Atonality is primarily associated with the early 20th century, particularly during the late 1910s and 1920s. This era witnessed a significant shift in musical composition, moving away from traditional tonal structures that had dominated Western music for centuries. Composers such as Arnold Schoenberg, Alban Berg, and Anton Webern were pivotal in developing and exploring atonality, which is characterized by the absence of a tonal center or key.
Schoenberg, in particular, is known for his twelve-tone technique, which further expanded the idea of atonality by providing a structured approach to composition without adhering to traditional tonal hierarchies. Thus, if you are looking for the era where atonality is most prominent, the early 20th century, especially the 1910s to the 1930s, would be the key period.