Prime 0 Row

The original row of the piece is known generally as the Prime 0 row ("P0"). Basic transformations of an ordered series of pitches are transposition, inversion, retrograde, and retrograde-inversion. In this modular 12 system, a set of pitch classes may be transposed by adding a number from 1 to 11 to the original row, such that any sum equalling 12 or greater will be reduced by 12 (e.g., 5 + 9 = 2 mod 12). The result of transformations by transposition, inversion, retrograde, and retrograde-inversion will always produce a new pitch class number from 0 to 11. In this way, the transformations are closed under addition.

For example, if the Prime 0 row P0 is given by

then by transposing P0 up by seven half steps, we obtain P7:





12-Tone Row Retrograde & Inversion