A primary concern of post-tonal theory has been to identify pitch-class transformations that reveal underlying symmetry. This work explores ways in which symmetries in pitch, and particularly in voice-leading, are dynamic entities, forged in a largely asymmetrical context. The two primary types of asymmetry explored are divergence, or departure from perfect contrary motion, and skewness, or departure from perfect parallel motion. These are studied in various two-part frameworks in musical examples by Donald Martino, Luigi Dallapiccola, Roger Sessions, Igor Stravinsky, Arnold Schoenberg, Ernst Krenek, and Arvo Pärt, among others. Each type is explored on its own; then a variety of techniques are developed for modeling their interaction. Finally, the different kinds of asymmetry suggest a variety of generalizations to counterpoint in three or more parts. Connections are drawn to various ideas about voice leading in writings by David Lewin and George Perle, among others.