I have started reading about Serialism and this post is actually my interpretation of 12-tone Serialism, which will be followed by subjects such a Rhythmic and Total Serialism in the next coming weeks.
Serialism is a method (or technique) of composition applying to pitch, rhythm, texture or even timbre. At the beginning Schoenberg suggested Serialism, but the method was used by Alban Berg and Anton Webern and later on by composers such as Luigi Nono, Pierre Boulez, Karlheinz Stockhausen, etc.
In 12-tone serialism a series of pitches are chosen among the 12 chromatic pitches and are used whether in prime (P), inversion (I), retrograde (R), or retrograde-inversion (RI). By application of any of the mentioned techniques to a series of 12 pitches, the new set of pitches will be a totally new one sharing no pitch with the Prime version. It is worth considering that this result is the desired result for Schoenberg, following his predecessors on the way of abandoning tonal center, and eventually arriving to the point of equal emphasis on either of the pitches. One of the examples of this usage is his Variations for Orchestra Op.31. In such manner of music, the accompaniment part(s) is (are) can be the I, R, IR of the theme, or a bit of it. Schoenberg mastered this method to a really complicated point, that in some cases recognizing the strategy he has used in a piece, takes long time, great concentration and developed knowledge of this method. Application of rhythmic modifications is possible in 12-tone serialism. The interesting point is that Schoenberg was interested in integrating 12-tone serialism with conventional textures (theme and accompaniment) and formal structures (such as sonata, variation) that obviously resulted in a great complexity in either of them.
Paul Griffiths, Heading: Serialism, http://www.oxfordmusiconline.com/subscriber/article/grove/music/25459?q=serialism&search=quick&pos=1&_start=1#firsthit