Born in Istanbul, Turkey, he grew up in Upstate New York and in New York City, and studied music at the Juilliard School's lower school, Haverford College, then received his master's degree from Harvard University, where he focused on Renaissance music, particularly the works of Orlando Gibbons.
He earned his doctorate in creative composition from the Eastman School of Music.
His teachers included Alfred Swan, Randall Thompson, Walter Piston, Bernard Rogers, Howard Hanson, Alan Hovhaness, and Robert Palmer.
During 1964-1965, Davison was placed in the Kansas City (Missouri) Schools as part of the Music Educators National Conference's Contemporary Music Project, where he composed numerous works for band, chorus, and orchestra.
He coauthored, with John Ashmead, a book about the songs of Robert Burns.