Cleoma Breaux Falcon’s daughter Lulu once told the story of her mother kicking a man in the eye while she performed onstage because she was fed up with his pestering. She also remembered Cleoma always cooking her breakfast, even after playing the night before, and always meeting her at school with a hot, home-cooked lunch.

Few women were bold enough to play the rowdy dancehalls, and they had to be tough. It was almost unthinkable for a woman to perform in any...