A lot of these "mad songs" seem to be from the sixteenth century, and all the ones I've seen have the same meter. The most famous one among poetry readers (it's called "Tom o' Bedlam", or "Loving-Mad Tom") begins

From the hag and hungry goblin
That into rags would rend ye,
The spirit that stands by the naked man
In the book of moons defend ye! That of your five sound senses
You never be forsaken,
Nor wander from yourselves with Tom
Abroad to beg your bacon.