The skill behind the cartoon is credited to two different people. The first saxophonist to be the chops for Lisa was a man named Kim Richmond. Richmond is a professional saxophonist as well as a composer. He played in the Air Force Big Band and arranged the California Jazz Orchestra to perform his own pieces.

The second man to play for Lisa is Terry Harrington. Not only does he play as Lisa, he writes (or improvises) her solos in various episodes.

The actual music that Lisa (or in reality, Harrington) plays is all jazz and blues. The intro to the show has some of Lisa's sax playing in it, which is distictively blues-y. Also, some of the solos she does are simple blues chromatic scale. In many of her solos, she plays very techincally, adding triplets to the jazz and blues scales many of her solos are based off of. And since this is a comedy cartoon, many of the solos are silly, like loud shrieks or playing off rythym on purpose. In fact, when Lisa plays horribly, blatting and off-rhythym, Homer says "Now you're swinging honey!"

Lisa's mentor on the show is a man by the name of "Bleeding Gums" Murphy. His first appearance on the show is him playing his sax on a brigde at night, which many believe to be a reference to Sonny Rollins. Rollins is a famous and influential saxophonist who got his career started at age 11, is still touring and recording at age 80, and was elected in to the Down Beat Jazz Hall of Fame in 1973. Obviously this reference to Sonny puts Murphy in to a category of phenomenal players. By being a mentor to Lisa, he partially elevates her to that level as well.
"Bleeding Gums" Murphy plays jazz and blues, and even performed a vocal/saxophone piece on TV that Lisa wrote. His support of Lisa helps her improve her skills as well as get recognition for the piece she wrote. An example of Murphy counnseling Lisa about blues takes place in the following conversation:
Bleeding Gums: "You know, you play pretty well for someone with no real problems."
Lisa: "Yeah, well I don't feel any better."
Bleeding Gums: "The blues isn't about making yourself feel better, it's about making other people feel worse. And makin' a few bucks while you're at it."

The mature cartoon "The Simpsons" has many comical aspects that make it popular. However one section of the show that is the most respectable is often looked over as an irrelevant feature. 8 year old Lisa Simpson is a phenomenal saxophonist on the show, playing a variety of jazz and blues on her baritone saxophone. Extremely gifted with an IQ of 159, Lisa is often seen as a child prodigy. Lisa's musical talent, combined with her brains and insight to the workings of the world subtly suggests that children are often overlooked, and in some cases they understand more than the adults around them.