On the Mathematics of Music: From Chords to Fourier Analysis
This work addresses the challenge of automated music analysis for applications in signal processing and music theory, but it appears incremental as it revisits existing mathematical methods.
The paper tackles the problem of extracting chord information from recorded music using mathematical tools, specifically Fourier analysis, to process audio data and identify chords.
Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from recorded music. We begin with a light introduction to the theory of music and motivate the use of Fourier analysis in audio processing. We introduce the discrete and continuous Fourier transforms and investigate their use in extracting important information from audio data.