Music Theory for the 21st-Century Classroom

Minimalist composer Steve Reich conceived of phase shifting in his early work in tape music, noting that tape loops of slightly differing lengths containing the same idea went slowly out of phase and very gradually back into phase when they were repeated incessantly (see It’s Gonna Rain¹ from 1965 and Come Out² from 1966). Reich applied this phase–shifting process to live performance in Piano Phase³ (1967), Violin Phase⁴ (1967), and Clapping Music⁵ (1972).

Below is the basic twelve–note pattern of Piano Phase along with a video demonstrating the phase–shifting.

During the phase–shifting process, one can think of the lower voices in the examples above as going through rotation. The example below shows rotation of a five–note pattern. The pattern rotates one note to the left, meaning the second note begins the pattern on the second line, the third note begins the pattern on the third line, etc., until the first note starts the pattern again to complete the phase–shifting process.

In a piece of music, the process would play out similar to the manner below, where one part maintains the original pattern while the second goes out of phase by continually rotating the original pattern one note to the left. In Piano Phase, Reich has the second pianist gradually increase in speed so the patterns go slowly out of phase, while in Clapping Music, Reich has the musicians change to the next rotation on the downbeat of a measure, without gradually speeding up.

One hears phase shifting in numerous works by Reich, including the second movement of his Three Movements.

It is worth mentioning that composers like Stravinsky applied rotation to serialism, which Joseph Straus details in Chapter 6 of his Introduction to Post–Tonal Analysis (4th edition).