Final answer:
The genre of program music that conveys a poetic idea, story, or scene is the Symphonic poem. This style of music became prominent during the Romantic era and remains significant in the classical music repertoire due to its emotive storytelling and flexible form.
Step-by-step explanation:
The genre of program music that conveys a poetic idea, story, or scene by presenting varied or transformed themes is known as a Symphonic poem. Program music aims to musically render an extra-musical narrative. The symphonic poem is flexible in form and allows the composer to freely express ideas without the structural constraints of traditional symphonic movements. This genre flourished during the Romantic era, which was characterized by a strong emphasis on emotion, individualism, and a break away from the strict forms of the Classical period.
Romantic era composers such as Franz Liszt pioneered the symphonic poem format, and others like Richard Strauss further developed it. Their music, along with that of other Romantic composers including Johannes Brahms, Pyotr Ilyich Tchaikovsky, and Robert Schumann, continues to be popular today. The ability for program music and symphonic poems to paint a scene or narrate a story through music is what makes these compositions unique and enduring.