"The uptempo tracks here are teeming with life. On "Blues Connotation" and "Folk Tale" the band sounds "in the moment" and brimming with ideas, as if these four- and five-minute compositions are far too brief to ever contain them all. The 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. Also adding to the loose sense of fun on tracks like "Poise" is the interplay between Coleman and Cherry. At times, they seem to be chasing each other around the tune, while other moments find them doing a modern take on the call-and-response ensemble soling of Dixieland. Despite the occasional rubbery rhythmic passage and playful tone, all the faster pieces here swing in the fullest sense of the word, with Blackwell and Haden's pulse set firmly in the tradition.

If the faster tracks on This Is Our Music come across as buoyant and almost pop, the more drawn-out pieces are mysterious and pleasantly disorienting. "Beauty Is a Rare Thing" is drifting and impressionistic, with Blackwell's drums and Haden's bowed bass used for color and shading instead of rhythm. Cherry and Coleman's lines are not concerned with melody or even pitch, but manage to find expression in a series of squeaks, groans, and grunts. The Quartet's take on the Gershwin standard "Embraceable You" (the only track not composed by Coleman, and indeed the only standard he recorded during this period) is necessarily more conventionally tuneful, but it still moves with a peculiar gait. The theme is familiar, but Blackwell uses mallets for the drums and barely touches the cymbals, and both Cherry and Coleman take serious liberties with the melody."

- Mark Richardson, Pitchfork