Sutmbled onto this thread and have been having some fond memories.

I was a trombonist in the 9th Infantry Division Band in the 70's. I always heard it sang to the tune of the National Emblem (as many have said here) like this:
And the Monkey Wrapped His Tail Around the Flagpole
To See his Asshole
It was Red
After the Monkey Wrapped His Tail Around the Flagpole
And Showed His Asshole
Then the Band Began to Play

It became quite a joke over time - when someone of authority would come into a room, one of the band members would play the first bar or two of National Emblem and everyone would laugh...