The late R.L. Burnside and Junior Kimbrough—guitarists, vocalists and composers—remain legendary as master purveyors of “hill country” blues, a style specific to north Mississippi, particularly in the area around the town of Holly Springs.

Remarkably, their respective, very talented grandsons, Cedric Burnside and Trenton Ayers, continue their legacy as the Cedric Burnside Project. “I think that’s a blessing,” says drummer, vocalist and ...