Open AccessStructural Mathematical Changes in Theoretical Music in the Early Renaissance
Author(s) -
Oscar João Abdounur
Publication year - 2019
Publication title -
international journal of mathematical, engineering and management sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 10
ISSN - 2455-7749
DOI - 10.33889/ijmems.2019.4.1-017
Subject(s) - the renaissance , musical , terminology , period (music) , golden ratio , character (mathematics) , musical form , music theory , literature , mathematics , epistemology , linguistics , philosophy , art , aesthetics , art history , geometry
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.