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  • Author or Editor: Matthieu Husson x
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This paper aims at complementing the cross-disciplinary intellectual portrait of Jean des Murs presented in this special issue from the particular perspective of his arithmetical and geometrical works. If looked at from this angle, the general question immediately implies new ones: what are the connections between Jean’s arithmetical or geometrical works and those in the other fields of the quadrivium? What is their importance in the global intellectual picture of Jean des Murs as a quadrivial author of the fourteenth century? In order to explore these different issues, I have chosen to focus on a specific question: to what extent do Jean des Murs’s mathematical works reflect a persistent effort throughout his career to address the various issues related to small amounts? Focusing on this particularly significant problem will give me the opportunity to cover a representative sample of Jean des Murs’s quadrivial works from a specific perspective. Music and astronomy address small amounts in different contexts and with different mathematical tools. However, some deeper similarities appear. They concern mainly the question of measure and incommensurability as well as the relation between mathematical and physical reasoning. Overall, they reflect the intellectual coherence between quadrivial sciences as attested by Jean des Murs’s works.

In: Erudition and the Republic of Letters
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This article analyses the conditions under which mathematics could enter the field of fourteenth-century music. It distinguishes between descriptive and argumentative uses of mathematics. Jean de Murs’ uses of arithmetic to study musical time is an example of the former, Jean de Boen’s study of the division of the whole tone an example of the latter. It is furthermore explained how the mathematical descriptions appear to bring into agreement two types of constraint, namely the physical characteristics of sound and the aesthetic principles of the medieval discourse about music. Within these constraints, mathematics manages to fulfill different argumentative roles: it has an ontological function when music is seen as a part of the quadrivium; but an explicative function in the framework of the scientia media and, in an more innovative spirit for Jean de Boens, it provides a definition of the possible in the argumentation about the division of the whole tone.

In: Early Science and Medicine

This is article serves as the introduction to a special issue on the intellectual activities of Jean des Murs, a mathematician, astronomer-astrologer, and music theorist active in France in the first half of the fourteenth century.

In: Erudition and the Republic of Letters