>Stower
thank you

I would argue that "dotted" hornpipes are not played in triplets (any more than a strathspey is), although it is easy to fall into doing that; and they certainly have 4 beats in a bar: but this does illustrate my point.
My understanding is that:-
In plainchant the long is divided into 2 or 3 breves, depending on whether the the time is perfect or imperfect.. In perfect time, if two breves are written the first is (often) twice the length of the second. If the number of breves is odd there is a triplet somewhere!