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There are **13** NRICH Mathematical resources connected to **Music**, you may find related items under Cross-curricular contexts.

Problem
Primary curriculum
Secondary curriculum
### Equal Temperament

The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Music to My Ears

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Clapping Times

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

Age 5 to 7

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Dancing with Maths

An article for students and teachers on symmetry and square dancing. What do the symmetries of the square have to do with a dos-e-dos or a swing? Find out more?

Age 7 to 16

Problem
Primary curriculum
Secondary curriculum
### Pythagoras’ Comma

Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Six Notes All Nice Ratios

The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Count the Beat

This article, written by Nicky Goulder and Samantha Lodge, reveals how maths and marimbas can go hand-in-hand! Why not try out some of the musical maths activities in your own classroom?

Age 5 to 11

Problem
Primary curriculum
Secondary curriculum
### Euclid's Algorithm and Musical Intervals

Use Euclid's algorithm to get a rational approximation to the number of major thirds in an octave.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tuning and Ratio

Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Oranges and Lemons, Say the Bells of St Clement's

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bell Ringing

Suppose you are a bellringer. Can you find the changes so that, starting and ending with a round, all the 24 possible permutations are rung once each and only once?

Age 11 to 14

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Ding Dong Bell

The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.

Age 11 to 18