What term refers to multiple improvised interpretations of the same melody played simultaneously?

The term that refers to multiple improvised interpretations of the same melody played simultaneously is heterophony. In heterophony, a single melody is ornamented or elaborated upon by various performers, often leading to different interpretations and variations of the same melodic line occurring at the same time. This approach is commonly found in various musical traditions around the world, where musicians take a shared melody and add their unique embellishments, resulting in a rich texture.

Polyphony, on the other hand, involves multiple independent melodies being played or sung simultaneously, which is distinct from the concept of a single melody undergoing variations by different voices or instruments. Monophony describes a single melodic line without accompaniment or harmony, while homophony features one primary melodic line accompanied by chords or harmonies. Each of these terms describes different textures and structures in music, but heterophony specifically captures the essence of varied interpretations of the same melodic idea.