is a conditioning factor here for me, but I don't know exactly how.

bankstop [ˈb̥æɪ̯ŋkˌsd̥ɑp̚]
bank's top [ˈb̥æɪ̯ŋk ˈsd̥ɑp̚]