Phasing
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In the compositional technique phasing, popularized by composer Steve Reich, the same part (a repetitive phrase) is played on two musical instruments, in steady but not identical tempo. Thus, the two instruments gradually shift out of unison, creating first a slight echo as one instrument plays a little behind the other, then a doubling with each note heard twice, then a complex ringing effect, and eventually coming back through doubling and echo into unison. Phasing is the rhythmic equivalent of cycling through the phase of two waveforms as in phasing. Note that the tempi of the two instruments are almost identical, so that both parts are perceived as being in the same tempo: the changes only separate the parts gradually. In some cases, especially live performance where gradual separation is extremely difficult, phasing is accomplished by periodically inserting an extra note into the phrase of one of the two players playing the same repeated phrase, thus shifting the phase by a single beat at a time, rather than gradually.
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 album Taking Tiger Mountain (By Strategy).
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.