The Matrix
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. Also, notice that the main diagonal of the matrix consists of the pitch class number 0. 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.
Retrograde
& Inversion
The
Procedure
