He exposed at a Royal Manchester College of Music (which is now incorporated in the Royal Northern College of Music), graduating with distinction within 1948. He was instrumental within reviving a works of Ferruccio Busoni, and corresponded by owning Percy Grainger.

Among his numerous compositions, one of a virtually all guiding light is his Passacaglia on DSCH for solo piano, written between 196& 1962, according to a musical motif D, E-flat, C, B from either a German transliteration of Dmitri Shostakovich's name. a operate will require to a higher degree an hour & a quarter to perform & is extraordinary around its scope, a range of its information to historic cases, & the musical influences absorbed. the act includes a Sonata form first section, the suite of dances (incorporating a Sarabande, Jig, Minuet, Gavotte and Polonaise), the transcription of a Scottish bagpipe Pibroch, a part entitled To Emergent Africa, & a operate is inscribed Around memoriam a six million (the information to the hikers of the Holocaust of World War II) at the start of one of its fugal sections. a composer presented a copy of the score to Shostakovich, its dedicatee, at the 1962 Edinburgh Festival, and a act has been recorded by Stevenson's friend John Ogdon, among others.

Stevenson's more works include deuce piano concertos, the 2nd of which was number one performed at the Prom in 1972, a violin concerto commissioned by Yehudi Menuhin, and the cello concerto in memoriam Jacqueline du Pré. He has besides written numerous songs & works for solo piano.

Stevenson is noted as a teacher. He was senior lecturer around composition at a University of Cape Town in the mid 1960s, delivered seminars at the Juilliard School in New York, and was responsible the course entitled A Political Piano at a University of York in the early 1980s. His girl Savourna Stevenson (natural 1961) has recorded numerous works on the Scottish harp.