Leonardo, Vol. 34, No. 1 (2001), pp. 63-68
...Music , Creativity and Scientific Thinking Robert S. Root-Bernstein Mathematics and music ! The most glaring possible opposites of human thought! and yet connected, mutually sustained! It is as if they would demonstrate the hidden consensus of all the actions of our mind, which in the revelations of genius makes us forefeel unconscious...
Sociology of Education, Vol. 75, No. 1 (Jan., 2002), pp. 44-68
...Arts (NEA Fact Sheet 2001), which noted that students who have studied the arts for four years score an average of 89 points higher on the SAT than do students who have not. It is also apparent in Shaw's (1999) notion of the " Mozart effect ," the belief that listening...
An Introduction to Fourier Analysis with Applications to Music
in Journal of Humanistic Mathematicsv4 n1 (20140131)
Summary In our modern world, we are often faced with problems in which a traditionally analog signal is discretized to enable computer analysis. A fundamental tool used by mathematicians, engineers, and scientists in this context is the discrete Fourier transform (DFT), which allows us to analyze individual frequency components of digital signals. In this paper we develop the discrete Fourier transform from basic calculus, providing the reader with the setup to understand how the DFT can be used to analyze a musical signal for chord structure. By investigating the DFT alongside an application in music processing, we gain an appreciation for the mathematics utilized in digital signal processing.