[2] The album was recorded at Atlantic Studios in New York City over the course of three sessions on July 19 and 26 and August 2, 1960, with seven selections culled from 23 masters.

[6] He also paid tribute to his bandmates, writing that "the experience of playing with these men is unexplainable and I only know that what they know is far beyond a technical explanation for me to convey to you.

"[6] In a retrospective review for AllMusic, Steve Huey noted that the word "our" in the title of the album "makes clear just how important the concept of group improvisation was to Coleman's goals.

He wrote that "[t]he uptempo tracks here are teeming with life" and noted that "sporadic surges in tempo are early experiments in elastic time (a trend that would be explored at great length as the 60s progressed), and these bursts of energy make these pieces seem, well, bountiful.

"[7] Writing for All About Jazz, C. Michael Bailey called This Is Our Music "the militantly expressed jumping-off point... on the way to the epochal Free Jazz", and stated that Coleman "takes a stand here, pushing his vision of musical freedom farther than on any previous release", and "fully leaps the edge of tradition into the chaotic and sublime future he, himself, was forging."

"[11] Pianist and composer Ethan Iverson called the version of "Embraceable You" on the album "probably the ultimate Rorschach test for Ornette’s fans and skeptics...These days I no longer hear the form as constantly getting lost, but instead as a through-composed collective improvisation.

He concludes that "Coleman was and remains principally absorbed in the immediacy of human emotion, and his impressionism is still the high-water mark in transposing a feeling.