To facilitate composing or analysis of serial music, it is useful to represent all four
transformations of a row in each of the transpositions (thus 48 possible forms) in a 12 x 12 matrix.
For example, look at the matrix of transpositions for the given Prime 0 row:
Notice that the first row of the matrix is the Prime 0 row, P0. Other prime rows are read left to right and are indexed by the leftmost entry of the row. For example, look at P6. Retrograde transformations are rows read right to left and are indexed by the leftmost entry of the row. For example, look at R9. Inversion transformations are columns read top to bottom and are indexed by the topmost entry of the column. For example, look at I8.
Retrogradeinversion transformations are columns read bottom to top and are indexed by the topmost entry of the column.
For example,
look at RI5.
