In this paper, we postulate that combining the domains of information visualization and music studies paves the ground for a more structured analysis of the design space of music notation, enabling the creation of alternative music notations that are tailored to different users and their tasks. Hence, we discuss the instantiation of a design and visualization pipeline for music notation that follows a structured approach, based on the fundamental concepts of information and data visualization. This enables practitioners and researchers of digital humanities and information visualization, alike, to conceptualize, create, and analyze novel music notation methods. Based on the analysis of relevant stakeholders and their usage of music notation as a mean of communication, we identify a set of relevant features typically encoded in different annotations and encodings, as used by interpreters, performers, and readers of music. We analyze the visual mappings of musical dimensions for varying notation methods to highlight gaps and frequent usages of encodings, visual channels, and Gestalt laws. This detailed analysis leads us to the conclusion that such an under-researched area in information visualization holds the potential for fundamental research. This paper discusses possible research opportunities, open challenges, and arguments that can be pursued in the process of analyzing, improving, or rethinking existing music notation systems and techniques.