open mike - the song you are giving is known in Germany well, too. Every verse has its own melody according to the character of its instrument.
Contrary to "I am a fine musician", however, the stanzas are not sung one after another but at the same time, as a piece of four voices, so giving the impression of a small band playing synchronically.
I enjoyed it very much in my youth with my scout troop. It also can be found in a couple of student song books for merriment while drinking.

Wilfried.