Naming Conventions for Rows

Every tone row has four basic forms, each available at twelve transpositions, yielding a total of 48 row forms. The Prime (P) is the row in its original ordering. The Retrograde (R) is the Prime read backwards — the last pitch class first, the first last. The Inversion (I) replaces each successive interval with its inversion: if the Prime moves up a major third, the Inversion moves down a major third (equivalently, each pc x becomes (−x) mod 12 relative to the starting pitch class). The Retrograde-Inversion (RI) is the Inversion read backwards.

Transposition levels are indicated by a subscript integer showing how many semitones above a reference point the form begins. The most common convention sets P0 as the prime form starting on the first pitch class of the row as the composer wrote it; I0 begins on the same pitch class but inverts the intervals. Under a different convention, P0 starts on C (pc 0), and all other transpositions are numbered by their starting pc. Always check which convention a textbook or score is using. The 48 forms are organized in a 12×12 matrix — often called the "magic square" or row chart — where rows read left to right give P forms, right to left give R forms, columns top to bottom give I forms, and bottom to top give RI forms.

To construct the matrix, write P0 across the top row. Compute the inversion of P0 down the left column: each successive entry is the previous entry plus the inverted interval of P0 at that position. Fill each remaining row by reading across from the left-column starting pitch class, applying the same ordered intervals as P0. Once built, the matrix makes it easy to read off any of the 48 row forms at a glance, and analysts use it to identify which form is operative at any moment in the score.