“That’s It!” starts with a flurry of pounding drums, a pulsing tuba and bursts of trumpets that make up just the beginning of an album of infectious, toe-tapping fun.

New Orleans’ Preservation Hall Jazz Band is releasing “That’s It!” on June 9, a superb album led by co-producer/trombonist Ben Jaffe and co-producer Jim James, the singer of My Morning Jacket.

It’s hard to believe that after 50 years of music, “That’s It!” is the Preservation Hall Jazz Band’s first album of all original recordings. After all, the band has released more than 30 studio, live and compilation albums since the 1960s.

Though the album is steeped in New Orleans tradition, this is a fresh and inventive jazz album.

All the members are from New Orleans, and Jaffe is the son of the band’s founders, Allan and Sandra Jaffe. The couple founded the band in 1961 in the New Orleans French Quarter to nurture and continue New Orleans Jazz.

That music is alive and well on “That’s It!” The opening title sounds like a long-lost gem from the golden age of jazz: It’s powerful, upbeat and full-steam ahead jazz. In fact, the entire album could be a misplaced classic dusted off from a studio’s archives.

The album is an expansive celebration of jazz. Though the long-running band promotes New Orleans jazz, this album is just as much a celebration of New Orleans culture and legend.

Many of the songs, like “Come With Me,” focus on New Orleans.

“Come with me to New Orleans, what a city you will see,” he sings.

It’s as though the musicians are using this album to declare that the culture, heritage and flavor of New Orleans are alive and well years after Hurricane Katrina decimated the historic city.

“Rattlin’ Bones” is played spooky, but fun as it’s set in a graveyard, which pays homage to some of supernatural flavors of New Orleans, backed by a fun array of screaming trumpets and smooth instrumentation.

Trombonist Freddie Lonzo’s sings in a rich, easy tone that’s both playful and serious.

While much of “That’s It!” plays like the soundtrack to one swinging New Orleans party, the music mixes toe-tapping tunes with more somber, sultry tunes like the beautiful “I think I Love You.”

“That’s It!” is a must-listen for any jazz fan.