Experiment and innovation reemerged as the driving forces in music during the third quarter of the twentieth century. It was a fascinating phase — and no less so because two of its main tendencies seem almost contradictory.

First of all, highly intellectual constructive tendencies came to the fore, inspired by Schoenberg’s serialism but going far beyond it. There were even efforts to “serialize” rhythm, dynamics, and timbre — that is, to set up predetermined series of note durations or tone colors or dynamic levels and compose with them in a fixed order. Never before had such complex mathematical theories been advanced to compose and explain music.

Meanwhile, other composers moved in the opposite direction, relinquishing control over some elements of musical construction and leaving them to chance. (We have already discussed an early anticipation of this move, The Unanswered Question by the ever-original Ives.) Some of these same composers also worked toward an extreme simplification of musical materials, offering a stark alternative to the cerebral complexities of post–World War II “total serialism.”

It may seem strange to find composers who followed such different paths grouped together under the same general rubric of avant-garde modernism. However, both groups, the complex constructivists and the chance composers, pursued the same goal: They all wanted to question the most fundamental premises that had guided music composition before them. Debussy might have blurred the identity of melodic themes, Stravinsky might have undermined the regularity of musical meter, and Schoenberg might have dispensed altogether with tonality. But mainstream modernism after 1945 questioned every one of these features of the musical tradition at once and others as well — to the point of even questioning the composer’s role in structuring a work at all.