Thirteenth-century music theory, which followed the ideas of Boethius, was very largely concerned with the numerical proportions associated with musical intervals. Numbers provided an intellectual foundation that did not suffer from the vagaries of the senses. In general neither Boethius nor his greatest exponent, Jacobus (writing c. 1320), explained how they obtained the numbers they used. In this essay I attempt to reconstruct their methods and show how they developed ideas from the first-century Nicomachus to achieve their aims. Jacobus is explicit in saying that the use of the relatively newly introduced methods of algorism – calculating with Arabic numerals – made his cogitations easier. I shall argue that the manuscripts we have of his Speculum musicae show that Jacobus did indeed use algorism in his work.

Though recent discoveries have improved our understanding of big, melismatic hockets from the late thirteenth century, there remains a pervasive uncertainty as to how hockets should be defined and identified on the small scale at which they characteristically manifest in thirteenth-century motets. In revisiting the mensural theorists up to Franco of Cologne, it was found that only Franco defines hockets as multi-voice phenomena: earlier texts define the hocket at the level of a single perfection, and as it reveals itself in the breaking of a single performing voice. Under a revised definition, 138 motet texts that use hockets have been identified in the Ars antiqua repertory. It was also found that another way of hearing the hocket, compatible with the first, is implied by Lambertus and pursued at length by the St. Emmeram Anonymous. These writers acknowledge but depart from the consensus that the hocket is sonically fragmented, also hearing it as a promise of the coordination achievable when musical time is measured. For St. Emmeram especially, the hocket has a dual character: its sonic fragmentation is contrived through integrated planning. To hear hockets integratively is difficult, and requires an effort of will that for this theorist has moral stakes.

The final sections of the article analyse the musicopoetic games of the motet Dame de valour (71)/Dame vostre douz regart (72)/Manere (M5). Similarly to the St. Emmeram theorist, the piece self-consciously highlights the difficulty and worth of close listening (a theme inspired by its tenor’s scriptural source), and does so with a hocket that marks a complementarity of breaking and integration, of a formal sort, several decades before Lambertus and St. Emmeram would reflect on the hocket’s dual character theoretically. The motet poses artfully some of the same questions about the audibility of form that preoccupy modern scholarship. These voices from the thirteenth century might remind us that ethical debates about correct listening are much older than current disciplinary concerns. But recognising the longevity of the debates does not force us to agree with old positions.

The ‘León Antiphoner’, León, Cathedral Library, MS 8, is the most complete manuscript containing Old Hispanic chant, comprising Office and Mass chants for the whole church year. As such, the León Antiphoner is the most studied Old Hispanic manuscript. Despite this, its dating is controversial and hypotheses have ranged from c. 906 (Menéndez Pidal) up to the eleventh century (Zapke and others). In this article, the dating and early history of the manuscript are reconsidered and an entirely new perspective is brought to bear on the questions of when, where, and for whom the manuscript was written. The reinterpretation of the cryptographic inscriptions found at the bottom of fols. 128v and 149r has made it possible to identify the patron of the Antiphoner as San Froilán, Bishop of León, and to date the manuscript’s production to the years 900–5. The scriptorium of the monastery of SS Cosmas and Damian in Abellar is suggested as the likeliest place of production of the Antiphoner.

The celebration of Christmas in Early Modern Europe underwent a significant transformation in the second half of the seventeenth century. Even after the Protestant Reformation, European Christmas traditions maintained numerous features of their medieval practices, such as carnivalesque celebrations, processions, masks, and riotous behaviour. This changed during the seventeenth century. Popular carnivalesque Christmas plays were prohibited and replaced with a more internalized devotion that emphasized the individual’s relationship with the newborn Child. This transformation was part of a larger paradigm shift in seventeenth-century religiosity, which replaced external and physical displays of piety with internalized devotional practices. These shifts also included new theologies of corporeality and gender, which likewise had an impact on the ways in which Christmas was celebrated. The theological shifts correlate with the rejection of the carnivalesque in the Early Modern period, as it was analysed by Mikhail Bakhtin.

Most of these changes took place in the 1670s and 1680s. Schütz’s Christmas Historia – which was composed before 1664 – represents a transitional phase and retains some earlier views of Christmas. The most obvious example is the Kindelwiegen (rocking of the child), the physicality of which was highly suspicious to theologians in the later seventeenth century. Schütz not only refers to this practice but incorporates it in the texture of his music.

In sixteenth-century Germany, both Catholics and Lutherans circulated and performed Josquin’s Missa Pange lingua, even though its model, the hymn Pange lingua, was associated with Eucharistic practices that were exclusively Catholic. This source-based study reveals how Lutherans selected the Missa Pange lingua for performance over other available masses and adapted it for their liturgical and pedagogical needs. Two printed sources of the mass offer perspectives on how Lutherans might have negotiated the polemical rituals and theology associated with the Missa Pange lingua alongside an aesthetic interest in the work. The intention of this study is not to de-emphasise the connection between the Missa Pange lingua and its borrowed melody or the initial Catholic identity of the mass. Rather, the Lutheran identity of the Missa Pange lingua provides an additional layer to the early reception history of this work and a case study of the Lutheran appropriation of Catholic music.