The problem is that there's no really tidy way to write hornpipes that are to be played as hornpipes (Don's right about the many "hornpipes" that end up being reels).

the triplets that find their way into hornpipes are really the key. The triplet feel is what provides the "lift". But to write a whole tune in triplets (mostly a series of a quarter note and eighth-note pairs with triplet brackets above them) is tedious to do and messy to look at.

Personally, I think the worst solution is the dotted-eighth/sixteenth pairs. Its equally messy. And just flat wrong, if you play it as written (making the dotted eighths long enough and the sixteenths short enough).

So we most often wind up with straight eigth notes. If you play them as written, wrong again! You get reel feel. You just have to know that if it is a hornpipe you need to stress the first note of each eighth-note pair a bit and shorten the second some. When your actual triplets fit in, so that the whole thing flows smoothly, you're doing it right.

Analogous to playing with a swing feel, really. You can't do justice to that in written notes either, without getting too detailed to make a clean score. So you write something like "swing feel" at the top and get players who've learned what you mean through experience.

So the answer to your original question, Nicole, is that for a hornpipe (as we use the term in modern times) a triplet (composed of eighth notes) equals two eighths played with a "triplety" feel equals one quarter note. And the same triplety feel underlies the quarter note that underlies the other two. Count "one-and-a, two-and-a, etc." under them all.

George