So I was playing around with some delay settings and came across a really cool way to achieve accompaniment. It's pretty odd to explain, so I'll just tell you where I got the idea from:
Clapping Music - Steve Reich
I was curious about achieving this not in a rhythmic sense but in a melodic sense, so I cobbled together a simple 8-note pattern. I set the delay up and brought it further from said pattern. In Renoise (a tracker DAW I've been using), it takes 64 lines to get back to the exact timing of the original pattern, so there were plenty of musical ideas available. I chose two, and I juxtaposed them so they form a short loop. They're to be uploaded shortly.
If anyone else who reads this cares to try it, I'd love to see the results.