Matemática na música a escala cromática e as progressões geométricas
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Data
2015-06-26
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Editor
Universidade Federal de Goiás
Resumo
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.
Descrição
Palavras-chave
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
Citação
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.