When I changed the time signature on my music app, the loop stayed the same length in beats, even though it no longer ended on a measure.
After forgetting to disable the loop as I always do, I heard the melody overlapped by itself with a two beat delay which sounded absolutely lovely.
I also played the completely wrong chord progression, which also sounded lovely.
So that I don't leave discovering these delights to chance, I should probably be trying these techniques systematically.