Two recent editions of Descartes' Compendium Musicae (by Fr. de Buzon and L. Zanoncelli) reintroduce ancient and unresolved historiographical questions: the identification of the ancient, medieval, and renaissance musical sources of the Cartesian treatise; the epistemological paradigm developed by Descartes within the context of late renaissance mathematicism; the role of music in Descartes' intellectual education and in the development of his ideas; the manuscript circulation of the Compendium and its influence on music theory in the 1620s and 1630s; the reception of the Compendium, from the posthumous edition of 1650 to Rameau's tribute in his Traité de l'harmonie of 1722. The answer to these questions may come from the firm historical and cultural grounding of the Compendium musicae in the tradition of musica speculativa and its renaissance updates, from which Descartes draws the epistemological models and the intellectual lexicon for the central theme of the treatise: geometricization of a sensation - i.e., sound - as a premise to musical listening, to experiencing the perceived musical continuum. This essay discusses this theoretical nucleus and the frame of problems within which it unfolds (the Euclidean structure of the treatise, the relationship between ratio and sensus, praenotanda, duration, imagination, deduction, and classification of consonances) in light of the state of late renaissance music theory, between the crisis of the numero sonoro in the tradition that had culminated with Zarlino and the new foundations laid in the 1630s by Mersenne and Galileo. A correct historical contextualization of Descartes' treatise is the premise for an evaluation of its significance in the "marvelous triennium" of 1618-21, inspired by his meeting with Isaac Beeckman (the dedicatee of the Compendium musicae) and scanned by the scientia penitus nova and by the inventum mirabile, of which the arithmo-geometry of the Compendium is a logical and chronological passage.
Gozza, Paolo (1995) Una matematica rinascimentale: la musica di Descartes. In: Il Saggiatore Musicale, Vol. 2, No. 2, pp. 237-257. Available at https://openmusiclibrary.org/article/103703/.