Music, Mathematics and Experimental Science

Music, Mathematics and Experimental Science

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Monochordum mundi by Robert Fludd

Monochordum mundi. Illustration from the Robert Fludd's Utriusque cosmi maioris scilicet et minoris metaphysica, physica atque_technica historia, 1617.
It summarizes Fludd's cosmology as a Pythagorean monochord comprising two octaves and divided into the basic harmonic intervals, the values of which had no experimental foundation.

This project aims at understanding mathematical and musical factors that led to a substantial change in the conception of western music in the Renaissance. Throughout its history from Antiquity to the Renaissance, western music developed from a cosmological-mathematical-speculative understanding, in which attention was mainly focused on a rational activity of speculation, and the purpose of the musical sound was to imitate a supramusical order and regularity to a mathematical-empirical understanding, in which the main emphasis lay on the quality of the sound itself and music was examined by means of its laws and effects in people.
The activity focuses on musical concepts such as temperament, consonance, music of the spheres, division of the tone, as well as on mathematical structural changes in the theories of ratio and in the fundaments of theoretical music in order to understand the substratum of such a change in the conception of western music. Specifically, it approaches the change of the mathematical base of scale from a scale including exclusively rational numbers to a scale based on irrational numbers in order to systematize the temperament; the transition of the concept of consonance from a numerological symbolism - embedded in a musical model based on ratios between commensurable magnitudes involving only the 4 first natural numbers - to a physical one; the originally Pythagorean concept of music of the spheres, which come from a speculative notion to a conception based on empirical data; practical needs, both in mathematics and in music, as the need for dividing the tone, claiming, contrarily to the predominant Platonic-Pythagorean tradition, that ratios should be conceived as a continuous magnitude; structural changes in theories of musical ratios which come from a geometrical conception to an arithmetical one; as well as changes in the mathematical foundation of music from a arithmetical basis to a geometrical one.

  • Abdounur, O. J., Compounding ratios and intervals: an educationl approach in mathematics and music. In: Kaijser, Sten (ed.) HPM 2004 - History and Pedagogy of mathematics. Uppsala, Sweden, 2004, pp.88-93
  • Abdounur, O. J., Matemática, música e cosmologia no Renascimento: mudanças de perspectiva. In: Sad, Lígia Arantes. Anais do VI Seminário Nacional de História da Matemática – Brasília: Cruzeiro Editora, 2005, p.139-146.
  • Abdounur, O. J., Ratios and music in the late Middle Ages: a preliminary survey. To appear in: Vendrix, Philippe (ed.). Musique et mathématique á la Renaissance. Collection "Epitome musical". Centre d'Études Supérieures de la Renaissance. Université François Rabelais. Paris: Minerve, pp.57-104.
  • Abdounur, O. J., Changes of paradigms in the relationship between mathematics and music from the late Middle Ages to the Renaissance. To appear in: Emmer, Michele (ed.), Matematica e Cultura. Milano: Springer Italia.
  • Abdounur, O. J., Conceptual changes in western Renaissance music with respect to its relationship with mathematics and cosmology. To appear in MPIWG Preprint.