I've been reading more about Schönberg and Brahms, and I found that the former adopted a development process inspired by the other. This is constant variation, in which themes are returned each time in a different varied form. I found references to this on allmusic.com in regards to the 5 piano pieces, as well as to his use of serialism (albeit in simplified form other than the waltzer) in them. I apologize that the bulk of my post is a quotation, but I always appreciate these kinds of analysis
"The first of the Five Pieces, Op. 23, marked Sehr langsam (Very slow), demonstrates Schoenberg's approach to the principle of developing variation. When the opening melody reappears, the pitches are the same, but they have been moved to different octaves, changing the shape of the phrase, and are presented in a different rhythmic configuration. The retention of the pitches alone is enough to constitute a return to the theme, and through this piece we can gain insight into how Schoenberg uses pitches, not rhythms or melodic shapes, at the core of a composition. This concept lead directly to his formation of the 12-tone method.
Variation procedures continue in the second movement, Sehr rasch (Very fast), although some analysts have uncovered a sonata form structure. In this brief piece, the vertical aspect of the music is a result of the linear melodic movement.
The third piece of the set, Langsam (Slow) — sometimes referred to as a fugue because of the alternating entrances at the beginning — is again driven by variation technique. A five-note motive is put through metamorphoses so intense that at times it seems a single pitch could be considered part of any one of several forms of the motive.
Rhythmic freedom characterizes the fourth piece, Schwungvoll (Full of vitality). Here, Schoenberg juxtaposes sections of dense and sparse textures, separated by brief pauses.
Although the first four works of Op. 23 exhibit 12-tone techniques to a limited degree, these apply to smaller collections of pitches, not the entire 12 of the chromatic scale. The fifth and final work of the set (Walzer), however, is based on the repetition of a series or row of all 12 pitches. Everything that happens in this piece, both vertically and horizontally, is derived from the same series of pitches appearing in the same order. This is Schoenberg's most transparent and straightforward usage of these techniques. Schoenberg's next works, particularly the Suite for Piano, Op. 25, and the Quintet for Winds, Op. 26, would witness an expansion of the method and a greater self-assuredness on the part of the composer."
Somehow I disagree with the last comment; right now I don't see his use of serialism in the suite as being self-assured by any means. The more I listen to the 5 pieces, the more they reveal themselves to me as being beautiful pieces ever the equal of his previous keyboard works. However, my favourite piece by the composer is still definately his Serenade, followed by Pierrot Lunaire and his 3 piano pieces.
I hate admitting that I require more experience with the "classics" of classical music, but I suppose that someday I'm going to have to listen to Brahms so I can futher understand his influence on Arnold.