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

Why a piano cannot be perfectly in tune: a maths EPQ idea

Why it works as an EPQ

Frequency ratios, powers of 2 and logarithms explain a compromise every musician lives with.

Scope and difficulty

Solid. Solid. Ratios and logarithms; recordings or a tuner app for evidence.

The maths

Builds on these A Level topics: Exponentials and logarithms · Sequences and series · Algebra and functions.

You would learn:

• Frequency ratios of intervals
• Cents and logarithms
• The Pythagorean comma

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 a scale from 3:2 fifths and show it does not close.
2. Calculate the size of the gap.
3. Compare equal temperament with just intervals in cents.
4. Judge the compromise, with listening tests if possible.

Pitfalls

• Claims about how intervals 'feel' with no evidence.
• Confusing frequency ratios and differences.

Where to start reading

• Music: A Mathematical Offering (Dave Benson)
• Search for: Pythagorean comma cents

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.

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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.