In J.R.R. Tolkien's The Lord of the Rings (book 1 of "The Fellowship of the Ring", chapter 7, "In the House of Tom Bombadil", specifically) the character Tom Bombadil sings many of his lines (much of which is nonsensical), eg.
Hey dol! merry dol! ring a dong dillo! \ Ring a dong! hop along! fa lal the willow! \ Tom Bom, Jolly Tom, Tom Bombadillo!
or, an example which contains actual words:
Old Tom Bombadil is a merry fellow; \ Bright blue his jacket is, and his boots are yellow.
Tom's prose lines also follow the same meter and mode as the verse, eg.
'Here's my Goldberry clothed all in silver-green with flowers in her girdle! Is the table laden? I see yellow cream and honeycomb, and white bread, and butter; milk, cheese, and green herbs and ripe berries gathered. Is that enough for us? Is the supper ready?'
'That is right!' said the old man. 'Now is the time for resting. Some things are ill to hear when the world's in shadow. Sleep till the morning-light, rest on the pillow! Heed no nighlty noise! Fear no grey willow!'
The placement of punctuation and the stresses force you to read the prose lines almost as if they too were verse, but it's not a mode which I recongize.
The only thing which I can find that has a similar meter is Cædmon's Hymn, and old english poem which Tolkien most certainly would have read, given his academic background. It has a famous Latin translation by Bede that follows a similar syllabic structure and meter to Bombadill's rhyming:
Nunc laudare debemus auctorem regni caelestis, potentiam creatoris, et consilium illius facta Patris gloriae: quomodo ille, cum sit aeternus Deus, omnium miraculorum auctor exstitit; qui primo filiis hominum caelum pro culmine tecti dehinc terram custos humani generis creavit. omnipotens
What is this mode or style called, and what are its defining characteristics?