Since the mid-20th century, approaches to musical notation have multiplied, giving rise to a multitude of terminologies and classifications. While there exists an extremely rich literature on new approaches to musical notation, it is easy to be confused by a nomenclature that is still under construction and has yet to be formalised. Based on a narrative review of the scientific literature comprising over 250 documents on new forms of notations, this article aims to present the main terminologies used to describe the different approaches to notation. This article proposes a framework illustrating what we observed as the most prominent notation approaches (action-based scores, animated scores, graphic scores, etc.) according to the types of indications (prescriptive and/or descriptive), the notation encoding (semantic and temporal encoding), and the mediums used for transmission (screen, printed, etc.). The contemporary notation framework aims to provide tools for the further analysis and classification of musical notation used in contemporary instrumental, electronic, and electroacoustic music.