This paper will discuss the relevance between mathematics and music throughout a few periods of history. The paper will first discuss how the Ancient Chinese hired mathematicians in order to “perfect the music” used in the court rooms. Mathematics was typically used in music to develop ratios and intervals that are found in music. This paper will then discuss the history of Fourier analysis, as well as give a brief history of Jean Baptiste Fourier. The Fourier analysis was used to find naturally occurring harmonics, to model sound, and to define sound by breaking it up into pieces. Many examples of the Fourier series and Fourier transform can be seen in relation to music. Some more simple examples will also be demonstrated, in order to understand how the Fourier series can model sound waves. While there are many other examples of how math has been used in music, these two aspects will be the main focus of this paper, with favorability placed on discussing the importance and relevance of the Fourier series. However, due to the inability to find sources, Fourier’s derivation of the series can only be mentioned in a simplistic manner. To find more examples of math and music more time and research would need to be done.
"The Historical Connection of Fourier Analysis to Music,"
The Mathematics Enthusiast: Vol. 14
, Article 7.
Available at: http://scholarworks.umt.edu/tme/vol14/iss1/7