Jazzman, a.k.a Jimmy Peake, is a gangster in Gotham City.
Jimmy Peake was a gangster in Gotham City involved in an illegal smuggling operation six years ago. When Lieutenant James Gordon busted Peake, Peake swore revenge upon being delivered to the authorities.
Six years later, Peake, now Jazzman, initiated a drug sale and lured the Police Department to a trap. When Gordon was set to get Jazzman, he was severely wounded and taken to the hospital.
Due to Gotham City Jail being overcrowded at the time, Judge Maria Vargas sentenced Jazzman to Stonegate Penitentiary to await trial. However, Jazzman escaped and instead of fleeing, he went straight to Gotham Hospital to finish off Gordon. Fortunately, Batman intervened and Jazzman was arrested when Harvey Bullock and the cops arrived.
Though not a "theme" villain like Joker, The Ventriloquist, or Two-Face, he does have the odd eccentricity of using a lot of music-related terms in his speech. One possible explanation is that he was once a famed musician but turned to crime for unknown reasons.