Irrationality in theoretical music in the Renassaince

• DOI: 10.22533/at.ed.61719230820

• Palavras-chave: atena

• Keywords: ratio, irrationality, mathematics education

• Abstract:

  This presentation 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”;

  exploring the educational potentiality of such

  a comprehension. 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 humanists very articulate with

  musical matters. In order to divide the tone,

  Erasmus preferred to use a numerical method

  to approach the geometrical mean, although

  his procedure did not recognize 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.

• Número de páginas: 15