Derived row

The opposite is partitioning, the use of methods to create segments from entire sets, most often through registral difference.

In music using the twelve-tone technique a partition is "a collection of disjunct, unordered pitch-class sets that comprise an aggregate".

A cross-partition is, "a two-dimensional configuration of pitch classes whose columns are realized as chords, and whose rows are differentiated from one another by registral, timbral, or other means.

"[4] This allows, "slot-machine transformations that reorder the vertical trichords but keep the pitch classes in their columns.

"[4] A mosaic is "a partition that divides the aggregate into segments of equal size", according to Martino (1961).

Symmetry diagram of Webern's Op. 24 row, after Pierre Boulez (2002). [ 2 ]
The mirror symmetry may clearly be seen in this representation of the Op. 24 tone row where each trichord (P RI R I) is in a rectangle and the axes of symmetry (between P & RI and R & I) are marked in red.