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This chapter focuses on the first serious effort made within the medieval Latin Church to correct the calculation of Easter by legislative means. This effort took place at the court of Pope Clement VI in Avignon, who invited skilled astronomers such as Jean des Murs and Firmin de Beauval to assist him in a planned reform of the Golden Number. The chapter explores the background to this papal initiative and the contributions made by its various protagonists, focusing in particular on a recently discovered Expositio kalendarii novi written by the monk Johannes de Termis in 1345. It also takes a closer look at the parallel discussions that took place in the Byzantine East, where the prospect of a calendar reform was first raised by Nicephorus Gregoras in 1324.

This chapter identifies three important developments in the field of late medieval computational astronomy and discusses their influence on the calendar-reform debate. First on is the evolution of astronomically ‘enhanced’ calendars and related lunar tables or almanacs, whose dissemination in a variety of forms and different languages became a central feature of astronomical culture between 1290 and 1500. Next in line are some new departures in observational and mathematical astronomy in the 1290s, which led Latin Christian authors to reconsider key questions such as the length and long-term variability of the solar year. Finally, there is the introduction of the Alfonsine Tables in 1320s Paris, which laid the basis for the gradual formation of a European-wide standard for computational astronomy, but also fostered continuing doubts about the accuracy of individual parameters and the Alfonsine theory of precession.

Medieval English music theory, almost always expressed in Latin, though not isolated from Continental—in particular French—developments, has a strong tendency to resist them and go its own way in both language and content; moreover, despite the early establishment of the name proprius cantus (‘properchant’) for the natural hexachord, it is more characteristically marked by divergence from one writer to another, so that even when doctrines are compatible the same thing may be called by different names and the same name may be applied to different things. This chapter studies the variations in conception, notation, and terminology exhibited in the works of numerous English authors from the 13th to the 16th centuries, noting differences from the far more standardised French Ars nova associated with the names of Philippe de Vitry and Jean des Murs.