If you have been given this assignment, you have been supplied with a score of Schoenberg's short piano piece, op. 19, no. 2 . A recording is linked on the main listening page.
With this piece we will start to go deeper analytically with a piece of freely atonal music, trying to get a sense of how the various parts relate in a way that gives a sense of overall progression or narrative.
We'll start with a simple observation: thirds are prominent in this piece, and major thirds seem to be more prevalent than minor thirds. Go through the score with an ear and an eye for thirds; what relationships and progressions stand out to you?
Now start to think about slightly larger sets -- trichords. What trichords seem important in this piece and why? Look and listen especially for trichords involving the thirds.
It is rare for more than three notes to sound at once in this piece; this makes the three more dense chords stand out. Find their set classes and interval vectors. How do these chords relate to stories about trichords? Do these chords relate to any collections that you know (e.g. whole tone, octatonic)?
Consider the possible role of such collections in this piece; do you find passages in which they might be relevant?