International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

Mathematics and Music in Context: The Contribution of Erasmus Horicius to the Emergence of the Idea of Modern Number

Oscar João Abdounur
University of São Paulo, Brazil.


Received on March 15, 2016
Accepted on May 25, 2016


This article covers questions of how the relationship between mathematics and theoretical music throughout western history shaped modern comprehension of critical notions such as “ratio” and “proportion”. In order to do that, it will be consider a procedure taken by Erasmus of Höritz, a Bohemian mathematician and music theorist who emerged in the early 16th century as a German humanist very articulate with musical matters. In order to divide the tone, Erasmus preferred to use a numerical method to approach the geometrical mean, although he did not recognize his procedure itself as an approximation of the true real number value of the geometric mean. The Early Modern Period saw the growing use of geometry as an instrument for solving structural problems in theoretical music, a change not independently from those occurred in the conception of ratio/number in the context of theoretical music. In the context of recovery of interest in Greek sources, Erasmus communicated to musical readers an important fruit of such a revival and was likely the first in the Renaissance to apply explicitly Euclidean geometry to solve problems in theoretical music. Although Erasmus also considered the tradition of De institutione musica of Boethius, he was based strongly on Euclid’s The Elements, using geometry in his De musica in different ways in order to solve musical problems. It is this comprehensive geometrical work rather than the summary arithmetical and musical books of Boethius that serves Erasmus as his starting-point. However, Erasmus proposed a proportional numerical division of the whole tone interval sounding between strings with length ratio of 9:8, since it was a primary arithmetical problem. This presentation aims at showing the educational potentiality of the implications of such a procedure of Erasmus on the transformation of conception of ratio and on the emergence of the idea of modern number in theoretical music contexts. Under a broader perspective, it aims at show the implications on education of a historical/epistemological and interdisciplinary appraisal of theoretical music and mathematics.

Keywords- Ratio, Irrationality, Number, Mathematics/music interrelationships.


Abdounur, O. J (2016). Mathematics and Music in Context: The Contribution of Erasmus Horicius to the Emergence of the Idea of Modern Number. International Journal of Mathematical, Engineering and Management Sciences, 1(2), 62-67.

Conflict of Interest



Barbera, A. (1991). The Euclidean Division of the Canon. Lincoln: Univ. Nebraska Press.

Bower, C. M. and Palisca, C. V. eds. (1989). Fundamentals of music. anicius manlius severinus Boethius.
New Haven & London: Yale University Press.

Erasmus Horitius. 1500 "De Musica" [ca. 1500], Reg. Lat. 1245, Biblioteca Apostolica Vaticana
Palisca, C. V. (1994) “The Musica of Erasmus of Höritz,” C. Palisca, Studies in the History of Italian
Music and Music Theory. Oxford: Clarendon Press, pp. 146-67.

Rommevaux, S., Vendrix, P., Zara, V. (2011). Proportions: science, musique, peinture & architecture.
Collection – études Renaissantes. Brepols: Turnhout.

Winnington-Ingram, R. P. (1995). “Aristonexus” In: The new Grove dictionary of music and musicians,
edited by Stanley Sadie, 592. London: Macmillan.

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