What is Absolute Music?

Roger Scruton has a most interesting answer to this question in The New Grove Dictionary of Music and Musicians, 2nd edition. He writes about people wanting a pure music, like pure Mathematics - music for its own sake, music without external influences. He goes on to say that this is impossible, pointing out that music is more than its sounds and structure - our experience of it is a vital ingredient.
The opposite of absolute music is thought to be program music - music that tells a story, or is inspired by a picture or poem. And music that accompanies or is accompanied by words - sung or spoken - can’t be absolute music. Wherever music is subservient to other art forms, or linked with them, the additional ingredients mean it is no longer just music.
When I was a child, I discovered that my father’s limited experience of orchestral music (presumably from his school days) meant that he thought that symphonies were always telling a story. When I was listening to my record of Beethoven’s Fifth Symphony which my Uncle Dave gave me, he would ask “And what’s happening here?” as if I could tell him that the loud part is all about say, a group of men fighting a battle.
Some composers do attempt to tell a story with their music, of course - such as Beethoven’s Pastoral Symphony which has titles for each movement:

1. Awakening of cheerful feelings on arrival in the countryside
2. Scene by the brook
3. Merry gathering of country folk
4. Thunder, Storm
5. Shepherd’s song. Cheerful and thankful feelings after the storm.

But attempts to tell a story with a piece of music can be unsuccessful. Would we have thought of the same program, if we had not been told? Or, does it sound rustic to us, because of all the music we have learned to associate with pastoral settings?
In a chapter in Fritz Spiegl’s Book of Musical Blunders and Other Musical Curiosities, titled after Stravinsky’s famous saying: Music expresses nothing, he tells the story of Victorian composer Francesco Berger composing a piano piece with a strict bar-by-bar musical program, but keeping it to himself. He played the piece to three of his fellow composers and asked each to write down what he thought the music portrayed.
The first, a Welshman, said in perfect seriousness, that the piece meant “Daybreak as seen from the lowest gallery of a Welsh coal-mine.”
The second declared it depicted a boar hunt in Russia.
The third thought the piano piece suggested an enamoured couple whispering love vows.
But Berger said he was trying to illustrate “The discovery by Pharaoh’s daughter of the infant Moses in the bulrushes!”
Spiegl also tells us about the time a lady told Richard Strauss that she could picture a succession of the hero’s conquests in his Don Juan tone poem. Strauss couldn’t resist asking her, if she’d noticed that one of the girls had red hair!