Later reissues replaced "Exhibition" with Alan Shorter's composition "Mephistopheles", though the track listing on the disk labels and LP cover remained unchanged.

The title of the track "27 Cooper Square" refers to an address in Manhattan's East Village which was formerly an artistic and musical hot spot, and home to LeRoi Jones, Archie Shepp, Elizabeth Murray, Sirone, among others.

In a review for AllMusic, Thom Jurek wrote: "While the music here feels, and for the most part is entirely improvised for maximum visceral effect, Brown already has his tone and style and is a clear standout.

"[5] Writing for Bandcamp Daily, Marc Masters commented: "Compared to the rest of the early ESP jazz catalog, Quartet is somewhat conventional, with clear structures behind each track.

"[8] Writing for Point of Departure, David Grundy described Brown as having a sound that "tended towards the abstrusely melodic, with a marked lyrical tendency offset by an astringent bite that could peel the paint off any wall", and also praised Shorter's playing, noting that the version of "Mephistopheles" on Marion Brown Quartet "is twice the length of that on The All-Seeing Eye, increasing the tempo from a lugubrious dirge to a faster clip.