As you will see from my notes, there are severraal other names for the tune.

Observe that the structure of the tune is rather like that of the McPeake's "Mongahan Fair", probably the "Derry Fair", c 1597, just a little after "Bragandary" appeared. The meter is a bit different, so they probably weren't the same tune in the late 16th century.
The structure is (1)introduction, (2) body, and (3) conclusion. The "Bragandary" meter of the (3)conclusion is pretty distinctive, and I've found it elsewhere on only 1 song, earlier. Anyhow, the (2) body part is a series of repeats which can be extended for as many lines as needed, and that's apparently why songs to "Bradandary" (under it's vaious titles) have variable numbers of lines.