![]() ![]() At this stage of the Greek language, the P2 particles are acknowledged to no longer be part of the living spoken language. particles in older stages of Greek, not much research has been conducted on the particles in late medieval Greek (LMG twelfth to fifteenth centuries). This is reflected in the interest of scholars: while there are many studies on. From the post-Classical period on, however, these small words gradually lose their importance in discourse and die out. Read moreĪncient Greek is widely regarded as a language with an extraordinary number of so-called “Wackernagel P2 particles” such as γάρ, δ(έ), and μέν, which serve a multitude of discourse functions. 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. 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. 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 distinguishes between descriptive and argumentative uses of mathematics. This article analyses the conditions under which mathematics could enter the field of fourteenth-century music. In the final analysis, it seems improbable that he was. It is unlikely, therefore, that Jacques would have referred to its existence, perhaps even dared to have mentioned it, provided he was acquainted with it. Be that as it may, the satirical tone of Jacques' text is foreign to the style of the decree. It concerns itself rather with certain musical practices (within the church) that Jacques himself even favored. ![]() Undoubtedly not directed toward ars nova, Pope John XXII's decree "Docta sanctorum patrum" cannot be counted as a second witness. Since Jacques de Liège provided the only written witness of what has been interpreted as the dispute between ars antiqua and ars nova, a challenge to this historiographical concept is thoroughly warranted. This article investigates its satiric and ironic elements particular to both style and argumentation, which may lead to a reassessment of how the author is characterized. The Speculum musicae of Jacques de Liège has often been considered a conservative, narrowminded treatise aimed at condemning ars nova. For him, the physical world is totally immersed in changes and movements, and this cannot but impede things from expressing the stable unity, which is required for contemplating the beautiful. In clear antithesis to the position taken by Augustine on the beauty of the rhythmic patterns that better represent the beauty of unity, Boethius does not relate the mathematical ratios of the consonances to an esthetical judgment by making use of the category of beauty. More complex, on the other hand, is the relationship between mathematics and beauty. More precisely, its ethical aim is to correct the specific form of movement of human beings, that is their actions, exemplified in the way in which mathematical ratios represent the forms of government and musical ratios evoke and heal psychophysical affections. His view emerges as coming out of a rather complex construction, which assigns the ethical scope of mathematics in indicating to the human mind how to correct the ratios that realize the best relationship in movements of the soul and the body. This attitude is examined in the present paper as regards Boethius’ response concerning the relation between numbers, ethics and aesthetics. Basing his reasoning on Nicomachus and Ptolemy, Boethius follows the philosophical tradition that had tried to reconcile Plato’s and Aristotle’s views. The convergence of the Neoplatonic/Neopythagorean approach with the Aristotelian organization of the sciences is one of the most interesting features that characterizes the two influential mathematical treatises on On Arithmetics (De institutione arithmetica) and On Music (De institutione musica) by Severinus Boethius.
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