Edmonson, who had Parkinson's disease and other illnesses, died Saturday at a hospital in Mesa, Ariz., said Mike Bartlett, a family spokesman.
folk music revival through about 10 albums that showcased their "trademark harmonies and electrifying guitar work," according to the All Music Internet database.
They played the Hollywood Bowl in 1963 with Peter, Paul & Mary, the legendary folk group that toured with the duo and recorded the Edmonson composition "If I Were Free."
Bud & Travis "helped to launch the folk renaissance with some of the most beautiful music we ever heard," Peter Yarrow of Peter Paul & Mary told The Times in an e-mail.
"Travis had a mellifluous voice" and the two groups "learned much from each other," Yarrow said.
Folk music historian Mary Katherine Aldin called Bud & Travis "virtuosos" who influenced the folk scene with their early arrival, expansive repertoire and embrace of Spanish-language folk songs. They recorded “La Bamba” and "Malaguena Salerosa," which reportedly sold a million copies in the 1950s.
"For many white folk audiences at the time, it was the only time they heard people sing in Spanish," said Aldin, a Los Angeles-area producer who reissues roots music.
The pair met when Edmonson's older brother brought his Army buddy, Dashiell, home in the late 1940s. They became a team known for their witty repartee after Edmonson, a tenor, left the Gateway singers, a folk group.
"He was fascinated by my Mexican music, and I was fascinated by his folk songs," Edmonson, who grew up in Nogales, Ariz., told the Tucson Weekly in 2001.
Their 1965 "Latin Album" was a "landmark . . . a world beat tutorial for an audience whose only Hispanic musical outlets were 'groovy' hipsters like Herb Alpert and Sergio Mendes," James Christopher Monger wrote for All Music.
The harmony that was a Bud & Travis trademark was not reflected offstage, and they broke up in 1965. Dashiell recorded with the Kinsmen, performed solo and died in 1989.
Edmonson went on to record three solo albums in the 1960s, spent the 1970s as a troubadour and settled in Arizona.
After an aneurysm-stroke paralyzed him on the left side in 1982, Edmonson continued to write and arrange music, and mentor other performers.
Born in Long Beach on Sept. 23, 1932, he was the youngest of four sons of Everett Edmonson and the former Lillian Munro. His father was a social worker and his mother a teacher.
At 7, he joined the church choir and later sang with a well-regarded mariachi band.
He studied anthropology at the University of Arizona and worked on a dictionary of the Yaqui language after living with the Native American tribe.
In the Army, Edmonson entertained troops across the country.
After his release, he played the Purple Onion, a celebrated San Francisco club, and met up again with Dashiell in Los Angeles.
As a favor to a friend, they sang on an L.A. radio show and knew they were on to something, Edmonson later recalled, when "the switchboard lit up like a Christmas tree."
Edmonson's survivors include his longtime companion, Rose Marie Heidrick; a son, Steve, who is a blues guitarist; and five daughters, Tammy, Erin, Ellen, Elizabeth and Linda.