Maths in music, art and sport · Ambitious · Dissertation or artefact

Why instruments sound different: a maths EPQ idea

Why it works as an EPQ

Any periodic sound is a sum of sine waves; recording instruments and analysing their spectra makes the mathematics concrete.

Scope and difficulty

Ambitious. Ambitious. Fourier series for simple waves; free software for the spectra.

The maths

Builds on these A Level topics: Trigonometry · Integration.

You would learn:

• Fourier series
• Harmonics
• Frequency spectra

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Build square and sawtooth waves from sines and show the coefficients.
2. Record two instruments playing the same note.
3. Compare their spectra.
4. Judge how far harmonics explain timbre.

Pitfalls

• Software output you cannot interpret.
• Ignoring attack and decay.

Where to start reading

• Music: A Mathematical Offering (Dave Benson)
• Search for: Fourier series square wave coefficients

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

Making something? Read the artefact guide first: an artefact still needs a research-based written report.

Similar ideas

• Perspective in Renaissance artHow did Renaissance artists use geometry to create perspective, and how accurate were they?Music, art and sportAccessibleDissertation or artefact
• Tilings and EscherWhich shapes can tile the plane, and how can symmetry be used to design an original Escher-style tiling?Music, art and sportAccessibleArtefact
• Predicting race timesCan you predict a marathon time from a 5 km race? Testing a power-law formulaMusic, art and sportAccessibleDissertation
• Game theory and penalty kicksWhere should a penalty taker aim? Game theory and mixed strategies in footballMusic, art and sportSolidDissertation

All maths in music, art and sport ideas · all 93 ideas

Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.