He is the second member of the San Francisco rock group to pass away this year.
"Martin was the most musically talented of all of us," frontman Bobby Gillespie wrote in a tribute.
The band said Hall passed after a "brief illness."
The British rocker had been battling a rare form of colon cancer for more than a year.
The rockabilly pioneer was frequently lauded by stars including Paul McCartney and Graham Nash as a major influence.
He also wrote songs recorded by Nina Simone, Nancy Wilson, Shirley Bassey and Mel Tillis and themes for 'Inside the Actors Studio' and the Barcelona Summer Olympics.
She appeared on 'I Love Lucy' and recorded an album of country tunes in 1980 that was released 33 years later.
The singer's son died Thursday after reportedly having issues with breathing.
The punk band's co-founder retired from performing in 2015 due to health issues.
The Nashville-based Cooper died Tuesday after a fall.
