NEW ORLEANS — If any popular-music festival was built to last an unbroken 50 years, it’s the New Orleans Jazz & Heritage Festival. It was already looking back when it started in 1970, assembling a Louisiana Heritage Fair of music and food traditions to glorify connection and continuity. Many of the musical styles it brought together were already generations old. So what’s another half-century?

This year’s Jazz Fest, as everyone calls it, finished its first four-day weekend on Sunday (it continues May 2-5). It’s an institution dedicated to its home city’s particular local and regional culture: not a trademark revived for anniversaries, like Woodstock, or a reboot tied to a cherished name, like the Newport Folk Festival. Jazz Fest’s booking policy leans toward musicians who share something — funk, fiddles, accordions, carnivals, French and Afro-Caribbean connections — with Louisiana lore. And the festival’s physical layout is designed to encourage discoveries. The path from the two main stages to the blues, gospel and jazz tents leads past a Cultural Exchange Pavilion featuring world music and the Jazz & Heritage stage with performances by brass bands and Mardi Gras Indians, New Orleans’s miracles.

Jazz Fest has built its attendance in recent years by adding more pop hitmakers at the top of its bills. But where many pop festivals are simply run-throughs of touring road shows, Jazz Fest visitors tend to incorporate something of New Orleans, having local musicians sit in and savoring the city’s charms. For her appearance on Saturday, Katy Perry performed her hits, but she had her stage set emblazoned with exhortations from the New Orleans-born poet Cleo Wade, and she used the Soul Rebels brass band as a horn section. More than 300 groups performed in the festival’s first four days. I heard a fraction of them, but here are 13 of the standouts.