What term defines music that is inspired by extra-musical associations, such as stories or paintings, particularly prominent in the 19th century?

The term that defines music inspired by extra-musical associations, such as stories, paintings, or other narrative elements, is indeed programmatic writing. This concept became particularly prominent during the 19th century, when composers sought to convey specific ideas or narrative content through their music. Programmatic compositions often include accompanying text or a title that guides the listener’s interpretation, enriching their experience by linking auditory elements to visual or literary sources. This practice allowed composers to explore themes and emotions in a more explicit way, expanding the possibilities of how music could interact with other forms of art.

The other options represent different musical concepts that do not focus on the narrative aspect. Abstract music refers to compositions without direct references to the outside world, emphasizing music's intrinsic qualities. Absolute music describes works that exist independently of any sort of narrative or programmatic idea, focusing solely on structural and formal aspects. Functional music typically refers to music created for specific purposes or settings, such as ceremonial or practical uses, rather than for the expression of a story.