It was initially released on Parker and Derek Bailey's Incus Records label in 1978,[1] and was reissued by Chronoscope (1999),[2] Psi (2015),[3] and Treader (2020).

[4] In the album liner notes, Parker wrote: "The aim in placing the one stereo microphone used was to find a position in which the sound of the saxophone in that room was reproduced most convincingly.

"[5] In a review for AllMusic, Henry M. Shteamer wrote that the album is "perhaps the next best thing to seeing him perform live," and commented: "When one listens to Evan Parker, one hears a note as well as all the residual tones around it; each breath ends up sounding like a battle between the different registers of the horn.

"[6] A review for All About Jazz states: "On Monoceros, Parker explores a wide range of soprano saxophone work, though most of it is hardly recognizable as such: squeaking, squawking, and birdlike noises persist throughout...

"[8] Henry Kuntz, in a review for Bells, said: "played at a high volume, Monoceros is as close a duplication of the way the music sounds in performance as you might hope to hear.