Leah Song and Chloe Smith, the effortlessly harmonizing sisters in the folk-jazz-world music group Rising Appalachia, learned how to hold an audience’s attention on the streets of New Orleans. After moving to the city in 2006, the siblings busked in the Royal Street area five and six days a week.

“We took it as our day job, nine to five,” older sister Song explained. “We’d throw our instruments on our backs and bike to ...