Complex sentence: For much of the rest of the 19th century, the square was an open air market, and "Creole of Color" brass and symphonic bands gave concerts, providing the foundation for a more improvisational style that would come to be known as "Jazz".
Split into simpler sentences: For much of the rest of the 19th century, the square was an open-air market. "Creoles of Color" brass and symphonic bands gave concerts, providing the foundation for a more improvisational style that would come to be known as "Jazz".