Matemática na música a escala cromática e as progressões geométricas

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Universidade Federal de Goiás


This paper presents a proposal for relationship studies between mathematics and music, a relationship that has been established since the dawn of humanity, and could be seen more clearly from the studies developed by Pythagoras. We approach the evolution of music in the historical context and introduce the basics of music theory, essential to establishing relationships with mathematics. Our e orts were focused on instruments with strings, by which present a relationship between a musical scale, called Chromatic and geometric progressions; also we present a relationship between musical intervals and right triangles. We present a mathematical relationship between music and colors, through their respective frequencies of sound and light. Also we address the present mathematics in the construction of some instruments with strings, via Golden Proportion, and nished the work presented some proposals for activities that can be worked in the classroom, aimed at high school students.



Musica, Matematica, Escala cromatica, Progressões geometricas, Instrumentos musicais, Trastes do violao, Cores e luz, Proporção aurea, Music, Mathematics, Chromatic scale, Geometric progressions, Musical instruments, The guitar frets, Colors and lights, Golden proportion


TEIXEIRA, Alexandre Carlos da Silva. Matemática na música a escala cromática e as progressões geométricas. 2015. 78 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Universidade Federal de Goiás, Catalão, 2015.