How did Arnold Schoenberg use a 12-tone row to create contrapuntal combinations?

Arnold Schoenberg utilized the 12-tone row—a specific, ordered sequence of the 12 notes of the chromatic scale—as the foundational "backbone" for his compositions to replace the structural principles of traditional tonality.123

Rather than serving as a theme with fixed rhythm or shape, the row acts as a musical idea that permeates the work. Schoenberg created contrapuntal combinations by deriving melodies, harmonies, and contrapuntal lines directly from this series. By systematically manipulating the row, he generated a continual variety of thematic shapes and contrapuntal textures.123

In his 12-tone works, such as the opera Moses und Aron, he demonstrated that an entire composition could be spun out of a single row. Because the method ensures that no single note predominates as a focal point, it allows for complex, interwoven contrapuntal structures that function independently of the hierarchical organization found in tonal music. This approach represents a significant evolution of the contrapuntal techniques previously explored by Romantic composers, adapted to a system where all 12 tones are related only to one another.312