Mathematics and music: systematization of analogies between mathematical and musical contents


Over time, mathematicians and physicians have found analogies between mathematics and music. At the same time, musicians have found support in mathematics to describe their art. This article consists of a systematization of the connections between mathematical and musical contents. Musical content was divided into the subjects of: 1) Musical theory and analysis, 2) Acoustics and 3) Musical composition. Subsequently, within each of these subjects, the associations with mathematics were systemized based on the organization of Programmes of Mathematics in Basic Education and their Curriculum Targets (3rd cycle) and of Programmes of Mathematics A and B of the 11th and 12th years of Portuguese Secondary Education. We conclude that the musical elements and concepts associated with mathematics are distributed over the areas of Arithmetic, Algebra, Trigonometry and, especially, Geometry.


Keywords: Mathematics and music relationship; Mathematics contents; Music contents; Mathematics programmes.


Carlos dos Santos-Luiz (1), Lisete Mónico (2), Sandra Campelos (3), Carlos Fernandes da Silva (4)

(1) i2ADS | Instituto Politécnico de Coimbra, Portugal

(2) Universidade de Coimbra, Portugal

(3) Colégio Internato dos Carvalhos, Portugal

(4) Universidade de Aveiro, Portugal

Year 2015
Type Journal Article with peer review
Publication Revista Portuguesa de Educação, 28(2)
Pages 271-293
Publisher CIEd - Universidade do Minho
ISBN / ISSN ISSN: 0871-9187
Language Português