Sunday, the Narragansett Bay Chorus will visit the Courthouse Center for the Arts for a night of a cappella barbershop-style harmony. The chorus is the performing unit of the Providence Chapter of the Barbershop Harmony Society, which is the largest male singing organization in the world. The night’s program will feature the foursomes Sync or Swim, a female group, and Trade Secrets, who have collectively won more Barbershop Harmony championships than any other foursome in the Northeast. Trade Secrets has appeared on a variety of television shows, including Conan O’Brien’s.