On the Mathematics of Music: From Chords to Fourier Analysis

TL;DR

This paper explores the application of Fourier analysis in music signal processing, specifically for extracting chord information from audio recordings, highlighting the mathematical tools used in audio analysis.

Contribution

It revisits Fourier analysis techniques in music signal processing, providing insights into their role in extracting musical features from audio data.

Findings

Fourier transforms effectively extract chord information from recordings

Mathematical tools facilitate analysis of musical signals

Fourier analysis bridges music theory and signal processing

Abstract

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.