Taking Back Sunday’s intimate introduction of its ambitious new album “Tidal Wave” at Irving Plaza proved a rousing success Thursday night.

“It means the world to us to be here to share this with you,” singer Adam Lazzara said after the opening barrage of three straight singles.

The band knows “Tidal Wave,” which debuted at No. 2 on Billboard’s alternative albums chart last week, is special and they wanted to give it a special launch, opting to play it in its entirety in smaller clubs rather than starting its tour in larger venues where fans might get restless for more familiar material.

As impressive as “Tidal Wave” is as a record, its songs get even stronger in concert.

The roaring opener “Death Wolf” showcases Mark O’Connell’s powerful hardcore drumming as much as Lazzara and guitarist John Nolan trading vocals, while the straight-up punk of the album’s title track had the crowd screaming along and forming a mosh pit. The rocking current single “You Can’t Look Back” hits a new gear when guitarist Eddie Reyes and bassist Shaun Cooper move from their restrained opening to an all-out Tom Petty-esque rave-up.

The band took to the stage to Billy Joel’s “New York State of Mind.” After a bit of teasing earlier from Lazzara, who joked the crowd only wanted to hear old songs, the band kicked off the second half of its set with “Cute Without the ‘E’ ” from its classic “Tell All Your Friends” album, which accompanied a bit of reminiscing about previous Irving Plaza shows.

However, with these “Tidal Wave” shows they are on the edge of something bigger artistically.