A Hard Day’s Math: Connections Between Mathematics and Music

Year: 2023 Authors: Jason Brown

Core claim

Mathematics helps explain musical structure, repetition, and authenticity, and can illuminate several mysteries in Beatles-related songs.

Topics

mathematics and music, musical aesthetics, Beatles songs, music authentication, Fourier transforms

Domains

calculus, linear algebra, number theory, combinatorics, statistics, music theory, sound analysis, musical aesthetics

Methods

pattern analysis, transformations, machine learning, Fourier transforms

Media

audio recordings, melody, chords, rhythmic patterns

Paper text

The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.

Brown

A Hard Day’s Math: Connections Between Mathematics and Music

Jason Brown

Dalhousie University, Halifax, Nova Scotia, Canada; jason.brown@dal.ca

Music is full of mathematics—from sums of trigonometric sound waves that comprise audio recordings to transitions between melody notes, between chords, and between onsets in a rhythmic pattern. A variety of mathematical tools (including calculus, linear algebra, number theory and combinatorics) are available for both musical analysis and generation. We will discuss: how patterns and transformations play a significant role in musical aesthetics; why we are drawn to the repetitive nature of the blues; why the bridge of I Want to Hold Your Hand is so mathematically perfect; what statistics and machine learning can say about music authentication; and how Fourier transforms can unravel a few musical mysteries surrounding A Hard Day’s Night.

Figure 1: The Lads

Figure 2: The Graph

Figure 3: The Songs

Figure 4: The Chord