The paucity of medieval sonority analysis is largely due to the limitations of our current analytical approaches. Systems such as those developed by Fuller (1986) and Hartt (2010) are classificatory and become more complicated with additional voices. A labeling system like chromatic set theory works for any number of voices and indicates exact intervallic content, but may not recognize transpositions within a diatonic framework.
However, traditional diatonic set theory is also misleading because the same set can represent two sonorities that are strikingly different -- aurally, functionally, or both. I propose an evolved system of mod7 notation utilizing "interval symbols" to show similarity in step-class content between sonorities while differentiating exact intervallic content. I apply this system to two tripla by Pérotin, Alleluya Nativitas gloriose virginis and Alleluya Posui adiutorium. Because a sonority's function and stability largely depend on dissonance content, I also propose a system of "dissonance values."
I then turn to the relationship between the "tonic" of Pérotin's tripla and a handful of sets that act analogously to the dominant chord in Common Practice music in that they are more stable than any sound besides the home sonority and provide the main contrast to it. Factors such as intervallic content (dissonance value), metric placement, number of occurrences, and interaction with the home sonority ultimately point to one set type as the primary stable point of contrast to the home sonority: the "dominant" set type.