A range of forms and genres of music survive from thirteenth-century Europe. Among these, the most well-documented is plainsong, a type of monophonic (single-voiced) chant that was sung for the Christian liturgy. In contrast, motets are polyphonic (multi-voiced) compositions with a tenor, typically the lowest voice, that is derived from plainsong and one or more upper voices with different texts in French and/or Latin. In this paper, we outline some foundational concepts of a method that we are developing to analyze the usage of intervals (the distances between pitches) in three- and four-voiced motets. The major advantage of our analytical approach is that it is adaptable: whereas previous work has posited a fixed system for defining sonority types (the combinations of categorized groups of simultaneously-sounding intervals), the computational approach that we use allows us to test different hypotheses. We construct our categories from thirteenth-century treatises and present-day musicological literature, and will use our results to refine our system of sonority types. Ultimately, our aim is to arrive at a better understanding of the arrangement of intervals in motets, and in doing so to achieve a synergy between computational corpus analysis and traditional methods of musicological analysis.