Oscar João Abdounur
Institute of Mathematics and Statistics, University of São Paulo, São Paulo Brazil.

DOI https://dx.doi.org/10.33889/IJMEMS.2019.4.1-017

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Abstract

This paper investigates interrelationships between theories of ratio and theoretical music originating in Antiquity, with special attention to the early Renaissance in Europe. It considers evidence from different theories of ratio, stressing tendencies in mathematical treatment involving such concepts, which show similarities with music in structure and⁄or terminology and also examines their reflection in music in the period in question. It could be said that from later times and in particular in Euclid's Elements Book V, ratios were seen as musical intervals generalized, whose nature was very different from numbers or magnitudes. The change is from operations with ratios related to contiguous musical intervals to theories admitting compounding ratios in general sense with an essentially arithmetic character, manifested for instance in the idea that a ratio is equal to a number. It will be investigated here some attributes of these competing theories of ratios, as well as its close relationships with theoretical music up to the 16th century.

Keywords- Structural changes, Theoretical music, Ratios, Mathematical changes, Mathematics/music relation.

Citation

Abdounur, O. J. (2019). Structural Mathematical Changes in Theoretical Music in the Early Renaissance. International Journal of Mathematical, Engineering and Management Sciences, 4(1), 191-198. https://dx.doi.org/10.33889/IJMEMS.2019.4.1-017.