Middle Byzantine notation, which is the most widely used musical notation of Byzantine music, has been used to notate Byzantine music between the mid-twelfth century and the early nineteenth century. Since its rules were never explicitly written down and enforced, but were instead informally interpreted, cantors, theorists and researchers do not universally agree on only one accepted interpretation. As a result, this type of music theory has never been studied in a systematic, formal way, while computational approaches have focused strictly on typesetting issues. The contribution of this paper is twofold; firstly, we present a formalization of the Middle Byzantine music notation and its theory rules, which were previously left to informal understanding; secondly, we devise a novel Knowledge Representation (KR) formalism, supporting the computational processing of the musical information captured by this notation. The new KR is explained in detail and demonstrated by representing one piece (Heirmos), as well as performing an indicative computational task.