He studied at the Eastman School of Music from 1962-1966, and at Harvard University from 1966 and 1972, where he obtained an M.A.
and a Ph.D.
in musicology.
Wright completed his Ph.D.
in 1972 with a thesis titled Music at the court of Burgundy, 1364-1419.
After a year teaching at the University of Kentucky in Lexington, he moved to Yale in 1973, serving as the chair of the department of music from 1986 to 1992.Wright specialises in music history.
His early work concentrated on Middle Ages and renaissance music.
More recently, he started to work on Mozart.
He received a Guggenheim Fellowship in 1982.
In 2004 he was awarded the honorary degree Doctor of Humane Letters from the University of Chicago and in 2010 was elected to the American Academy of Arts and Sciences.
In 2016 he was awarded Yale's Sewall Prize for excellence in undergraduate teaching and in 2018 the Yale Phi Beta Kappa Devane Medal for excellence in teaching and scholarship.
On May 15, 2013, Wright was named the first Academic Director of Online Education at Yale University.