A Clever Turn of Phase
You most likely have an effects box or plug-in that offers flanging--a process that involves splitting a signal into two copies, slightly delaying one of the copies, and varying the delay time. Flanging was originally a real-time tape process in which an audio signal is recorded and played back simultaneously on two tape recorders. The term flanging refers to applying pressure to the flange of the feed reel on one of the recorders, thereby slowing it down and causing a slight delay in one of the copies. Varying the pressure varies the tape speed, producing the familiar whooshing sound associated with flanging.
Mixing two copies of the same audio file while slightly delaying one of them causes some frequencies to be attenuated while others are enhanced. That is the result of shifting the phase of the individual sine wave components of one signal with respect to the other. For example, if the delay causes a half wavelength shift at a particular frequency, that frequency will be cancelled entirely, whereas if it causes a full wavelength shift, that frequency will be doubled in level. Other amounts of shift cause varying degrees of attenuation or enhancement. If you don't vary the delay time, you'll get a coloration of the signal without the more noticeable motion associated with flanging.
Slightly delaying a loop and mixing it with a copy is easy in a multitrack audio program. Just put the loops on different audio tracks and nudge one of the loops slightly forward in time. It's a process that works well with atmospheres and ambient loops. Shifting the copy by a slightly different amount for each repetition of the loop adds slight timbral variations that make the loop more interesting without being obvious. Moving adjacent repetitions of the loop by different amounts produces a small gap or overlap, depending on which copy is moved more. That may be masked by the track playing the other copy of the loop, but if there's an audible problem, it's easily repaired by slightly adjusting the loop lengths or applying a short crossfade.
As you'll discover, some shifts sound better than others, and the only way to know is to try them out. For that, it's convenient to set the working tempo so that the loop fills an exact number of measures, because that makes it easy to cycle a single repetition while nudging one of the copies. If you plan to repeat the loop a large number of times in your song, you don't really need to set up an individual offset for each repetition. You can save time by doing a small number of repetitions, then rendering the result to create a new, longer loop. For the best results, use a repetition number that doesn't divide evenly into the size of your song sections. For example, if your song is divided into 16-bar sections, render an odd number of repetitions so the new, longer loop doesn't cycle exactly with the song sections.