Among his notable publications are critical editions of works by Guillaume de Machaut and Francesco Landini, the former of which he established the standard numbering scheme for.
He was born in Allenstein, East Prussia (today Olsztyn), then part of the German Empire.
In 1958 he succeeded Jacques Handschin as professor and director of the musicology institute at the University of Basel.
Schrade's critical editions of works by Guillaume de Machaut, Francesco Landini, and other medieval composers (in the Polyphonic Music of the Fourteenth Century series) are still of utmost importance for early music performers.
[1] Schrade founded and edited the Yale University Collegium Musicum series of critical editions (which included, during his time, first publications of the Wickhambrook Lute Manuscript, works by Alessandro Scarlatti, Michael Haydn, and others) and the Yale Studies in the History of Music series of publications; he also worked as co-editor of several journals, such as Journal of Renaissance and Baroque Music and Annales musicologiques.