This chapter introduces the first of the fifteenth-century teacher Johannes Tinctoris’ three ‘registers’ of polyphony: the music for the Mass, beginning with the Mass cycle (setting the Ordinary of the Mass, in liturgical terms) and its development during the Renaissance, then the Propers of the Mass, then finally the Requiem. Whereas the setting of Propers and their chants is a practice as old as polyphony itself, the Mass cycle and the Requiem were more recent phenomena. Guillaume Du Fay’s ‘Missa L’Homme armé’ appears as a case-study, showing how the Mass cycle builds on the work of previous composers of Mass-music in England and aspects of the isorhythmic tradition (which in a sense it supersedes), whilst introducing new elements that condition the form’s later history through to the end of the Renaissance. The end of the chapter highlights the porousness of practice sketched earlier with regard to the boundary between mass-music and motets, discussed in the following chapter.