Phasing is a compositional technique inspired on tape phasing (also, tape flanging or double-flanging) -an audio effect.
The first use of flanging as an audio effect is credited to Ken Townsend, an engineer at London's Abbey Road Studio where the Beatles recorded their albums. In 1966, Townsend developed flanging for John Lennon who sought a mechanical process to emulate the sound of double-tracked vocals without actually recording two different tracks. The effect was created by running two identical copies of one tape on open-reel analogue machines, and then recording the combined output of the two onto a third reel. By exercising light hand-pressure on one of the playback reels, it caused that tape to run slightly slower than the other. The delay imposed on one tapes when combined with the output of the untouched tape alters the original frequency spectrum, creating peaks and notches around certain frequencies changing accordingly to the the actual time difference between sources (usually, around 20 ms). Consequently, certain frequencies in the signal are boosted (said to be in-phase, constructive interference) or canceled out (said to be out-of-phase, destructive interference).
As a compositional technique, phasing behaves in a similar way to the related audio effect, except that it operates on a much larger time-scale: two voices playing the same identical material at the same time (said in unison or to be in-phase), where one of the voices gradually shifts out in time from the other, usually by inserting in the repeating cycle a discrete unit of a time per cycle (in the form of an extra note or extra rest), hence delaying the following iteration of the rhythmic pattern or motive.
It has been popularized by many composers, including Gyorgi Ligeti (1923-2006), and most notably Steve Reich (1936), who made it a trademark of Minimalism in music.