No matter how you feel about the Grateful Dead and the jam band culture it spawned, you have to appreciate the loftiness of its goals.

These musicians try to deliver sounds like mantras, repeating and extrapolating them until they wash over an audience, shimmering in transcendence.

That’s the best-case scenario, of course. On Sunday evening, the Mickey Hart Band tried its best to reach those heights — and while I can’t say the extended jams transported me to a higher plane, they were delivered with polish, exuberance and a welcome amount of restraint.

Hart, 70, carries the weight of his former band’s towering mythology well. The former Grateful Dead percussionist and world-music aficionado bounced around the stage while his seven-piece band delivered the sun-soaked chords of “Scarlet Begonias,” sprinkling tasteful runs on his cluster of congas and toms.

The tune went over like gangbusters with the tie-dyed faithful, as did the ensuing “Fire on the Mountain,” its lite reggae groove proving to be the perfect framework for that swaying-while-making-shooting-stars-with-your-hands dance.

Both of these songs were stretched beyond the 10-minute mark, with “Begonias” devolving from a lazy river sing-along to a proggy, synth-heavy Mars rover mission.

It was interesting as far as these things go, thanks to Hart’s deeply talented ensemble — singers Crystal Monee Hall and Joe Bagale made the verses the most exciting moments, but the chemistry between Hart, percussionist Sikiru Adepoju and drummer Greg Schutte kept the jams taut.

Deadline constraints kept me from seeing the entire set, but Hart had certainly made his point to me — he’s never going to stop reaching for that moment. Whether he ever gets there or not, the ambition alone is something special.

Joe Sweeney is a freelance writer from Cape Elizabeth.