The moderns' art of music, according to Jacobus, is incommensurable with the art of the antiqui. Chapter 5 examines the philosophical background to the conceptualisation of rhythmic duration in the ars nova. I argue that two metaphysical debates of the late thirteenth and early fourteenth centuries illuminate the differences between Des Murs’s systematisation of mensural notation and the ars antiqua system favoured by Jacobus. Additionally, even though neither Des Murs nor Jacobus actually included any illustrative diagrams in their discussions of musica mensurabilis, I argue that a visually based conceptualisation of how musical notes relate to each other informed Des Murs’s new system. Des Murs theorises musical time as a continuum, where note durations vary by degrees along this line of time. For Jacobus, the forms of musical notes that represent duration can only make sense within a traditional tree-like hierarchy, with each species of note distinct in their name, definition, and essence. An analysis of these opposing ontologies reveals some of the reasons behind the irreconcilable differences between Des Murs and Jacobus.