I can't speak for any other composers, but I have, on occasion, dreamed that I or someone else was performing a song, and when I woke up it was stuck in my head and turned out not to have existed prior to that time. It's a great way to write songs when it happens (my lifetime total is 3 songs) but it can be upsetting when you can't remember it when you wake up. The most maddening experience of this nature was a dream in which the music playing was gorgeous, and changed keys frequently, but in an elegant and harmonious fashion. Of course, when I woke up I couldn't remember a note of it, just the sense of this elegant and constant key change.

It wasn't until years later when my wife and daughters were studying piano that I finally heard a piece of music that did this (and much more elegantly than my dream song) and it was only 300-odd years old: Bach's Sinfonia No. 9 BWV 795.

Bach was a great musical experimenter, and his music is like the audio embodiment of pure mathematics. I remember reading an article once about a medium who claimed to communicate with dead composers, and she said Bach loved the possibilities of computer music. While I don't really buy the notion that all the great composers channel their post-mortal communications through one person, I have to admit that this one snippet sounded plausible - yes, of all the famous composers who've lived and died, can't you imagine J. S. Bach sitting at a workstation with Logic or Digital Performer?

This one piece sounds like Bach sat down and consciously tried to create a piece which changed key as often as possible without losing the thread. It's dark, it's moody, it's disorienting, and in the hands of Glenn Gould, it's incredible. (Gould played all the Inventions and Sinfonia, and when he didn't like one he would play it impossibly fast - clearly he liked this one)