# Mathematics and Music - November 2006, All Stages

## Problems

### Clapping Times

##### Stage: 1 Challenge Level:

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?

### Sounds Great!

##### Stage: 1 Challenge Level:

Investigate the different sounds you can make by putting the owls and donkeys on the wheel.

### We'll Bang the Drum

##### Stage: 1 Challenge Level:

How many different rhythms can you make by putting two drums on the wheel?

### Music to My Ears

##### Stage: 2 Challenge Level:

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?

### Beat the Drum Beat!

##### Stage: 2 Challenge Level:

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

### Play a Merry Tune

##### Stage: 2 Challenge Level:

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

### Oranges and Lemons, Say the Bells of St Clement's

##### Stage: 3 Challenge Level:

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

### You Owe Me Five Farthings, Say the Bells of St Martin's

##### Stage: 3 Challenge Level:

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

### When Will You Pay Me? Say the Bells of Old Bailey

##### Stage: 3 Challenge Level:

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

### Six Notes All Nice Ratios

##### Stage: 4 Challenge Level:

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

### Pythagoras’ Comma

##### Stage: 4 Challenge Level:

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.

### Equal Temperament

##### Stage: 4 Challenge Level:

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.

### Tuning and Ratio

##### Stage: 5 Challenge Level:

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

### Euclid's Algorithm and Musical Intervals

##### Stage: 5 Challenge Level:

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

### Rarity

##### Stage: 5 Challenge Level:

Show that it is rare for a ratio of ratios to be rational.