Luderin Darbone and Edwin Duhon still remember the night in 1934 when the Hackberry Ramblers went electric.

The problem until that time, explains Darbone, the 80-year-old fiddler and co-founder of the group, was that string bands like the Ramblers couldn’t be heard in crowded Louisiana dance halls—not the way accordion-based Cajun bands could. “With our fiddle and two guitars, they could hear us maybe twenty feet,” he recalls. “They could pick out the tapping of our feet on the wooden floo...