A Quarry for Melodies

The following quotes are from Rosen's brilliant little book,
Arnold Schoenberg.  Italics are mine.

The series:

The series, in fact, is not an order of pitches but of what is called pitch-classes.  For example, in the first two notes of the series of [Schoenberg's] opus 25 . . . as long as some E, high or low, is followed by any F, the serial conditions are satisfied.  Tonal music had gone only part of the way to asserting the equivalence of all octaves, but Schoenberg's serialism went much further, and made it the structural foundation of his music. (p.82) 

The series is not a musical idea in the normal sense of that phrase.  It is not properly speaking something heard, either imaginatively or practically; it is transmuted into something heard. The motif, on the other hand, is an idea heard, and Schoenberg's development of motivic material . . . is remarkably sophisticated . . . . (p.78)

The waltz [no. 5 of opus 23] breaks open the previous aesthetic with great consequences for the future by its nonmelodic conception of the basic motif or set: except at the beginning, the order of twelve notes is not a melody, but a quarry for melodies. (p.77)

All the music of this immense work [Moses und Aron] is drawn from the transformations of a single series: it is the triumph of Schoenberg's ideal of drawing a wealth of themes from a single source.  The series is no longer conceived in any way as melodic, but the main interest still lies in the creation of melodies. (p.94)

Unit of composition:

The periodic nature of serialism means, too, that the fundamental unit of music composed in this form is not the note but the series as a whole, a larger unit and harder to grasp–for composer as well as listener. (p.104) 

The series has a rhythm of its own opposed to the classical forms in that it is periodic, constantly recurring.  By this quality it transcends its inner organization.  The periodicity is of an exceptional sort in that it is totally independent of pulsation, unrelated to a measurable tempo. (p.103)

Counting notes:

Schoenberg . . . wished the public to remain unaware of the serial techniques. (p.88)

Charles Rosen