Oddly enough, they did not.

The Muppets have released a total of 26 albums, starting with the soundtrack to "The Frog Prince," a TV special aired in 1971, but never a dedicated Dr. Teeth and the Electric Mayhem release.

Odd since that band became a sort of symbol of Muppet music after its introduction on "The Muppet Show" in 1976. They served as the house band on the iconic variety series and regularly performed alongside the huge music stars who appeared.

Though they never got a record of their own, many of the Muppet albums did feature the band, led by the fur-hat-wearing, gold-tooth-smiling leader Dr. Teeth (said to be modeled after '70s blues rocker Dr. John). Their first recorded appearance is on the 1977 "Muppet Show" album, simply a compilation of songs from the show, whereon they performed the torch standard "Tenderly." 

They appeared on eight Muppet albums, most recently 2006's "A Red and Green Christmas," performing the modern holiday standards "'Zat You, Santa Claus?" and "Run, Run Rudolph."

The band appeared in the Muppet movies as well, but only showed up on one of the soundtracks -- doing "Can You Picture That?" from the original 1979 film, "The Muppet Movie." Dr. Teeth appears solo (without the Electric Mayhem) on the "Muppets Take Manhattan" soundtrack.

Interestingly enough, Dr. Teeth and the Electric Mayhem's most famous song isn't even theirs. Most people credit the oft-recorded Muppet classic "Mahna Mahna" song to the band, but it was actually performed (repeatedly) by the aptly named character Mahna Mahna. Doing that song, a running bit on the long-running show, was his only job.

The official members of the band were Dr. Teeth, Sgt. Floyd Pepper (an homage to both the band Pink Floyd and the Beatles classic Sgt. Pepper's Lonely Hearts Club Band), the flower-childish Janice (named after '60s songstress Janis Joplin), sax player Zoot (named for real-life saxophonist Zoot Sims), and the most famous member of all, their drummer Animal.