Since the relationships between keys is usually an important component of sonata-allegro form, I thought it would be interesting to expand its use to atonal music. Instead of using themes in two closely related keys, I used themes with similar sets of interval classes.
My first theme is based on the interval classes 1, 5, and 6 (minor 2nd or major 7th, perfect 4th or 5th, and tritone) while my second theme is based on 1, 5, and 4 (major 3rd or minor 6th). Because they share two interval classes in common, they sound closely related and allow for a smooth "modulation".
For my developement section, I fragment and sequence motives from the themes resulting in harmonic intervals extending beyond the interval classes found in either of the themes. This is meant to be analogous to the modulation to more distant keys found in a traditional development section.
For my recapitulation, both themes are repeated, but the second theme is "transposed" to the first set of interval classes. This is accomplished by replacing the intervals of a major third with tritones. This is meant to correspond with a standard sonata-allegro movement resolving to the tonic key.
Enjoy!