What is a twelve-note row/series?

A 12-note row is the structural unit of a 12-note composition, which is bound to the fixed succession of 12 notes (11 intervals). It is to be formed according to rules that prevent any suggestion of tonal connection. Repetitions of notes before the end of the row are permitted only as an exception. Anything that can lead to the preponderance of one note (a tonal centre of gravity) has to be avoided.

The 12-note row can appear in its basic form, in inversion, in retrograde motion and in retrograde inversion. These four modes can be transposed on any of the 12 notes, so that 48 modes can be derived from one basic form. 

The notes of the row are not related to the root tone but only to one another. The same applies to the various melodic figures in which they occur during the work 

The row is the basis for the structural material of a composition and need not be identical with its theme. 

Any row can develop horizontally and vertically, it can proceed in individual notes or in clusters in several voices. The course of the row is repeated during the composition and can appear simultaneously or successively with its inversion, its retrograde respectively its retrograde inversion.  

"Composition with twelve notes only related to each other" (Summary) 

Twelve-note row