The technique originated in Reich's tape music, where the composer sets off several copies of the same tape loop simultaneously on different machines. Over time, the slight differences in the speed of the different tape machines causes a flanging effect and then rhythmic separation to occur. Examples include Reich's Come Out and It's Gonna Rain. This technique was then extended to acoustic instruments as described in the above paragraph and later the change in phase was made immediate, rather than gradual, as in Reich's Clapping Music.
As the cycle unfolds, often other melodies will be created by the differing instances of the original phrase being played together. As in Steve Reich's Violin Phase, the composer will sometimes have an additional instrument or live performer with the tape who playing these secondary, extracted melodies to accentuate them.
An example of phasing in popular music is "The True Wheel" on Brian Eno's Taking Tiger Mountain By Strategy (album).
The playing of different repeated phrases in the same tempo but having different metrical lengths (beats in the bar), as in the music of Philip Glass and others, is not phasing but may be considered polyrhythms.