Composing microtonal

All my experiments with microtones are mainly inspired by things like gamelan music where its really that the music adheres to modes that don't necessarily adhere to equal temperament rather than an extension of equal temperament. That can be quite pretty sometimes (check out Music From the Morning of the World: The Balinese Gamelan from the Nonesuch Explorer Series).

A lot of times I'll use it for embellishment. I'll bend a note up a quartertone instead of a semitone, which is a device used by bands like Sonic Youth and Deerhoof. A lot of early blues guitarists used to bend up between the minor and major third. I've also heard it make a regular melody or chord progression sound more tense or "unhinged."

Also, a lot of composers use it to create masses of sound. They use it to make even denser clusters or slides which the brain registers as a single mass of noise. This is fun to do too. The Darmstadt composers were all over this, but for a reference in popular music think the mass of strings towards the end of "How to Disappear Completely" by Radiohead.

Pay in mind that timbre is important in all of these cases.