The Minimalist Approach
In 1965 and 1966, Steve Reich composed two minimalist pieces consisting entirely of repetitions of a speech loop. Copies of the same loop were played on two tape recorders, but one copy was spliced slightly shorter than the other. As a result, the loops started in synchronization and slowly drifted out of phase. The key word here is slowly. The minimalist nature of the process requires that the evolution be barely perceptible, with the result that at various times you suddenly become aware that you are hearing an entirely new cadence or rhythm.
Creating that kind of phase process in a digital audio sequencer is again extremely simple. Place single copies of the clip to be looped on two tracks, and use a high zoom level to slightly shorten one of the clips by a few milliseconds. (You don't necessarily have to restrict yourself to the same clip for both tracks.) Then loop both clips for enough repetitions that the clips eventually come back into alignment.
You can calculate the number of repetitions required to come full circle by dividing the time difference into the total time for the unaltered clip. For example, if the original clip is three seconds long and you shorten the copy by 10 ms, you will need 300 repetitions (3,000/10). At three seconds per repetition, that will take 900 seconds or 15 minutes.
You might not have use for a 15-minute, minimalist, shifting-phase loop in any of your songs, but there's more here than meets the ear. And the process is not just applicable to spoken word loops--it produces very interesting results with background parts such as strings, pads, and background vocals. The idea is not to use the whole thing, but to cull it for interesting new loops.
The audio example StringPhase.mp3 is the first minute of a 12-minute piece made using a string loop. The example StringClips.mp3 is made up of nine different loops cut from the full 12-minute piece. (Each loop repeats four times.)
It is easiest to find and extract loops if you start by setting the song tempo so that the original loop occupies a single bar. Once you've looped the clips, render the two tracks to a new audio file, mute the original tracks, and place the rendered file on a new track. Listen to the whole thing, marking measures of particular interest, or simply audition single measures at random until you find something you like. When you find a repetition you like, listen to several repetitions on either side of it--there will be very slight differences, and you may find one you prefer. When you've zeroed in on a specific repetition, slice the audio file at the measure boundaries, and you have a new loop.