There were many "bawdy songs' written a few hundred years ago.
Some of my fav "bawdy songs" known as 'catches,' or later 'rounds,' were written by the master composers--what some people would call the "classical" composers. An old boyfriend way back in college brought me a book of such, and most of them were written by Purcell, who wrote much beautiful sacred music & orchestral works. Here's a couple of my alltime favs:

             Full bags
a "catch" by Colonel Jacob Allistree circa mid 1600's

Full bags, a brisk bottle and a beautiful face
Are the three greatest blessings poor mortals embrace.

But alas we grow muckworms if bags do not fill,
And a bonny gay Dame often ends in a pill.

Then hey for brisk claret whose pleasures ne'er waste,
By a bumper we're rich and by two we are chaste.

and . . .

    Sir Walter enjoying his damsel
a catch collected or written by Sir Henry Purcel circa 1680's

Sir Walter enjoying his damsel one hight,
He tickled and pleased her to so great a height,

That she could not contain t'wards the end of the matter
But in raputre cried out "Oh sweet Sir Walter,

Oh sweet Sir Walter, Oh sweet Sir Walter,
Oh sweet Sir, sweet Sir Walter.
Oh swisser swasser, swisser, swasser, swisser swasser etc."

Till her father, who came up the stair,
did with Sir Walter and singe off his hair,
crying "swisser swasser, swisser, swasser,
take that as the cure" and he cut off Sir Walter.