Long recognized as one of the most important medieval treatises on music, the Musica of Hermannus Contractus is here presented in a newly revised translation, with commentary reflecting the best current scholarship. A polymath and monk, Hermannus Contractus (1013-54) contributed to the important advancements made in European arts and sciences in the first half of the eleventh century, writing on history, astronomy, and time-keeping devices, among other topics, and composing several chants. His music theory, founded on a systematic treatment of traditional concepts and terminology dating back to the ancient Greeks, is concerned largely with the organization of pitch in Gregorian chant. Hermann's approach stems from Germanic species-based thought, and is marked by a distinction between aspects of form and aspects of position, privileging the latter. He expresses this in terms imported from then-new developments in Italian music theory, thus acting as a nexus for the two traditions. Numerology and number symbolism play significant roles in Hermann's theories, and his critiques of other theorists offer insights into medieval intellectual life