3 March 1927 – 5 May 1998
Founding member of Skatalites, The and Supersonics, The. Very important jamaican saxophone player.

He was born in Havana, Cuba. When his father worked at Panama Canal, the familly moved to Jamaica in 1933. He went to Alpha School, which gave him a good musical eduction. His career started in 1943 when he performed in Eric Dean Orchestra, one of the best at that time on the whole island. Then he switched to Don Hitchman's sextet. This band was one of the first jamaican Bands ever got recorded (1952/1953). This happened at the first radio station in Jamaica, Z or Zed QI. In the early fifties, Tommy was a soloist in the greatest band to coalesce in Jamaica before The Skatalites, Roy Coburn's Blu-Flames featuring Don Drummond, Cluett Johnson and Ken Williams (6). In 1954 he moved to Nassau, Barbados to play gigs in Clubs next to Ernest Ranglin. 1956 he moved to Miami, Florida where he first got into contact with Jazz music. He was heavily influenced by hearing John Coltrane, whose tunes he first played when he moved back to Jamaica in 1962. He played with a lot of musicians, which can be found on a lot of early ska recordings, but until 1964 he always denied offer by Clement "Coxsone" Dodd and Arthur "Duke" Reid. He was a known musician for adding Jazz to ska music. On sundays, he always went to play a regular session with other musicians like Jackie Mittoo, Lloyd Knibbs and Johnny Moore, which got later released as Jamaica Jazz. Out of this session emerged one of Jamaica's most important bands Skatalites, The(June 1964). The Skatalites made several hundred instrumental recordings, mostly for Dodd's Studio One and backed the gamut of Jamaica's vocalists on hundreds more. After Don Drummond murdered his girlfriend in 1965, they crashed and split up. McCook was now producing records for Reid's Treasure Isle. At that point he started his new band Supersonics, The. Tommy led them until they disintegrated on a trip to Montreal Canada in 1969. In 1973 he went to the U.K. to work with Jimmy Cliff's band for a BBC special on Cliff meeting Jazz artist Herbie Mann. After 1975 he played at Channel One's studio band Revolutionaries, The. In 1983, Tommy started to reanimate the Skatalites, which worked out well and they as they saw that they could make out a living of touring, they restarted. He stopped playing around 1995, when his health condition got worse. He died on May 5, 1998 leaving his second wife, eight children and fourteen grand children.