Available in English for the first time, Prosdocimo's Tractatus plane musice (1412) and Tractatus musice speculative (1425) are exemplary texts for understanding the high sophistication of music theory in the early fifteenth century. Known for considering music as a science based on demonstrable mathematical principles, Prosdocimo praises Marchetto for his theory of plainchant but criticizes his influential Lucidarium for its heterodox mathematics*.* In dismissing Marchetto as a “mere performer,” Prosdocimo takes up matters as broad as the nature and definition of music and as precise as counterpoint, tuning, and ecclesiastical modes. The treatises also reveal much about Prosdocimo’s understanding of plainchant; his work with Euclid's Elementa; and his familiarity with the music theory of Boethius, Macrobius, and Johannes de Muris. A foremost authority on Italian music theory of the Middle Ages and early Renaissance, Jan Herlinger consults manuscripts from Bologna, Cremona, and Lucca in preparing these valuable first critical editions.