## MATH2340 The Mathematics of Music

### 10 creditsClass Size: 70

Module manager: Dr Rob Sturman
Email: R.Sturman@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2021/22

### Pre-requisite qualifications

A level Mathematics, or equivalent.

This module is approved as a discovery module

### Module summary

Links between mathematics and music have been established for centuries, and properties of numbers and patterns have helped to shape musical culture in a variety of ways. This module aims to explore these links, and to investigate how some mathematical concepts lie naturally at the heart of music theory, while others have been usefully employed to understand or create music.The module will include discussions of the physics of sound, the mathematics behind musical tuning, aspects of symmetry in music, mathematically-inspired modern compositional techniques, and describe mathematically the structure of music.

### Objectives

On completion of this module, students should be able to:
- show familiarity with the historical connections between mathematics and music
- be able to analyse compositions in terms of simple symmetry and geometry
- be able to describe the properties of different tuning and temperament systems
- demonstrate understanding of the physics of sound waves and their relationship to consonance and dissonance
- be able to investigate compositional techniques based on mathematics.

### Syllabus

a) Sound: waves; Fourier series; Helmholtz and consonance
b) Rhythm: Notation; Medieval notation; Metre and scansion; Fibonacci sequence; Dance and Jazz rhythms
c) Tuning: The harmonic series; Pythagorean tuning; Tempering; Equal temperament; Nonlinear scales; Microtonality
d) Structure: Predictability in music; Structure of a melody; Noise
e) Symmetry: Group theory; Change-ringing; Tone rows; Counterpoint
f) Compositional techniques: Music of chance; Fractal music.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Lecture 33 1.00 33.00 Private study hours 67.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 100.00

### Private study

Studying and revising of course material.
Completing of assignments and assessments.

### Opportunities for Formative Feedback

Essay to be submitted half way through the term, will be marked and handed back to students.

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment Essay . 50.00 Online Assessment . 20.00 Written Work . 30.00 Total percentage (Assessment Coursework) 100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated