Trained as a music educator and trombonist, Baker spent the early part of his career in the 1940s and 1950s as a jazz musician, performing and recording in the United States and in Europe. A facial injury suffered in an automobile accident in 1953 ended his career as a trombonist, but Baker switched to cello and turned his attention to teaching and musical composition. In 1966 he joined the music faculty at Indiana University in Bloomington, where he established the school's jazz studies program. He was later named an IU distinguished professor and chair of the university's Jazz Studies department in the
Jacobs School of Music. In addition, he became one of the co-musical directors of the
Smithsonian Jazz Masterworks Orchestra in 1991. He composed music, mostly on commission, and wrote hundreds of scholarly works related to music. He was active in numerous musical arts organizations. Baker returned to Indiana and taught private music lessons in Indianapolis and performed in local bands. He did not resume his academic teaching career until 1966. During the 1950s Baker played in several big bands, including
Lionel Hampton's orchestra. After moving to California in 1956, he played with the West Coast jazz orchestras of
Stan Kenton and
Maynard Ferguson before returning to Indianapolis to lead his jazz band for two years. He performed in clubs across the United States, including the
Five Spot Café in New York City with
George Russell in the late 1950s. In 1960 he toured Europe as a member of
Quincy Jones's band. Baker was also able to play trombone with Russell's orchestra on
Living Time (1972), a collaboration with
Bill Evans, before the jaw injury finally caused him to give up the trombone and focus on teaching and composition. Baker is credited on sixty-five recordings, including performances on two of Russell's albums,
Stratusphunk (1960) and
The Stratus Seekers (1962). He is also credited with writing 400 articles. Baker's best-known composition, which also received significant media attention, was Concertino for Cell Phones and Orchestra, a commission from Chicago Sinfonetta. Baker's other compositions include a tribute to
Martin Luther King Jr. in 1968, a violin concerto for
Josef Gingold, a flute concerto for James Pellerite, as well as Cello Concerto (1975), which he dedicated to cellist
János Starker, and "Ode to Starker" (1999). He received over 500 commissions from individuals and ensembles, including compositions that he wrote for Gingold, Starker,
Ruggiero Ricci,
Harvey Phillips, trumpeter David Coleman, the
New York Philharmonic, the
Saint Paul Chamber Orchestra, the
Beaux Arts Trio, the
Fisk Jubilee Singers, and the
Audubon Quartet, in addition to the
Louisville Symphony, Ohio Chamber Orchestra, and the
International Horn Society. Other musical groups have recorded his compositions. The
Buselli–Wallarab Jazz Orchestra's album
Basically Baker (2005) includes interpretations of his compositions, many of them written for
big bands and ensembles. ==Later years==