He also studied piano with Odessa's only piano teacher, Mrs. Felts, who attempted to interest him in the music of Bach and Beethoven. 
Following high school, Reed studied music at the University of Missouri beginning in 1929, transferring in 1933 to Louisiana State University where he received his Bachelor of Music (1934) and Master of Music (1936) degrees, both in music composition (studying with Helen Gunderson), as well as a Bachelor of Arts (1937) degree in French.
While a freshman at the University of Missouri he became interested in jazz big band performance, later arranging for the university's big band. 
In 1937 he enrolled at the Eastman School of Music (studying composition with Howard Hanson and Bernard Rogers, conducting with Paul White, musicology with Howard Gleason, and music theory with Allen I. McHose), receiving a Ph.D. in composition in 1939.
In 1942, at the Berkshire Music Center (Tanglewood), Massachusetts, he studied composition with Bohuslav Martinů, and contemporary music with Aaron Copland, Leonard Bernstein, and Stanley Chappel.
In the summer of 1947, he studied composition with Roy Harris at Colorado Springs, Colorado, and also attended lessons with Arnold Schoenberg.

Many of Reed's students have gone on to fame as composers and arrangers; these include Loris Chobanian, Dinos Constantinides, Clare Fischer, David Gillingham, Adolphus Hailstork, Jere Hutcheson, David Maslanka, and Greg Steinke. Most of these reunited to celebrate Reed's 95th birthday at Michigan State University in the summer of 2005.
Reed's best known and most widely performed work is the three-movement concert band composition La Fiesta Mexicana (1949), composed with the support of a Guggenheim Fellowship.
The work is based on Aztec, Roman Catholic, mariachi, and other musics Reed heard while in Mexico City, Cuernavaca, and Chapala, Mexico for six months (1948-49).
He returned to Mexico in 1960 for a month's further study.
He has also studied folk music in the Caribbean in February 1976, and in Norway in the summer of 1977. 
Reed later studied Native American musics in Taos, New Mexico and Arizona,
and eventually composed a trilogy of chamber operas based on Native American legends: Earth Trapped (Sioux, 1960), Living Solid Face (Algonquin, 1974), and Butterfly Girl and Mirage Boy (Hopi-Aztec, 1980). His band composition Missouri Shindig (1951) is based on the American fiddle tune "Give the Fiddler a Dram," which his father had particularly enjoyed playing.
Spiritual (1947), Reed's first composition for band, is based on his recollection of overhearing the exuberant religious expression of African American churchgoers while passing by their churches as a child.
Reed's music is published by G. Schirmer, Warner Brothers, Ballerbach Music, Harrock Hall Music, Triplo Press, Allyn & Bacon, Boosey & Hawkes, Edwin A. Fleisher, EMI Mills, Neil A. Kjos, Ludwig, and H O Reed Music.