If it takes extraordinary intelligence to be a comedian, then to create musical comedy also requires extraordinary musical skill and knowledge. Since the era of recorded music (and probably before it), America has been blessed with some amazing musical comedians. They have enriched our lives, at least those that understand the humor. For those unfamiliar and even those who have heard them, the following is a brief list of great musical funny "maestros," mentioning at least one of their works to help you get properly introduced.
Old movie fans should be familiar with Spike Jones and the City Slickers, a wacky group of musicians who used anything but the original instruments to present their version of classical works, including cow bells and whistles. Their version of the opera Carmen has both opened and closed the world of opera to me. After listening to it, besides crying from laughing, I was curious to hear the real version but unfortunately found it far less entertaining the Spike Jones version. Here is the link: https://www.youtube.com/watch?v=UG087P1JTIQ.
From a similar time, Harpo Marx played the harp at least once on each Marx Brother movie. Actually, he never really learned how to play properly until after he retired but who knew that besides professional harpists? His humor is expressed not so much in the music but in his interaction with the harp and his surroundings. It has to be seen to be appreciated: https://www.youtube.com/watch?v=569Gy8BE5P4.
Victor Borge is a bridge to the modern era. A virtuoso pianist, he didn't take himself too serious, preferring to "ham it up" in front of audiences. This lack of seriousness, I believe, opened up the world of classical music to millions in addition to getting them to laugh, always a good deed. If you have any doubt about his talent, get together with another pianist and try doing this at home: https://www.youtube.com/watch?v=4jgESE9oJRE.
The 1960's turned all values upside down, not always for the better, including musical ones. One Las Vegas performer was Liberace. Like Victor Borge, he preferred not be a boring classical musician. His style was much more flamboyant but as Marilyn Monroe, would say, some like it hot. He plays the music straight but his taste in clothes, or lack thereof, make it impossible to take him serious, exactly as he intended. See for yourself: https://www.youtube.com/watch?v=-WC1OsdX2LM.
Nobody took on the music establishment more than Prof. Schickele, the infamous musicology that brought us P.D.Q. Bach, the lost son of the famous Bach. He applied "tongue in cheek" professional musicology, creating a hilarious synergy of classic and modern. My two favorites are his baseball commentary to Beethoven's Fifth Symphony, which actually makes some good points, (https://www.youtube.com/watch?v=MzXoVo16pTg), and, in a different vein, his modern version of a round: https://www.youtube.com/watch?v=OkjR3cdXSS8.
The Canadian Brass Ensemble is an amazing group of fine musicians that entertain their audience with both well played music and comedy. They respect the genre but add humor, often through actions, a bit like Harpo Marx. My favorite is their tribute to ballet music, whose humor is based on the fact they supposedly have never seen a ballet since their back is always to the stage. Enjoy: https://www.youtube.com/watch?v=AjRLQeNUjfk.
Finally, growing up in the sixties and seventies, Tom Lehrer was a part of my life. His ringing political commentary is still sadly relevant today. Listen to Who's Next and National Brotherhood Week and try to find something that has changed besides the names (for your convenience: https://www.youtube.com/watch?v=oRLON3ddZIw and https://www.youtube.com/watch?v=CgASBVMyVFI). However, he was also a tremendous musician in his own right. His versions of Clementine and a tango will change your view of these classics. Listen and appreciate: https://www.youtube.com/watch?v=1b3coO_6MwY and https://www.youtube.com/watch?v=TytGOeiW0aE. They have stood the test of time since they still make me laugh.
Serious music and comedy are not mutually exclusive but require genius of a special kind. These comic musicians, regardless of their or your age, cannot help bring a smile.
P.S. I have excluded rock musicians that were less than serious, such as Tom Waits I rather have a bottle in front of me than a frontal lobotomy, because I am not familiar with them. I will leave that group for someone else. As they say in boring theses: "Further research should examine the use of humor in modern rock music in the period 1970-2017."