Final answer:
The term used to describe spontaneous sets of variations on a stated musical theme is improvisation, which is distinct from avant-garde, Baroque, or atonality.
Step-by-step explanation:
The term used to describe spontaneous sets of variations on a stated musical theme is improvisation. Improvisation in music involves creating and performing music in real-time without the need for written notation or full preparation. This form of musical expression allows musicians to invent melodies, harmonies, and rhythms on the spot, often within the framework of a given musical structure or theme.
In contrast, terms like avant-garde refer to innovative, boundary-pushing art, Baroque is a period and style of music from the 17th to the early 18th century known for its ornamentation and complexity, and atonality refers to music that lacks a tonal center or key, a concept associated with composers like Arnold Schoenberg who experimented with new musical scales and forms.