It's not quite the same thing, but last week I was listening to a presentation, and the presenter naturally dropped into a very regular meter with his delivery - very much the way you would read rhyming couplets. It was weirdly hypnotic, to the point where I stopped listening to the words and got lost in the rhythm of the sounds he was making, as if it was music.
I'm not musically trained, and almost all of the structure and techniques being employed in songs go over my head, but recently I've started listening to the Strong Songs podcast by Kirk Hamilton (he of Kotaku fame). He breaks down the music in well known catchy songs to a really forensic level - to the point where they are just sounds, and then layers them back together to show how this all work together to hook into your brain. It's worth a listen.
Anyway, welcome to the forum and great topic.