Final answer:
The school of composers known for a smooth style of polyphony is the Ars subtilior, which was prominent in the late 14th century and featured complex, refined works.
Step-by-step explanation:
The school of composers that wrote a smooth style of polyphony is the Ars subtilior. This musical style emerged in the late 14th century, centered in what is now southern France. The Ars subtilior (which means "more subtle art") composers are known for their complex and refined works with intricate rhythms and notational innovations. This style was a development of the Ars Nova movement of the 14th century, characterized by its complexity and intellectual sophistication. It stands in contrast to the smoother, simpler style of other schools like the Burgundian school, which came slightly later and was known for its clarity and lyricism.