"Birth of the Cool" refers to three separate 1949/1950 recording sessions by the Miles Davis nonet of eleven tracks that were only released under this title as a complete set in 1957 (after a partial 1954 release under the title "Classics in Jazz").
The tracks from the first January 1949 session (Move, Jeru, Budo, Godchild) were issued soon after recording as two pairs of singles.
Kenny Clarke participated in the second date, on April 22, 1949, when Davis was filling in for Fats Navarro in Tadd Dameron's band, with a revised lineup of J. J. Johnson (trombone), Sandy Siegelstein (French horn), Bill Barber (tuba), Lee Konitz (alto), Gerry Mulligan (baritone), John Lewis (piano) and Nelson Boyd (bass). The nonet recorded Mulligan's "Venus de Milo", Lewis's "Rouge", Carisi's "Israel", and "Boplicity", a collaboration between Davis and Evans, credited to the pseudonym "Cleo Henry" (the name of Miles Davis' mother, as Davis wanted it in a different music publishing house than the one he was signed with). From this session only "Israel" and "Boplicity" were doubled together on a 78 and released at the time. Another point of interest (from the 78rpm disc images) is the rare listing of Kenny Clarke under his Islamic name L.A. (Liaquat Ali) Salaam (which he had adopted in 1946 after conversion upon discharge from the military).
All Music summarizes that "Birth of the Cool remains one of the defining, pivotal moments in jazz. This is where the elasticity of bop was married with skillful, big-band arrangements and a relaxed, subdued mood that made it all seem easy, even at its most intricate. After all, there's a reason why this music was called cool; it has a hip, detached elegance, never getting too hot, even as the rhythms skip and jump. Indeed, the most remarkable thing about these sessions is that they sound intimate, as the nonet never pushes too hard, never sounds like the work of nine musicians. Furthermore, the group keeps things short and concise (probably the result of the running time of singles, but the results are the same), which keeps the focus on the tones and tunes. The virtuosity led to relaxing, stylish mood music as the end result -- the very thing that came to define West Coast or "cool" jazz -- but this music is so inventive, it remains alluring even after its influence has been thoroughly absorbed into the mainstream."
Burt Korall in his "Drummin' Men" writes (regarding Clarke's contribution) that "Clarke's work on this project – and many others during this period – brought together, in appropriate ratio, intelligence, emotion, and instinct. He quietly gave the music a sense of design and swing."