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Eudoxus of Cnidus on Consonance, Reason/Ratio, and Divine Pleasure

Victor Gysembergh

Freie Universität Berlin, Germany

Only one fragment of the great scientist Eudoxus of Cnidus (ca. 390-337) deals with music, and more specifically, συμφωνία (Theon of Smyrna, Introductio arithmetica, p. 61 Hiller). Therefore, scholars of ancient music have generally overlooked it. Recently, the authenticity of the mention of Eudoxus has even been doubted (C. Huffman, Archytas of Tarentum, Cambridge, 2005, p. 477).

However, when interpreted against the backdrop of Eudoxus’ philosophical hedonism, this fragment reveals an original conception of music in connection with reason/ratio and divine pleasure. Based on my forthcoming edition of the fragments of Eudoxus of Cnidus (Collection des Universités de France, 2019), I would therefore like to discuss how Eudoxus took over Archytas of Tarentum’s research in harmonics and developed it further in his own conceptual framework to define consonance as a means of attaining pleasure (ἡδονή), which he equated with the one god.

Eudoxus’ hedonism assigned a central role to the concept of λόγος, understood both as the quantitative relationships (ratios) governing the structure of being, and as the ability (reason) of some beings to grasp these relationships in their quest for pleasure. Thus, harmony constitutes a prime example of how rational study of the numerical structure of being can be conducive to pleasure.

This original development of the Pythagorean theory of music by Eudoxus will then be assessed in the broader context of the 4th c. BCE discussion on the nature of sound documented, e.g., by Aristoxenus of Tarentum. It will be argued that Eudoxus postulated the double nature of sound, both as number and as motion. This can be seen both as an attempt to reconcile both parties in this heated debate, and as an important physical confirmation for the unity of λόγος, which Eudoxus had demonstrated mathematically in his theory of proportions.

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Music and the Divine

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