There are those who think Grace Potter & The Nocturnals are one of the best, tightest, most joyful and energetic rock-and-roll bands in America. And those who are about to find out.

The band blew a big thank-you kiss to its most loyal hometown fans this week in the form of a special live performance of their stellar new album, The Lion The Beast The Beat, at the Higher Ground in Burlington, Vermont. The new album is big and brash, like the stage strut that Potter, who turns 29 later this month, has perfected after a good eight years on the road. It straddles the crossroads where rock, pop and jambands meet, and the band torched through all 11 tracks on the album in order, for a worshipful crowd of true believers (tickets to the show went to the first 500 people who purchased The Lion The Beast The Beat at a single record store in Burlington).

This is a big album in a lot of ways: big ambition, big sound, big payoff. The band has upped their game in every way, from Potter’s vocals, which have reached a whole new of intensity, to the guitar interplay between Scott Tournet and Benny Yurco, superb on album and even better live. The songs on The Lion The Beast The Beat cry out for big venues (not for nothing is the band opening a string of stadium shows for country artists Tim McGraw and Kenny Chesney this summer). In the smaller confines a club like the Higher Ground, Potter had to limit her prowling to just a few square feet of stage, not nearly enough room to really unleash the beast.

The show opened with the pounding of Matt Burr’s drums that herald the intro to the new album’s title track, and never really let up. There’s not a dud track on the album, but it’s real strength is that songs 8, 9, 10 and 11 are just as good as tracks 1, 2, 3 and 4. It rewards those who listen to it in its entirety, and some of the highlights of the show at the Higher Ground were deep tracks like “Turntable,” “Keepsake,” “One Heart Missing” and album-closer “The Divide.”

The band’s new bass player, Michael Libramento, plays his bass upside down and left-handed, but otherwise seems to be a good person. He may have to take on the John Entwistle role as the lone tether that keeps the whole enterprise from swirling too far out of control when the other four let loose.

After running through The Lion The Beast The Beat, Potter and company came back for a double-encore of some of their signature live songs, including “Stop the Bus,” “Paris,” “Medicine” and “Nothing But The Water.” Potter vowed at one point that she would never stop coming back to the venerable Higher Ground, but one senses that there may not be too many more small club shows in this band’s future.