Not jokes about musicians, jokes where a melody is part of the setup or the punchline. Do you know any? I know one–I’ll tell it later in the thread if no one else has.
Knock knock.
Who’s there?
Sam and Janet.
Sam and Janet who?
Sam and Janet evening! Some enchanted evening, from South Pacific
Doh!
A deer!
A female deer.
I demand you explain this!
(yeah, it’s from the simpsons, right? Or maybe it originated somewhere else? Anyway, I don’t get it) 
What does the Lone Ranger do in the bathroom? Take a dump, take a dump, take a dump-dump-dump! Sorry.
What did the Pink Panther say when he stepped on an ant?? Dead ant. Dead ant. Dead ant, dead ant, dead ant, dead ant, dead aaaaaant!
I know a couple, but you actually have to sing the tunes. It would be impossible to tell the jokes in writing. One’s about a jazz musician who dies and goes to heaven, but there’s no jazz in heaven. The other is about a sax player who can’t play the bridge to Somewhere Over the Rainbow.
Just the punchlines:
Guess who drowned in the lake today, doo dah, doo dah (very stupid joke.)
Pardon me, Roy. Is that the cat that chewed your new shoes?
punchline: “I left my harp in Sam Clam’s disco”
Well, there’s always the story of the Fabulous Tiz Bottle . . .
Beethoven’s manservant came to tender his resignation. Poor Ludwig was distraught: “Heinrich! Whatever will I do without you? You are a jewel of a servant, and what it more, my most fruitful inspiration!” Heinrich was amused. “Master is pleased to jest. What, a genius like him who has already written four of the most divine symphonies ever to grace the ear of the listener? Inspired by a tuneless clod like me? Why, that is funny! Ha-ha-ha-haaa! Ha-ha-ha-haaa!”
So there’s this wonderful monastery where the monks perform each of the nine services of the day in chanting. Every morning they get up for Matins and the Abbot greets the monks by chanting “Good morning, brothers”, and in response they chant back in unison “Good morning, Father.” and then they chant the service. It’s beautiful. They chant through the cycle of services during the day, and at Vespers, the Abbot chants “Good evening, brothers” and the monks respond with “Good evening, Father.”
It’s a beautiful morning, one Matins, as all the brothers file into the chapel to begin the service. The sky is blue, the birds are singing, it’s a great morning to be alive. The atmosphere in the chapel is relaxed and joyful as the Abbot chants “Good morning brothers.” A disharmony of voices is heard; most of the monks chant back, “Good morning, Father,” but one monk, distracted, chants “Good evening, Father.”
Suddenly there is a tension in the air. The Abbot looks grim as he peers at each of the monks, searching their faces. He clears his throat and lifts his voice in song:
“Someone chanted evening”
Frog goes into a bank with a little geegaw and meets with the new loan officer Miss Paddywhack. . .yadda yadda yadda
“That’s a knick knack Paddywhack, give the frog a loan.”
A guy gets a job driving a school bus. The first day he goes out, driving a bus with Sesame Street characters on it. He thinks the route is cool because he only has to make three stops and pick up four kids.
First stop two very fat girls get on the bus. First one says “My name’s Patty.” Second one says "My name’s Patty too.
Second stop a really strange kid gets on and says “My name’s Ross and I’m so special everyone calles me Special Ross.”
Third stop a black kid gets on and says “Yo, whazzup? I’m Lester G.”
The guy starts driving them to the school when he smells smothing awful. He looks in the rear view mirror and sees that Lester G has taken off his sneaker and is picking at a huge bunion on his foot. The guy drivers to the school at 100 miles per hour, drops the kids off, goes back to the garage, gets off the bus and screams “I QUIT.”
The supervisor asks “What’s wrong?”
The guy says “What’s wrong? What’s wrong? I’ll tell you what’s wrong”
You’ve got me driving two obese Pattys, Special Ross, Lester G picking bunions on a Sesame Street bus.
One of my favorite bad puns:
Ringo became a gentleman farmer, but was having no success. His neighbor’s animals were all strong and healthy, so he went and asked him the secret to his success.
“well, for chickens, you wanna plant some corn.” The farmer said.
“Right, a field of corn for chickens.” Ringo replied.
“And for horses, you wanna plant some corn.” The farmer said.
“Right, a field of corn for horses.” Ringo replied.
“And for cows, you wanna…”
“I know, I know,” Rigno butts in, “I want a field of corn.”
“No,” replied the farmer, “everyone knows it strawberry fields for heifers.”
Don’t get it. Please explain.
Strawberry Fields Forever (The Beatles)
The Beatles song, “Strawberry Fields Forever.” I don’t understand the song, just the joke.
Many classic feghoots were song lyrics. My favorite:
“A gritty pearl is Michael, L.L.D.”
There’s also the classic:
“That’s just the furry with the syringe on top.”
There’s also Isaac Asimov’s story “Death of a Foy,” which ends:
Give my big hearts to Maud, Ray.
Remember me to Harold’s choir
Tell all the Foys on Sortibackenstrete
that I will soon be there. . . " (Technically, the made-up word that ends the third stanza disqualifies it from being a feghoot, since the pure form requires only existing words.)