In 1949, Brubeck with Tjader and bassist Ron Crotty, both fellow octet members, formed a more commercially viable trio and cut their first records, which gained a national audience. After surviving a near-fatal diving accident in 1951, Brubeck formed a quartet by adding Desmond.
Brubeck continued performing with the latest version of his quartet until just past his 90th birthday, despite needing heart surgery and a pacemaker.
In a 2010 interview, Brubeck, who converted to Catholicism in 1980, envisioned an afterlife where he'd again see his family and jazz friends, including Louis Armstrong, Duke Ellington and Count Basie.
"If there's a heaven," Brubeck said, "let it be a good place for all of us to jam together and have a wonderful, wonderful musical experience."
Brubeck is survived by his wife of 70 years, a daughter and four musician sons. Another son died in 2009.