If one were only to consider his professional achievements, the years 1956 to 1969 could easily qualify as the most productive of Rochberg's entire career. In addition to enjoying the positive critical reception of three major works—the Symphony no. 2 (1956), Contra Mortem et Tempus (1965), and Music for the Magic Theater (1965)—he also received two Guggenheim Fellowships a decade apart (1956 and 1966), was awarded the prestigious Naumberg Recording Award in 1961, and earned an academic position at the University of Pennsylvania that allowed him to devote more time to composing. Over the course of these thirteen years, Rochberg completed twenty-five works, including four major orchestral compositions, three works for small chamber orchestra, nine instrumental chamber works, five settings for vocalists, and four solo keyboard works, including the well-known Nach Bach (1966). It was a prolific period of accomplishment that would have been the envy of any young composer entering his prime.

Privately, however, his emotional world felt as if it were spiraling out of control. As he noted in his autobiography, the “war experience had etched itself deep into my soul, and afterward I lived with an ever-sharpening awareness of … the abyss I saw, in a world coming apart at the seams.” In 1956, directly after the completion of his Second Symphony, Rochberg struggled with a foreboding sense of doom that adversely impacted his ability to compose. The political state of the world—specifically the collapse of colonial power in Egypt—had made him fearful for Western culture and the positive cultural values he believed it espoused. “The West is breaking up. We are the last generations,” he lamented in his journal. “What an agony to live between music and the world. In music we order the conditions of the world. We free ourselves from bonds, from restraints the world imposes on us as humans.”

In 1969, Rochberg assembled ideas drawn from his personal journals into the essay “No Center,” a quasi-poetic manifesto for a new aesthetic philosophy: ars combinatoria, or the art of combination. Therein, he advocated for a postmodern technique of assemblage and collage that would result in “a complex of attitudes and ideas … surrounded by a vague aura of association.” But Rochberg's philosophical conceit was more existential than the mere collection of objects and stylistic gestures into new musical contexts. In his mind, ars combinatoria was not a compositional technique or theory but an “exploration of deep inner space, mental space.” It promoted artistic expressions of human connection that reflected “a state of mind and soul against death and time” as well as “the survival of our inmost, immaterial essence.” At the core of his philosophy were the values of love and inclusivity, which manifested themselves in the repetition and embrace of the canonical repertory. As Rochberg described, “Everything we love belongs to us. That includes the past and the future. We are the present.” He continued: “360 degrees of past, present, future. All around me. I can look in any direction I want… . Inclusivity… . The liberation of the imagination … implies the freedom to move where the ear takes us and to bring together everything which seems good to it… . We can choose and create our own time.” The result was a rich multi-directionality limited only by one's imagination and aural reach.

While it has been suggested that Rochberg drew inspiration from the philosophical ideas of Gottfried Wilhelm Leibniz, who wrote about an “art of combination” in his Dissertatio de arte combinatoria (1666), the composer actually seized on the term after reading Labyrinths (1962), a collection of writings by the Argentinian writer Jorge Luis Borges.