What compositional method is characterized by the systematic ordering of pitch classes?

The compositional method characterized by the systematic ordering of pitch classes is known as Serialism. This technique was developed in the early 20th century and involves using a predetermined series of pitches, often encompassing all twelve tones of the chromatic scale. Each pitch in the series is treated with equal importance, eliminating traditional tonal hierarchy and allowing for a structured yet varied musical outcome.

In Serialism, the composer manipulates the series through various techniques such as transposition, inversion, retrograde, and fragmentation, creating a composition that remains cohesive while exploring different musical ideas. This method provided a way to compose music that deviates from traditional tonal frameworks, making it a revolutionary approach to music composition.

Other options reflect different compositional methods that do not prioritize the systematic ordering of pitch classes in the same way. For example, Polytonality involves the use of multiple tonal centers simultaneously, Quartal Harmony focuses on building harmony using fourths, and Atonality refers to music that does not adhere to established tonal centers but does not involve the strict organization characteristic of Serialism.