O gráfico dos sons

• Autor(a) principal: Martins, Marcos Assumpção
• Data de Publicação: 2014
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/4877
• topic: Mathematics; Music; Sonic spectra; Graphs of functions; Analysis; Matemática; Música; Espectros sonoros; Gráficos de funções; Análise; Matemática - Música; Funções (Matemática) - Estudo e ensino; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

This paper presents a proposal for a more differentiated lesson based on spectral sound analysis with the intention of studying graphs of functions, especially trigonometric functions. After a brief discussion of historical studies and research of the relationship between mathematics and music in his introduction, it is proposed a basic study of the main methods of analysis of these spectra. Such methods - Bank of harmonic filters (Phase Vocoder) and the method of tracking frequency (mq) - are also useful for the synthesis of monophonic audio signals, being based on the sums of sinusoids model and very dependent of Fourier Transforms implemented in a format digital of a computer. This study allows the reader to get a sense of the main techniques and their main methods so that can decide your application in classrooms of various levels of discernment. This also aims to present mathematical applications in this process, especially Fourier series. In the secondly moment, more importantly, we have a presentation of the proposed pedagogical work: the study of graphs produced in classroom for the sounds emitted by volunteer students or pre-existing recordings. The implementation of the activity is guided to seek a sound recording made in room, preferably by students, creating your chart in order to be able to explore features such as periods of maximum and minimum and shapes of these spectra. Having this, each teacher will have in hand a wider range of tools to explore various subjects in mathematics, as well as understand, know and approaching a little more music