Imagine that you're a composer, and that you ish to write a 12-tone piece. In the process of developing your Po, you've carefully considered the issues presented on the "Kinds of Row Forms" page--but there's more. The items presented on this page are certainly related to the construction of a Po, but they also have to do with the combination of different row forms--in other words,, this deals with why the particular row forms are used.
Aggregates: Schoenberg was very concerned with avoiding octave doublings of pitch classes when two or more voices present 12-note row forms simultaneously. When all 12 pitch classes appear in a texture within a relatively short space of time, this is called an aggregate.
Combinatoriality: this is the term applied (first by Milton Babbitt) to describe aggregates systematically produced by parts of two different row forms (usually a P form and an I form) when presented simultaneously. Generally what happens is that the first hexachord of one row form and the first hexachord of another row form presented simultaneously contain completely different pitch classes; thus, all 12 notes are used within a small span of time and an aggregate is produced.
Invariant Subsets: an invariant subset is some segment of one form of a tone row preserved in another form of the same row. Using an example from a tonal row: given the pitch class collections CDEFGA and DEFGAB, the segment DEFGA is invariant. The idea of invariant subsets is an important concept when determining why composers used the row form they did. Notice carefully that the actual pitch groupings themselves are called invariant subsets while the concept is often called invariance. If you think for a moment, you'll realize that this is sort of the antithesis of combinatoriality--invariant subsets create the recurrence of paired or grouped pitches, thus associating them closely with one another; this is quite the opposite of combinatoriality. While Schoenberg and Babbitt are known for combinatoriality, the composer most often associated with invariance is Webern.
Overlap of Tone Rows: this simply means that two adjacent row forms are used because the last few pitch classes of the first are the same as the first few pitch classes of the second. For example, if one row ends with the pitch classes A D E and the next begins with A D E, one can state them only once; thus, an overlap is created. Webern is best known for this.
Rotation: the creation of new rows by moving pitches from the end of a row to the beginning, in order. This is often applied to rotation of the two hexachords separately to derive new hexachords. Stravinsky is best known for this technique.
Secondary Set: successive statements of noncorresponding six-note segments (second half of one row form, first half of the next, etc.) so that an ordered presentation of all 12 pitch classes (an aggregate) is present, but the ordering is not one of the forms from the matrix. Perhaps the best-known composer who uses this technique is Milton Babbitt.
"Total" Serialism: the application of ordering procedures to aspects other than pitch, usually rhythmic rows or dynamic rows are used. It's sometimes known as multi-parametric serialism; Milton Babbitt, and others used it in various ways.