Wheat also wrote music, along with his lyricist partner, Bill Loughborough. Their composition Better Than Anything, now a jazz standard, has been recorded by dozens of performers over the decades, and is part of the live acts of Lena Horne, Phylicia Rashad, Irene Kral, Bob Dorough and Al Jarreau. Their next song, Coo Coo U, was recorded both by The Kingston Trio and by The Manhattan Transfer. Wheat embraced George Russell's Lydian Chromatic Concept of Tonal Organization for improvisation; he would sing intriguing scales while playing a guitar accompaniment based on the theory.
Wheat was best known as the first upright bass accompanist for The Kingston Trio, the fourth member on stage and an integral part of the music and the group's musicologist. He is remembered for his subtle jazz influence during their early recordings, playing on the 1958 Gold Hit record, Tom Dooley and eleven of the Trio's Capitol Records albums, including the critically acclaimed Here We Go Again. He toured extensively, playing college campuses across America, well-known coffee houses in Greenwich Village and the hungry i in San Francisco. He also appeared on many television shows of the time, among them Milton Berle's Texaco Star Theater, Jack Benny, The Dinah Shore Chevy Show, The Pat Boone Show, and The Perry Como Show. Mr. Wheat is seen on the cover of the Trio's Goin' Places album. When asked in an interview, whether Buckwheat was considered a Beatnik since he grew up in the Beat generation, Dave Guard answered of his mentor, "Not sure, but he knew where to get it" referring to marijuana.
In 1961 Wheat left the Trio along with Dave Guard to form The Whiskeyhill Singers. The new group toured, recorded an album where along with Guard's banjo work on Bonnie Ship, The Diamond, the group's rendition of the classic good-bye song Isa Lei, using nothing but Buckwheat's bass for back-up, is intensely moving and reminiscent of his compelling bass line and acoustical guitar behind Guard's soulful Fast Freight, recorded with the Trio in 1958. The Whiskeyhill Singers also came to attention after their recording of traditional American folk songs for the soundtrack of the MGM Cinerama motion picture, "How the West Was Won" (1962). They were also approached to record the main title song for the 1960 John Wayne film "The Alamo", but Dave Guard, after his Remember The Alamo was rejected and Wayne asked him to record Green Leaves of Summer instead, turned the offer down. (The latter song, recorded by The Brothers Four, became a hit record as Wayne had hoped).
Wheat had long been an advocate of George Russell's "Lydian Chromatic Concept of Tonal Organization for Improvisation", the art of tonal gravity. In 1948 Harry Partch, an American composer, developed a microtonal system of music that depended on custom-built, specialized instruments of various and exotic designs, which could play non-tempered scales, for its performance. Buckwheat (the name Wheat used in later life) and his Sausalito California roommate, Bill Loughborough, a musician and electronic engineer, built instruments for Partch, such as a marimba played with a large soft mallet over the resonator, delivering barely-audible, low-Hertz tones. Loughborough borrowed diagnostic and metric instruments from the Mare Island Navy Yard; using an oscilloscope and audio oscillator, they were able to work at a technical level not previously possible. Together they moved onto a Sausalito barge with Jak Simpson, who in 1954 founded a business named the "Boobam Bamboo Drum Company". Buckwheat, who was also working on the President Lines cruises to the Orient as a bass player, would buy large-diameter giant bamboo in the Philippines and bring them back on the ship to build the South Pacific Island bamboo drums, which they manufactured in Mill Valley, California, as Boobam's, ('bam' and 'boo' switched around). The drums fascinated several jazz groups, which added them to their percussion sections. In 1956, Chet Baker's Ensemble used them to perform on the Today Show.
The drums' unique sound inspired Nick Reynolds of the Kingston Trio, who eagerly included BooBam on their tour, with Buckwheat's percussion solo being featured on O Ken Karanga, along with Buckwheat's last performance with group on the album College Concert, the Trio's first live recording with John Stewart at UCLA in 1961. After the demise of the Whiskeyhill Singers, Buck became the bassist/arranger for folk duo Bud & Travis. He is heard on two of their albums; Live at the Cellar Door and Perspective on Bud & Travis on the Liberty label.